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| <div class="title">prob.sql_in</div> </div> |
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| <a href="prob_8sql__in.html">Go to the documentation of this file.</a><div class="fragment"><div class="line"><a name="l00001"></a><span class="lineno"> 1</span> <span class="comment">/* ----------------------------------------------------------------------- */</span><span class="comment">/**</span></div> |
| <div class="line"><a name="l00002"></a><span class="lineno"> 2</span> <span class="comment"> *</span></div> |
| <div class="line"><a name="l00003"></a><span class="lineno"> 3</span> <span class="comment"> * @file prob.sql_in</span></div> |
| <div class="line"><a name="l00004"></a><span class="lineno"> 4</span> <span class="comment"> *</span></div> |
| <div class="line"><a name="l00005"></a><span class="lineno"> 5</span> <span class="comment"> * @brief SQL functions for evaluating probability functions</span></div> |
| <div class="line"><a name="l00006"></a><span class="lineno"> 6</span> <span class="comment"> *</span></div> |
| <div class="line"><a name="l00007"></a><span class="lineno"> 7</span> <span class="comment"> * @sa For an overview of probability functions, see the module</span></div> |
| <div class="line"><a name="l00008"></a><span class="lineno"> 8</span> <span class="comment"> * description \ref grp_prob.</span></div> |
| <div class="line"><a name="l00009"></a><span class="lineno"> 9</span> <span class="comment"> *</span></div> |
| <div class="line"><a name="l00010"></a><span class="lineno"> 10</span> <span class="comment"> */</span><span class="comment">/* ----------------------------------------------------------------------- */</span></div> |
| <div class="line"><a name="l00011"></a><span class="lineno"> 11</span> </div> |
| <div class="line"><a name="l00012"></a><span class="lineno"> 12</span> m4_include(`SQLCommon.m4<span class="stringliteral">')</span></div> |
| <div class="line"><a name="l00013"></a><span class="lineno"> 13</span> <span class="stringliteral"></span><span class="comment"></span></div> |
| <div class="line"><a name="l00014"></a><span class="lineno"> 14</span> <span class="comment">/**</span></div> |
| <div class="line"><a name="l00015"></a><span class="lineno"> 15</span> <span class="comment">@addtogroup grp_prob</span></div> |
| <div class="line"><a name="l00016"></a><span class="lineno"> 16</span> <span class="comment"></span></div> |
| <div class="line"><a name="l00017"></a><span class="lineno"> 17</span> <span class="comment">@about</span></div> |
| <div class="line"><a name="l00018"></a><span class="lineno"> 18</span> <span class="comment"></span></div> |
| <div class="line"><a name="l00019"></a><span class="lineno"> 19</span> <span class="comment">The Probability Functions module provides cumulative distribution, density/mass,</span></div> |
| <div class="line"><a name="l00020"></a><span class="lineno"> 20</span> <span class="comment">and quantile functions for a wide range of probability distributions.</span></div> |
| <div class="line"><a name="l00021"></a><span class="lineno"> 21</span> <span class="comment"></span></div> |
| <div class="line"><a name="l00022"></a><span class="lineno"> 22</span> <span class="comment">Unless otherwise documented, all of these functions are wrappers around</span></div> |
| <div class="line"><a name="l00023"></a><span class="lineno"> 23</span> <span class="comment">functionality provided by the boost C++ library [1, “<a href=</span></div> |
| <div class="line"><a name="l00024"></a><span class="lineno"> 24</span> <span class="comment">"http://www.boost.org/doc/libs/1_49_0/libs/math/doc/sf_and_dist/html/math_toolkit/dist.html"</span></div> |
| <div class="line"><a name="l00025"></a><span class="lineno"> 25</span> <span class="comment">>Statistical Distributions and Functions</a>”].</span></div> |
| <div class="line"><a name="l00026"></a><span class="lineno"> 26</span> <span class="comment"></span></div> |
| <div class="line"><a name="l00027"></a><span class="lineno"> 27</span> <span class="comment">For convenience, all cumulative distribution and density/mass functions (CDFs</span></div> |
| <div class="line"><a name="l00028"></a><span class="lineno"> 28</span> <span class="comment">and PDF/PMFs in short) are defined over the range of all floating-point numbers</span></div> |
| <div class="line"><a name="l00029"></a><span class="lineno"> 29</span> <span class="comment">including infinity. Inputs that are \c NULL or \c NaN (not a number) will always</span></div> |
| <div class="line"><a name="l00030"></a><span class="lineno"> 30</span> <span class="comment">produce a \c NULL or \c NaN result, respectively. Inputs that are plus or minus</span></div> |
| <div class="line"><a name="l00031"></a><span class="lineno"> 31</span> <span class="comment">infinity will return the respective limits.</span></div> |
| <div class="line"><a name="l00032"></a><span class="lineno"> 32</span> <span class="comment"></span></div> |
| <div class="line"><a name="l00033"></a><span class="lineno"> 33</span> <span class="comment">A quantile function for a probability distrution with CDF \f$ F \f$ takes a</span></div> |
| <div class="line"><a name="l00034"></a><span class="lineno"> 34</span> <span class="comment">probability argument \f$ p \in [0,1] \f$ and returns the value \f$ x \f$ so that</span></div> |
| <div class="line"><a name="l00035"></a><span class="lineno"> 35</span> <span class="comment">\f$ F(x) = p \f$, provided such an \f$ x \f$ exists and it is unique. If it does</span></div> |
| <div class="line"><a name="l00036"></a><span class="lineno"> 36</span> <span class="comment">not, the result will be</span></div> |
| <div class="line"><a name="l00037"></a><span class="lineno"> 37</span> <span class="comment">\f$</span></div> |
| <div class="line"><a name="l00038"></a><span class="lineno"> 38</span> <span class="comment"> \sup \{ x \in D \mid F(x) \leq p \}</span></div> |
| <div class="line"><a name="l00039"></a><span class="lineno"> 39</span> <span class="comment">\f$</span></div> |
| <div class="line"><a name="l00040"></a><span class="lineno"> 40</span> <span class="comment">(interpreted as 0 if the supremum is over an empty set) if \f$ p < 0.5 \f$, and</span></div> |
| <div class="line"><a name="l00041"></a><span class="lineno"> 41</span> <span class="comment">\f$</span></div> |
| <div class="line"><a name="l00042"></a><span class="lineno"> 42</span> <span class="comment"> \inf \{ x \in D \mid F(x) \geq p \}</span></div> |
| <div class="line"><a name="l00043"></a><span class="lineno"> 43</span> <span class="comment">\f$</span></div> |
| <div class="line"><a name="l00044"></a><span class="lineno"> 44</span> <span class="comment">if \f$ p \geq 0.5 \f$. Here \f$ D \f$ denotes the domain of the distribution,</span></div> |
| <div class="line"><a name="l00045"></a><span class="lineno"> 45</span> <span class="comment">which is the set of reals \f$ \mathbb R \f$ for continuous and the set of</span></div> |
| <div class="line"><a name="l00046"></a><span class="lineno"> 46</span> <span class="comment">nonnegative integers \f$ \mathbb N_0 \f$ for discrete distributions.</span></div> |
| <div class="line"><a name="l00047"></a><span class="lineno"> 47</span> <span class="comment"></span></div> |
| <div class="line"><a name="l00048"></a><span class="lineno"> 48</span> <span class="comment">Intuitively, the formulas in the previous paragraph deal with the following</span></div> |
| <div class="line"><a name="l00049"></a><span class="lineno"> 49</span> <span class="comment">special cases. The 0-quantile will always be the “left end” of the support,</span></div> |
| <div class="line"><a name="l00050"></a><span class="lineno"> 50</span> <span class="comment">and the 1-quantile will be the “right end” of the support of the distribution.</span></div> |
| <div class="line"><a name="l00051"></a><span class="lineno"> 51</span> <span class="comment">For discrete distributions, most values of \f$ p \in [0,1] \f$ do not admit an</span></div> |
| <div class="line"><a name="l00052"></a><span class="lineno"> 52</span> <span class="comment">\f$ x \f$ with \f$ F(x) = p \f$. Instead, there is an \f$ x \in \mathbb N_0 \f$</span></div> |
| <div class="line"><a name="l00053"></a><span class="lineno"> 53</span> <span class="comment">so that \f$ F(x) < p < F(x + 1) \f$. The above formulas mean that the</span></div> |
| <div class="line"><a name="l00054"></a><span class="lineno"> 54</span> <span class="comment">value returned as \f$ p \f$-quantile is \f$ x \f$ if \f$ p < 0.5 \f$, and it</span></div> |
| <div class="line"><a name="l00055"></a><span class="lineno"> 55</span> <span class="comment">is \f$ x + 1 \f$ if \f$ p \geq 0.5 \f$. (As a special case, in order to ensure</span></div> |
| <div class="line"><a name="l00056"></a><span class="lineno"> 56</span> <span class="comment">that quantiles are always within the support, the \f$ p \f$-quantile will be 0</span></div> |
| <div class="line"><a name="l00057"></a><span class="lineno"> 57</span> <span class="comment">if \f$ p < F(0) \f$).</span></div> |
| <div class="line"><a name="l00058"></a><span class="lineno"> 58</span> <span class="comment"></span></div> |
| <div class="line"><a name="l00059"></a><span class="lineno"> 59</span> <span class="comment">The rationale for choosing this behavior is that \f$p\f$-quantiles for</span></div> |
| <div class="line"><a name="l00060"></a><span class="lineno"> 60</span> <span class="comment">\f$ p < 0.5 \f$ are typically requested when interested in the value</span></div> |
| <div class="line"><a name="l00061"></a><span class="lineno"> 61</span> <span class="comment">\f$ x \f$ such that with confidence level <strong>at least</strong></span></div> |
| <div class="line"><a name="l00062"></a><span class="lineno"> 62</span> <span class="comment">\f$ 1 - p \f$ a random variable will be \f$ > x \f$ (or equivalently, with</span></div> |
| <div class="line"><a name="l00063"></a><span class="lineno"> 63</span> <span class="comment">probability <strong>at most</strong> \f$ p \f$, it will be \f$ \leq x \f$).</span></div> |
| <div class="line"><a name="l00064"></a><span class="lineno"> 64</span> <span class="comment">Likewise, \f$p\f$-quantiles for \f$ p \geq 0.5 \f$ are typically requested when</span></div> |
| <div class="line"><a name="l00065"></a><span class="lineno"> 65</span> <span class="comment">interested in the value \f$ x \f$ such that with confidence level <strong>at</span></div> |
| <div class="line"><a name="l00066"></a><span class="lineno"> 66</span> <span class="comment">least</strong> \f$ p \f$ a random variable will be \f$ \leq x \f$. See also</span></div> |
| <div class="line"><a name="l00067"></a><span class="lineno"> 67</span> <span class="comment">[1, “<a href=</span></div> |
| <div class="line"><a name="l00068"></a><span class="lineno"> 68</span> <span class="comment">"http://www.boost.org/doc/libs/1_46_1/libs/math/doc/sf_and_dist/html/math_toolkit/policy/pol_tutorial/understand_dis_quant.html"</span></div> |
| <div class="line"><a name="l00069"></a><span class="lineno"> 69</span> <span class="comment">>Understanding Quantiles of Discrete Distributions</a>”].</span></div> |
| <div class="line"><a name="l00070"></a><span class="lineno"> 70</span> <span class="comment"></span></div> |
| <div class="line"><a name="l00071"></a><span class="lineno"> 71</span> <span class="comment">@usage</span></div> |
| <div class="line"><a name="l00072"></a><span class="lineno"> 72</span> <span class="comment"></span></div> |
| <div class="line"><a name="l00073"></a><span class="lineno"> 73</span> <span class="comment">- Cumulative distribution functions:</span></div> |
| <div class="line"><a name="l00074"></a><span class="lineno"> 74</span> <span class="comment"> <pre>SELECT <em>distribution</em>_cdf(<em>random variate</em>[, <em>parameter1</em> [, <em>parameter2</em> [, <em>parameter3</em>] ] ])</pre></span></div> |
| <div class="line"><a name="l00075"></a><span class="lineno"> 75</span> <span class="comment">- Probability density/mass functions:</span></div> |
| <div class="line"><a name="l00076"></a><span class="lineno"> 76</span> <span class="comment"> <pre>SELECT <em>distribution</em>_{pdf|pmf}(<em>random variate</em>[, <em>parameter1</em> [, <em>parameter2</em> [, <em>parameter3</em>] ] ])</pre></span></div> |
| <div class="line"><a name="l00077"></a><span class="lineno"> 77</span> <span class="comment">- Quantile functions:</span></div> |
| <div class="line"><a name="l00078"></a><span class="lineno"> 78</span> <span class="comment"> <pre>SELECT <em>distribution</em>_quantile(<em>probability</em>[, <em>parameter1</em> [, <em>parameter2</em> [, <em>parameter3</em>] ] ])</pre></span></div> |
| <div class="line"><a name="l00079"></a><span class="lineno"> 79</span> <span class="comment"></span></div> |
| <div class="line"><a name="l00080"></a><span class="lineno"> 80</span> <span class="comment">For concrete function signatures, see \ref prob.sql_in.</span></div> |
| <div class="line"><a name="l00081"></a><span class="lineno"> 81</span> <span class="comment"></span></div> |
| <div class="line"><a name="l00082"></a><span class="lineno"> 82</span> <span class="comment">@examp</span></div> |
| <div class="line"><a name="l00083"></a><span class="lineno"> 83</span> <span class="comment"></span></div> |
| <div class="line"><a name="l00084"></a><span class="lineno"> 84</span> <span class="comment">@verbatim</span></div> |
| <div class="line"><a name="l00085"></a><span class="lineno"> 85</span> <span class="comment">sql> SELECT normal_cdf(0);</span></div> |
| <div class="line"><a name="l00086"></a><span class="lineno"> 86</span> <span class="comment"> normal_cdf</span></div> |
| <div class="line"><a name="l00087"></a><span class="lineno"> 87</span> <span class="comment">------------</span></div> |
| <div class="line"><a name="l00088"></a><span class="lineno"> 88</span> <span class="comment"> 0.5</span></div> |
| <div class="line"><a name="l00089"></a><span class="lineno"> 89</span> <span class="comment"></span></div> |
| <div class="line"><a name="l00090"></a><span class="lineno"> 90</span> <span class="comment">sql> SELECT normal_quantile(0.5, 0, 1);</span></div> |
| <div class="line"><a name="l00091"></a><span class="lineno"> 91</span> <span class="comment"> normal_quantile</span></div> |
| <div class="line"><a name="l00092"></a><span class="lineno"> 92</span> <span class="comment">-----------------</span></div> |
| <div class="line"><a name="l00093"></a><span class="lineno"> 93</span> <span class="comment"> 0</span></div> |
| <div class="line"><a name="l00094"></a><span class="lineno"> 94</span> <span class="comment">(1 row)</span></div> |
| <div class="line"><a name="l00095"></a><span class="lineno"> 95</span> <span class="comment">@endverbatim</span></div> |
| <div class="line"><a name="l00096"></a><span class="lineno"> 96</span> <span class="comment"></span></div> |
| <div class="line"><a name="l00097"></a><span class="lineno"> 97</span> <span class="comment">@literature</span></div> |
| <div class="line"><a name="l00098"></a><span class="lineno"> 98</span> <span class="comment"></span></div> |
| <div class="line"><a name="l00099"></a><span class="lineno"> 99</span> <span class="comment">[1] John Maddock, Paul A. Bristow, Hubert Holin, Xiaogang Zhang, Bruno Lalande,</span></div> |
| <div class="line"><a name="l00100"></a><span class="lineno"> 100</span> <span class="comment"> Johan Råde, Gautam Sewani and Thijs van den Berg:</span></div> |
| <div class="line"><a name="l00101"></a><span class="lineno"> 101</span> <span class="comment"> <em>Boost Math Toolkit</em>, Version 1.49, available at:</span></div> |
| <div class="line"><a name="l00102"></a><span class="lineno"> 102</span> <span class="comment"> http://www.boost.org/doc/libs/1_49_0/libs/math/doc/sf_and_dist/html/index.html</span></div> |
| <div class="line"><a name="l00103"></a><span class="lineno"> 103</span> <span class="comment"></span></div> |
| <div class="line"><a name="l00104"></a><span class="lineno"> 104</span> <span class="comment">@sa File prob.sql_in documenting the SQL functions.</span></div> |
| <div class="line"><a name="l00105"></a><span class="lineno"> 105</span> <span class="comment">*/</span></div> |
| <div class="line"><a name="l00106"></a><span class="lineno"> 106</span> </div> |
| <div class="line"><a name="l00107"></a><span class="lineno"> 107</span> <span class="comment"></span></div> |
| <div class="line"><a name="l00108"></a><span class="lineno"> 108</span> <span class="comment">/**</span></div> |
| <div class="line"><a name="l00109"></a><span class="lineno"> 109</span> <span class="comment"> * @brief Bernoulli cumulative distribution function</span></div> |
| <div class="line"><a name="l00110"></a><span class="lineno"> 110</span> <span class="comment"> *</span></div> |
| <div class="line"><a name="l00111"></a><span class="lineno"> 111</span> <span class="comment"> * @param x Random variate \f$ x \f$</span></div> |
| <div class="line"><a name="l00112"></a><span class="lineno"> 112</span> <span class="comment"> * @param sp Success probability \f$ p \in [0,1] \f$</span></div> |
| <div class="line"><a name="l00113"></a><span class="lineno"> 113</span> <span class="comment"> * @return \f$ \Pr[X \leq x] \f$ where \f$ X \f$ is a Bernoulli-distributed</span></div> |
| <div class="line"><a name="l00114"></a><span class="lineno"> 114</span> <span class="comment"> * random variable with success probability \f$ \mathit{sp} \f$</span></div> |
| <div class="line"><a name="l00115"></a><span class="lineno"> 115</span> <span class="comment"> */</span></div> |
| <div class="line"><a name="l00116"></a><span class="lineno"> 116</span> CREATE FUNCTION MADLIB_SCHEMA.bernoulli_cdf(</div> |
| <div class="line"><a name="l00117"></a><span class="lineno"> 117</span>  x DOUBLE PRECISION,</div> |
| <div class="line"><a name="l00118"></a><span class="lineno"> 118</span>  sp DOUBLE PRECISION</div> |
| <div class="line"><a name="l00119"></a><span class="lineno"> 119</span> ) RETURNS DOUBLE PRECISION</div> |
| <div class="line"><a name="l00120"></a><span class="lineno"> 120</span> AS 'MODULE_PATHNAME<span class="stringliteral">'</span></div> |
| <div class="line"><a name="l00121"></a><span class="lineno"> 121</span> <span class="stringliteral">LANGUAGE C</span></div> |
| <div class="line"><a name="l00122"></a><span class="lineno"> 122</span> <span class="stringliteral">IMMUTABLE STRICT;</span></div> |
| <div class="line"><a name="l00123"></a><span class="lineno"> 123</span> <span class="stringliteral"></span><span class="comment"></span></div> |
| <div class="line"><a name="l00124"></a><span class="lineno"> 124</span> <span class="comment">/**</span></div> |
| <div class="line"><a name="l00125"></a><span class="lineno"> 125</span> <span class="comment"> * @brief Bernoulli probability mass function</span></div> |
| <div class="line"><a name="l00126"></a><span class="lineno"> 126</span> <span class="comment"> *</span></div> |
| <div class="line"><a name="l00127"></a><span class="lineno"> 127</span> <span class="comment"> * @param x Random variate \f$ x \f$</span></div> |
| <div class="line"><a name="l00128"></a><span class="lineno"> 128</span> <span class="comment"> * @param sp Success probability \f$ \mathit{sp} \in [0,1] \f$</span></div> |
| <div class="line"><a name="l00129"></a><span class="lineno"> 129</span> <span class="comment"> * @return \f$ f(x) \f$ where \f$ f \f$ is the probability mass function of</span></div> |
| <div class="line"><a name="l00130"></a><span class="lineno"> 130</span> <span class="comment"> * a Bernoulli-distributed random variable with success probability</span></div> |
| <div class="line"><a name="l00131"></a><span class="lineno"> 131</span> <span class="comment"> * \f$ \mathit{sp} \f$</span></div> |
| <div class="line"><a name="l00132"></a><span class="lineno"> 132</span> <span class="comment"> */</span></div> |
| <div class="line"><a name="l00133"></a><span class="lineno"> 133</span> CREATE FUNCTION MADLIB_SCHEMA.bernoulli_pmf(</div> |
| <div class="line"><a name="l00134"></a><span class="lineno"> 134</span>  x INT4,</div> |
| <div class="line"><a name="l00135"></a><span class="lineno"> 135</span>  sp DOUBLE PRECISION</div> |
| <div class="line"><a name="l00136"></a><span class="lineno"> 136</span> ) RETURNS DOUBLE PRECISION</div> |
| <div class="line"><a name="l00137"></a><span class="lineno"> 137</span> AS 'MODULE_PATHNAME<span class="stringliteral">'</span></div> |
| <div class="line"><a name="l00138"></a><span class="lineno"><a class="code" href="prob_8sql__in.html#aea21a931dc5578a570e3370af3d8d43a"> 138</a></span> <span class="stringliteral">LANGUAGE C</span></div> |
| <div class="line"><a name="l00139"></a><span class="lineno"> 139</span> <span class="stringliteral">IMMUTABLE STRICT;</span></div> |
| <div class="line"><a name="l00140"></a><span class="lineno"> 140</span> <span class="stringliteral"></span><span class="comment"></span></div> |
| <div class="line"><a name="l00141"></a><span class="lineno"> 141</span> <span class="comment">/**</span></div> |
| <div class="line"><a name="l00142"></a><span class="lineno"> 142</span> <span class="comment"> * @brief Bernoulli quantile function</span></div> |
| <div class="line"><a name="l00143"></a><span class="lineno"> 143</span> <span class="comment"> *</span></div> |
| <div class="line"><a name="l00144"></a><span class="lineno"> 144</span> <span class="comment"> * @param p Probability \f$ p \in [0,1] \f$</span></div> |
| <div class="line"><a name="l00145"></a><span class="lineno"> 145</span> <span class="comment"> * @param sp Success probability \f$ \mathit{sp} \in [0,1] \f$</span></div> |
| <div class="line"><a name="l00146"></a><span class="lineno"> 146</span> <span class="comment"> * @return 0 if \f$ p \leq 1 - \mathit{sp} \f$ and 1 otherwise</span></div> |
| <div class="line"><a name="l00147"></a><span class="lineno"> 147</span> <span class="comment"> */</span></div> |
| <div class="line"><a name="l00148"></a><span class="lineno"> 148</span> CREATE FUNCTION MADLIB_SCHEMA.bernoulli_quantile(</div> |
| <div class="line"><a name="l00149"></a><span class="lineno"> 149</span>  p DOUBLE PRECISION,</div> |
| <div class="line"><a name="l00150"></a><span class="lineno"> 150</span>  sp DOUBLE PRECISION</div> |
| <div class="line"><a name="l00151"></a><span class="lineno"> 151</span> ) RETURNS DOUBLE PRECISION</div> |
| <div class="line"><a name="l00152"></a><span class="lineno"> 152</span> AS 'MODULE_PATHNAME<span class="stringliteral">'</span></div> |
| <div class="line"><a name="l00153"></a><span class="lineno"> 153</span> <span class="stringliteral">LANGUAGE C</span></div> |
| <div class="line"><a name="l00154"></a><span class="lineno"> 154</span> <span class="stringliteral">IMMUTABLE STRICT;</span></div> |
| <div class="line"><a name="l00155"></a><span class="lineno"><a class="code" href="prob_8sql__in.html#a434b3ad1f3964835834dc2a942b820ef"> 155</a></span> <span class="stringliteral"></span></div> |
| <div class="line"><a name="l00156"></a><span class="lineno"> 156</span> <span class="stringliteral"></span><span class="comment"></span></div> |
| <div class="line"><a name="l00157"></a><span class="lineno"> 157</span> <span class="comment">/**</span></div> |
| <div class="line"><a name="l00158"></a><span class="lineno"> 158</span> <span class="comment"> * @brief Beta cumulative distribution function</span></div> |
| <div class="line"><a name="l00159"></a><span class="lineno"> 159</span> <span class="comment"> *</span></div> |
| <div class="line"><a name="l00160"></a><span class="lineno"> 160</span> <span class="comment"> * @param x Random variate \f$ x \f$</span></div> |
| <div class="line"><a name="l00161"></a><span class="lineno"> 161</span> <span class="comment"> * @param alpha Shape \f$ \alpha > 0 \f$</span></div> |
| <div class="line"><a name="l00162"></a><span class="lineno"> 162</span> <span class="comment"> * @param beta Shape \f$ \beta > 0 \f$</span></div> |
| <div class="line"><a name="l00163"></a><span class="lineno"> 163</span> <span class="comment"> * @return \f$ \Pr[X \leq x] \f$ where \f$ X \f$ is a beta distributed random</span></div> |
| <div class="line"><a name="l00164"></a><span class="lineno"> 164</span> <span class="comment"> * variable with shape parameters \f$ \alpha \f$ and \f$ \beta \f$</span></div> |
| <div class="line"><a name="l00165"></a><span class="lineno"> 165</span> <span class="comment"> */</span></div> |
| <div class="line"><a name="l00166"></a><span class="lineno"> 166</span> CREATE FUNCTION MADLIB_SCHEMA.beta_cdf(</div> |
| <div class="line"><a name="l00167"></a><span class="lineno"> 167</span>  x DOUBLE PRECISION,</div> |
| <div class="line"><a name="l00168"></a><span class="lineno"> 168</span>  alpha DOUBLE PRECISION,</div> |
| <div class="line"><a name="l00169"></a><span class="lineno"> 169</span>  beta DOUBLE PRECISION</div> |
| <div class="line"><a name="l00170"></a><span class="lineno"><a class="code" href="prob_8sql__in.html#a7133c2e86fd2f6384416ee0e4fd3a60b"> 170</a></span> ) RETURNS DOUBLE PRECISION</div> |
| <div class="line"><a name="l00171"></a><span class="lineno"> 171</span> AS 'MODULE_PATHNAME<span class="stringliteral">'</span></div> |
| <div class="line"><a name="l00172"></a><span class="lineno"> 172</span> <span class="stringliteral">LANGUAGE C</span></div> |
| <div class="line"><a name="l00173"></a><span class="lineno"> 173</span> <span class="stringliteral">IMMUTABLE STRICT;</span></div> |
| <div class="line"><a name="l00174"></a><span class="lineno"> 174</span> <span class="stringliteral"></span><span class="comment"></span></div> |
| <div class="line"><a name="l00175"></a><span class="lineno"> 175</span> <span class="comment">/**</span></div> |
| <div class="line"><a name="l00176"></a><span class="lineno"> 176</span> <span class="comment"> * @brief Beta probability density function</span></div> |
| <div class="line"><a name="l00177"></a><span class="lineno"> 177</span> <span class="comment"> *</span></div> |
| <div class="line"><a name="l00178"></a><span class="lineno"> 178</span> <span class="comment"> * @param x Random variate \f$ x \f$</span></div> |
| <div class="line"><a name="l00179"></a><span class="lineno"> 179</span> <span class="comment"> * @param alpha Shape \f$ \alpha > 0 \f$</span></div> |
| <div class="line"><a name="l00180"></a><span class="lineno"> 180</span> <span class="comment"> * @param beta Shape \f$ \beta > 0 \f$</span></div> |
| <div class="line"><a name="l00181"></a><span class="lineno"> 181</span> <span class="comment"> * @return \f$ f(x) \f$ where \f$ f \f$ is the probability density function of</span></div> |
| <div class="line"><a name="l00182"></a><span class="lineno"> 182</span> <span class="comment"> * a beta random variable with shape parameters \f$ \alpha \f$ and</span></div> |
| <div class="line"><a name="l00183"></a><span class="lineno"> 183</span> <span class="comment"> * \f$ \beta \f$</span></div> |
| <div class="line"><a name="l00184"></a><span class="lineno"> 184</span> <span class="comment"> */</span></div> |
| <div class="line"><a name="l00185"></a><span class="lineno"> 185</span> CREATE FUNCTION MADLIB_SCHEMA.beta_pdf(</div> |
| <div class="line"><a name="l00186"></a><span class="lineno"> 186</span>  x DOUBLE PRECISION,</div> |
| <div class="line"><a name="l00187"></a><span class="lineno"> 187</span>  alpha DOUBLE PRECISION,</div> |
| <div class="line"><a name="l00188"></a><span class="lineno"><a class="code" href="prob_8sql__in.html#a72e1cca872da35592075dbcfb18aed3f"> 188</a></span>  beta DOUBLE PRECISION</div> |
| <div class="line"><a name="l00189"></a><span class="lineno"> 189</span> ) RETURNS DOUBLE PRECISION</div> |
| <div class="line"><a name="l00190"></a><span class="lineno"> 190</span> AS 'MODULE_PATHNAME<span class="stringliteral">'</span></div> |
| <div class="line"><a name="l00191"></a><span class="lineno"> 191</span> <span class="stringliteral">LANGUAGE C</span></div> |
| <div class="line"><a name="l00192"></a><span class="lineno"> 192</span> <span class="stringliteral">IMMUTABLE STRICT;</span></div> |
| <div class="line"><a name="l00193"></a><span class="lineno"> 193</span> <span class="stringliteral"></span><span class="comment"></span></div> |
| <div class="line"><a name="l00194"></a><span class="lineno"> 194</span> <span class="comment">/**</span></div> |
| <div class="line"><a name="l00195"></a><span class="lineno"> 195</span> <span class="comment"> * @brief Beta quantile function</span></div> |
| <div class="line"><a name="l00196"></a><span class="lineno"> 196</span> <span class="comment"> *</span></div> |
| <div class="line"><a name="l00197"></a><span class="lineno"> 197</span> <span class="comment"> * @param p Probability \f$ p \in [0,1] \f$</span></div> |
| <div class="line"><a name="l00198"></a><span class="lineno"> 198</span> <span class="comment"> * @param alpha Shape \f$ \alpha > 0 \f$</span></div> |
| <div class="line"><a name="l00199"></a><span class="lineno"> 199</span> <span class="comment"> * @param beta Shape \f$ \beta > 0 \f$</span></div> |
| <div class="line"><a name="l00200"></a><span class="lineno"> 200</span> <span class="comment"> * @return \f$ x \f$ such that \f$ p = \Pr[X \leq x] \f$ where \f$ X \f$ is</span></div> |
| <div class="line"><a name="l00201"></a><span class="lineno"> 201</span> <span class="comment"> * beta distribution random variable with shape parameters \f$ \alpha \f$</span></div> |
| <div class="line"><a name="l00202"></a><span class="lineno"> 202</span> <span class="comment"> * and \f$ \beta \f$</span></div> |
| <div class="line"><a name="l00203"></a><span class="lineno"> 203</span> <span class="comment"> */</span></div> |
| <div class="line"><a name="l00204"></a><span class="lineno"> 204</span> CREATE FUNCTION MADLIB_SCHEMA.beta_quantile(</div> |
| <div class="line"><a name="l00205"></a><span class="lineno"> 205</span>  p DOUBLE PRECISION,</div> |
| <div class="line"><a name="l00206"></a><span class="lineno"> 206</span>  alpha DOUBLE PRECISION,</div> |
| <div class="line"><a name="l00207"></a><span class="lineno"><a class="code" href="prob_8sql__in.html#aa105049e6e3bb9b3891b0ed1b343e28e"> 207</a></span>  beta DOUBLE PRECISION</div> |
| <div class="line"><a name="l00208"></a><span class="lineno"> 208</span> ) RETURNS DOUBLE PRECISION</div> |
| <div class="line"><a name="l00209"></a><span class="lineno"> 209</span> AS 'MODULE_PATHNAME<span class="stringliteral">'</span></div> |
| <div class="line"><a name="l00210"></a><span class="lineno"> 210</span> <span class="stringliteral">LANGUAGE C</span></div> |
| <div class="line"><a name="l00211"></a><span class="lineno"> 211</span> <span class="stringliteral">IMMUTABLE STRICT;</span></div> |
| <div class="line"><a name="l00212"></a><span class="lineno"> 212</span> <span class="stringliteral"></span></div> |
| <div class="line"><a name="l00213"></a><span class="lineno"> 213</span> <span class="stringliteral"></span><span class="comment"></span></div> |
| <div class="line"><a name="l00214"></a><span class="lineno"> 214</span> <span class="comment">/**</span></div> |
| <div class="line"><a name="l00215"></a><span class="lineno"> 215</span> <span class="comment"> * @brief Binomial cumulative distribution function</span></div> |
| <div class="line"><a name="l00216"></a><span class="lineno"> 216</span> <span class="comment"> *</span></div> |
| <div class="line"><a name="l00217"></a><span class="lineno"> 217</span> <span class="comment"> * @param x Random variate \f$ x \f$</span></div> |
| <div class="line"><a name="l00218"></a><span class="lineno"> 218</span> <span class="comment"> * @param n The number of trials \f$ n \in \mathbb N_0 \f$</span></div> |
| <div class="line"><a name="l00219"></a><span class="lineno"> 219</span> <span class="comment"> * @param sp Success probability \f$ \mathit{sp} \in [0,1] \f$</span></div> |
| <div class="line"><a name="l00220"></a><span class="lineno"> 220</span> <span class="comment"> * @return \f$ \Pr[X \leq x] \f$ where \f$ X \f$ is a binomially distributed</span></div> |
| <div class="line"><a name="l00221"></a><span class="lineno"> 221</span> <span class="comment"> * random variable with \f$ n \f$ trials and success probability</span></div> |
| <div class="line"><a name="l00222"></a><span class="lineno"> 222</span> <span class="comment"> * \f$ \mathit{sp} \f$</span></div> |
| <div class="line"><a name="l00223"></a><span class="lineno"> 223</span> <span class="comment"> */</span></div> |
| <div class="line"><a name="l00224"></a><span class="lineno"> 224</span> CREATE FUNCTION MADLIB_SCHEMA.binomial_cdf(</div> |
| <div class="line"><a name="l00225"></a><span class="lineno"> 225</span>  x DOUBLE PRECISION,</div> |
| <div class="line"><a name="l00226"></a><span class="lineno"><a class="code" href="prob_8sql__in.html#a32433aa742c0504d33e98e28a3e2f190"> 226</a></span>  n INT4,</div> |
| <div class="line"><a name="l00227"></a><span class="lineno"> 227</span>  sp DOUBLE PRECISION</div> |
| <div class="line"><a name="l00228"></a><span class="lineno"> 228</span> ) RETURNS DOUBLE PRECISION</div> |
| <div class="line"><a name="l00229"></a><span class="lineno"> 229</span> AS 'MODULE_PATHNAME<span class="stringliteral">'</span></div> |
| <div class="line"><a name="l00230"></a><span class="lineno"> 230</span> <span class="stringliteral">LANGUAGE C</span></div> |
| <div class="line"><a name="l00231"></a><span class="lineno"> 231</span> <span class="stringliteral">IMMUTABLE STRICT;</span></div> |
| <div class="line"><a name="l00232"></a><span class="lineno"> 232</span> <span class="stringliteral"></span><span class="comment"></span></div> |
| <div class="line"><a name="l00233"></a><span class="lineno"> 233</span> <span class="comment">/**</span></div> |
| <div class="line"><a name="l00234"></a><span class="lineno"> 234</span> <span class="comment"> * @brief Binomial probability mass function</span></div> |
| <div class="line"><a name="l00235"></a><span class="lineno"> 235</span> <span class="comment"> *</span></div> |
| <div class="line"><a name="l00236"></a><span class="lineno"> 236</span> <span class="comment"> * @param x Random variate \f$ x \f$</span></div> |
| <div class="line"><a name="l00237"></a><span class="lineno"> 237</span> <span class="comment"> * @param n The number of trials \f$ n \in \mathbb N_0 \f$</span></div> |
| <div class="line"><a name="l00238"></a><span class="lineno"> 238</span> <span class="comment"> * @param sp Success probability \f$ \mathit{sp} \in [0,1] \f$</span></div> |
| <div class="line"><a name="l00239"></a><span class="lineno"> 239</span> <span class="comment"> * @return \f$ f(x) \f$ where \f$ f \f$ is the probability mass function of</span></div> |
| <div class="line"><a name="l00240"></a><span class="lineno"> 240</span> <span class="comment"> * a binomially distributed random variable with \f$ n \f$ trials and</span></div> |
| <div class="line"><a name="l00241"></a><span class="lineno"> 241</span> <span class="comment"> * success probability \f$ \mathit{sp} \f$</span></div> |
| <div class="line"><a name="l00242"></a><span class="lineno"> 242</span> <span class="comment"> */</span></div> |
| <div class="line"><a name="l00243"></a><span class="lineno"> 243</span> CREATE FUNCTION MADLIB_SCHEMA.binomial_pmf(</div> |
| <div class="line"><a name="l00244"></a><span class="lineno"> 244</span>  x INT4,</div> |
| <div class="line"><a name="l00245"></a><span class="lineno"> 245</span>  n INT4,</div> |
| <div class="line"><a name="l00246"></a><span class="lineno"><a class="code" href="prob_8sql__in.html#aa5000bad6e2e4af1c8cbfec7ea884476"> 246</a></span>  sp DOUBLE PRECISION</div> |
| <div class="line"><a name="l00247"></a><span class="lineno"> 247</span> ) RETURNS DOUBLE PRECISION</div> |
| <div class="line"><a name="l00248"></a><span class="lineno"> 248</span> AS 'MODULE_PATHNAME<span class="stringliteral">'</span></div> |
| <div class="line"><a name="l00249"></a><span class="lineno"> 249</span> <span class="stringliteral">LANGUAGE C</span></div> |
| <div class="line"><a name="l00250"></a><span class="lineno"> 250</span> <span class="stringliteral">IMMUTABLE STRICT;</span></div> |
| <div class="line"><a name="l00251"></a><span class="lineno"> 251</span> <span class="stringliteral"></span><span class="comment"></span></div> |
| <div class="line"><a name="l00252"></a><span class="lineno"> 252</span> <span class="comment">/**</span></div> |
| <div class="line"><a name="l00253"></a><span class="lineno"> 253</span> <span class="comment"> * @brief Binomial quantile function</span></div> |
| <div class="line"><a name="l00254"></a><span class="lineno"> 254</span> <span class="comment"> *</span></div> |
| <div class="line"><a name="l00255"></a><span class="lineno"> 255</span> <span class="comment"> * @param p Probability \f$ p \in [0,1] \f$</span></div> |
| <div class="line"><a name="l00256"></a><span class="lineno"> 256</span> <span class="comment"> * @param n The number of trials \f$ n \in \mathbb N_0 \f$</span></div> |
| <div class="line"><a name="l00257"></a><span class="lineno"> 257</span> <span class="comment"> * @param sp Success probability \f$ \mathit{sp} \in [0,1] \f$</span></div> |
| <div class="line"><a name="l00258"></a><span class="lineno"> 258</span> <span class="comment"> * @return If \f$ p < 0.5 \f$ the maximum \f$ x \f$ such that</span></div> |
| <div class="line"><a name="l00259"></a><span class="lineno"> 259</span> <span class="comment"> * \f$ p \geq \Pr[X \leq x] \f$. If \f$ p \geq 0.5 \f$ the minimum \f$ x \f$</span></div> |
| <div class="line"><a name="l00260"></a><span class="lineno"> 260</span> <span class="comment"> * such that \f$ p \leq \Pr[X \leq x] \f$. Here, \f$ X \f$ is a</span></div> |
| <div class="line"><a name="l00261"></a><span class="lineno"> 261</span> <span class="comment"> * binomially distributed random variable with \f$ n \f$ trials and</span></div> |
| <div class="line"><a name="l00262"></a><span class="lineno"> 262</span> <span class="comment"> * success probability \f$ \mathit{sp} \f$.</span></div> |
| <div class="line"><a name="l00263"></a><span class="lineno"> 263</span> <span class="comment"> */</span></div> |
| <div class="line"><a name="l00264"></a><span class="lineno"> 264</span> CREATE FUNCTION MADLIB_SCHEMA.binomial_quantile(</div> |
| <div class="line"><a name="l00265"></a><span class="lineno"><a class="code" href="prob_8sql__in.html#aa0614475b8685bf8e37533d2ac5bb116"> 265</a></span>  p DOUBLE PRECISION,</div> |
| <div class="line"><a name="l00266"></a><span class="lineno"> 266</span>  n INT4,</div> |
| <div class="line"><a name="l00267"></a><span class="lineno"> 267</span>  sp DOUBLE PRECISION</div> |
| <div class="line"><a name="l00268"></a><span class="lineno"> 268</span> ) RETURNS DOUBLE PRECISION</div> |
| <div class="line"><a name="l00269"></a><span class="lineno"> 269</span> AS 'MODULE_PATHNAME<span class="stringliteral">'</span></div> |
| <div class="line"><a name="l00270"></a><span class="lineno"> 270</span> <span class="stringliteral">LANGUAGE C</span></div> |
| <div class="line"><a name="l00271"></a><span class="lineno"> 271</span> <span class="stringliteral">IMMUTABLE STRICT;</span></div> |
| <div class="line"><a name="l00272"></a><span class="lineno"> 272</span> <span class="stringliteral"></span></div> |
| <div class="line"><a name="l00273"></a><span class="lineno"> 273</span> <span class="stringliteral"></span><span class="comment"></span></div> |
| <div class="line"><a name="l00274"></a><span class="lineno"> 274</span> <span class="comment">/**</span></div> |
| <div class="line"><a name="l00275"></a><span class="lineno"> 275</span> <span class="comment"> * @brief Cauchy cumulative distribution function</span></div> |
| <div class="line"><a name="l00276"></a><span class="lineno"> 276</span> <span class="comment"> *</span></div> |
| <div class="line"><a name="l00277"></a><span class="lineno"> 277</span> <span class="comment"> * @param x Random variate \f$ x \f$</span></div> |
| <div class="line"><a name="l00278"></a><span class="lineno"> 278</span> <span class="comment"> * @param location Location \f$ x_0 \f$</span></div> |
| <div class="line"><a name="l00279"></a><span class="lineno"> 279</span> <span class="comment"> * @param scale Scale \f$ \gamma > 0 \f$</span></div> |
| <div class="line"><a name="l00280"></a><span class="lineno"> 280</span> <span class="comment"> * @return \f$ \Pr[X \leq x] \f$ where \f$ X \f$ is a Cauchy-distributed random</span></div> |
| <div class="line"><a name="l00281"></a><span class="lineno"> 281</span> <span class="comment"> * variable with location and scale parameters \f$ x_0 \f$ and</span></div> |
| <div class="line"><a name="l00282"></a><span class="lineno"> 282</span> <span class="comment"> * \f$ \gamma \f$, respectively</span></div> |
| <div class="line"><a name="l00283"></a><span class="lineno"> 283</span> <span class="comment"> */</span></div> |
| <div class="line"><a name="l00284"></a><span class="lineno"> 284</span> CREATE FUNCTION MADLIB_SCHEMA.cauchy_cdf(</div> |
| <div class="line"><a name="l00285"></a><span class="lineno"> 285</span>  x DOUBLE PRECISION,</div> |
| <div class="line"><a name="l00286"></a><span class="lineno"><a class="code" href="prob_8sql__in.html#a49f421c58d2e1abd63b83d71af9edf21"> 286</a></span>  location DOUBLE PRECISION,</div> |
| <div class="line"><a name="l00287"></a><span class="lineno"> 287</span>  scale DOUBLE PRECISION</div> |
| <div class="line"><a name="l00288"></a><span class="lineno"> 288</span> ) RETURNS DOUBLE PRECISION</div> |
| <div class="line"><a name="l00289"></a><span class="lineno"> 289</span> AS 'MODULE_PATHNAME<span class="stringliteral">'</span></div> |
| <div class="line"><a name="l00290"></a><span class="lineno"> 290</span> <span class="stringliteral">LANGUAGE C</span></div> |
| <div class="line"><a name="l00291"></a><span class="lineno"> 291</span> <span class="stringliteral">IMMUTABLE STRICT;</span></div> |
| <div class="line"><a name="l00292"></a><span class="lineno"> 292</span> <span class="stringliteral"></span><span class="comment"></span></div> |
| <div class="line"><a name="l00293"></a><span class="lineno"> 293</span> <span class="comment">/**</span></div> |
| <div class="line"><a name="l00294"></a><span class="lineno"> 294</span> <span class="comment"> * @brief Cauchy probability density function</span></div> |
| <div class="line"><a name="l00295"></a><span class="lineno"> 295</span> <span class="comment"> *</span></div> |
| <div class="line"><a name="l00296"></a><span class="lineno"> 296</span> <span class="comment"> * @param x Random variate \f$ x \f$</span></div> |
| <div class="line"><a name="l00297"></a><span class="lineno"> 297</span> <span class="comment"> * @param location Location \f$ x_0 \f$</span></div> |
| <div class="line"><a name="l00298"></a><span class="lineno"> 298</span> <span class="comment"> * @param scale Scale \f$ \gamma > 0 \f$</span></div> |
| <div class="line"><a name="l00299"></a><span class="lineno"> 299</span> <span class="comment"> * @return \f$ f(x) \f$ where \f$ f \f$ is the probability density function of</span></div> |
| <div class="line"><a name="l00300"></a><span class="lineno"> 300</span> <span class="comment"> * a Cauchy-distributed random variable with location and scale parameters</span></div> |
| <div class="line"><a name="l00301"></a><span class="lineno"> 301</span> <span class="comment"> * \f$ x_0 \f$ and \f$ \gamma \f$, respectively</span></div> |
| <div class="line"><a name="l00302"></a><span class="lineno"> 302</span> <span class="comment"> */</span></div> |
| <div class="line"><a name="l00303"></a><span class="lineno"> 303</span> CREATE FUNCTION MADLIB_SCHEMA.cauchy_pdf(</div> |
| <div class="line"><a name="l00304"></a><span class="lineno"> 304</span>  x DOUBLE PRECISION,</div> |
| <div class="line"><a name="l00305"></a><span class="lineno"> 305</span>  location DOUBLE PRECISION,</div> |
| <div class="line"><a name="l00306"></a><span class="lineno"><a class="code" href="prob_8sql__in.html#a2d8874c2a5679403a473bfedb14467a4"> 306</a></span>  scale DOUBLE PRECISION</div> |
| <div class="line"><a name="l00307"></a><span class="lineno"> 307</span> ) RETURNS DOUBLE PRECISION</div> |
| <div class="line"><a name="l00308"></a><span class="lineno"> 308</span> AS 'MODULE_PATHNAME<span class="stringliteral">'</span></div> |
| <div class="line"><a name="l00309"></a><span class="lineno"> 309</span> <span class="stringliteral">LANGUAGE C</span></div> |
| <div class="line"><a name="l00310"></a><span class="lineno"> 310</span> <span class="stringliteral">IMMUTABLE STRICT;</span></div> |
| <div class="line"><a name="l00311"></a><span class="lineno"> 311</span> <span class="stringliteral"></span><span class="comment"></span></div> |
| <div class="line"><a name="l00312"></a><span class="lineno"> 312</span> <span class="comment">/**</span></div> |
| <div class="line"><a name="l00313"></a><span class="lineno"> 313</span> <span class="comment"> * @brief Cauchy quantile function</span></div> |
| <div class="line"><a name="l00314"></a><span class="lineno"> 314</span> <span class="comment"> *</span></div> |
| <div class="line"><a name="l00315"></a><span class="lineno"> 315</span> <span class="comment"> * @param p Probability \f$ p \in [0,1] \f$</span></div> |
| <div class="line"><a name="l00316"></a><span class="lineno"> 316</span> <span class="comment"> * @param location Location \f$ x_0 \f$</span></div> |
| <div class="line"><a name="l00317"></a><span class="lineno"> 317</span> <span class="comment"> * @param scale Scale \f$ \gamma > 0 \f$</span></div> |
| <div class="line"><a name="l00318"></a><span class="lineno"> 318</span> <span class="comment"> * @return \f$ x \f$ such that \f$ p = \Pr[X \leq x] \f$ where \f$ X \f$ is a</span></div> |
| <div class="line"><a name="l00319"></a><span class="lineno"> 319</span> <span class="comment"> * Cauchy-distributed random variable with location and scale parameters</span></div> |
| <div class="line"><a name="l00320"></a><span class="lineno"> 320</span> <span class="comment"> * \f$ x_0 \f$ and \f$ \gamma \f$, respectively</span></div> |
| <div class="line"><a name="l00321"></a><span class="lineno"> 321</span> <span class="comment"> */</span></div> |
| <div class="line"><a name="l00322"></a><span class="lineno"> 322</span> CREATE FUNCTION MADLIB_SCHEMA.cauchy_quantile(</div> |
| <div class="line"><a name="l00323"></a><span class="lineno"> 323</span>  p DOUBLE PRECISION,</div> |
| <div class="line"><a name="l00324"></a><span class="lineno"> 324</span>  location DOUBLE PRECISION,</div> |
| <div class="line"><a name="l00325"></a><span class="lineno"><a class="code" href="prob_8sql__in.html#aebfad9365a7fc7a553c3b5c7931f2450"> 325</a></span>  scale DOUBLE PRECISION</div> |
| <div class="line"><a name="l00326"></a><span class="lineno"> 326</span> ) RETURNS DOUBLE PRECISION</div> |
| <div class="line"><a name="l00327"></a><span class="lineno"> 327</span> AS 'MODULE_PATHNAME<span class="stringliteral">'</span></div> |
| <div class="line"><a name="l00328"></a><span class="lineno"> 328</span> <span class="stringliteral">LANGUAGE C</span></div> |
| <div class="line"><a name="l00329"></a><span class="lineno"> 329</span> <span class="stringliteral">IMMUTABLE STRICT;</span></div> |
| <div class="line"><a name="l00330"></a><span class="lineno"> 330</span> <span class="stringliteral"></span></div> |
| <div class="line"><a name="l00331"></a><span class="lineno"> 331</span> <span class="stringliteral"></span><span class="comment"></span></div> |
| <div class="line"><a name="l00332"></a><span class="lineno"> 332</span> <span class="comment">/**</span></div> |
| <div class="line"><a name="l00333"></a><span class="lineno"> 333</span> <span class="comment"> * @brief Chi-squared cumulative distribution function</span></div> |
| <div class="line"><a name="l00334"></a><span class="lineno"> 334</span> <span class="comment"> *</span></div> |
| <div class="line"><a name="l00335"></a><span class="lineno"> 335</span> <span class="comment"> * @param x Random variate \f$ x \f$</span></div> |
| <div class="line"><a name="l00336"></a><span class="lineno"> 336</span> <span class="comment"> * @param df Degrees of freedom \f$ \nu > 0 \f$</span></div> |
| <div class="line"><a name="l00337"></a><span class="lineno"> 337</span> <span class="comment"> * @return \f$ \Pr[X \leq x] \f$ where \f$ X \f$ is a chi-squared distributed</span></div> |
| <div class="line"><a name="l00338"></a><span class="lineno"> 338</span> <span class="comment"> * random variable with \f$ \nu \f$ degrees of freedom</span></div> |
| <div class="line"><a name="l00339"></a><span class="lineno"> 339</span> <span class="comment"> */</span></div> |
| <div class="line"><a name="l00340"></a><span class="lineno"> 340</span> CREATE FUNCTION MADLIB_SCHEMA.chi_squared_cdf(</div> |
| <div class="line"><a name="l00341"></a><span class="lineno"> 341</span>  x DOUBLE PRECISION,</div> |
| <div class="line"><a name="l00342"></a><span class="lineno"> 342</span>  df DOUBLE PRECISION</div> |
| <div class="line"><a name="l00343"></a><span class="lineno"> 343</span> ) RETURNS DOUBLE PRECISION</div> |
| <div class="line"><a name="l00344"></a><span class="lineno"><a class="code" href="prob_8sql__in.html#ae8aa9b741e89c8d9236a682d218006e0"> 344</a></span> AS 'MODULE_PATHNAME<span class="stringliteral">'</span></div> |
| <div class="line"><a name="l00345"></a><span class="lineno"> 345</span> <span class="stringliteral">LANGUAGE C</span></div> |
| <div class="line"><a name="l00346"></a><span class="lineno"> 346</span> <span class="stringliteral">IMMUTABLE STRICT;</span></div> |
| <div class="line"><a name="l00347"></a><span class="lineno"> 347</span> <span class="stringliteral"></span><span class="comment"></span></div> |
| <div class="line"><a name="l00348"></a><span class="lineno"> 348</span> <span class="comment">/**</span></div> |
| <div class="line"><a name="l00349"></a><span class="lineno"> 349</span> <span class="comment"> * @brief Chi-squared distribution probability density function</span></div> |
| <div class="line"><a name="l00350"></a><span class="lineno"> 350</span> <span class="comment"> *</span></div> |
| <div class="line"><a name="l00351"></a><span class="lineno"> 351</span> <span class="comment"> * @param x Random variate \f$ x \f$</span></div> |
| <div class="line"><a name="l00352"></a><span class="lineno"> 352</span> <span class="comment"> * @param df Degrees of freedom \f$ \nu > 0 \f$</span></div> |
| <div class="line"><a name="l00353"></a><span class="lineno"> 353</span> <span class="comment"> * @return \f$ f(x) \f$ where \f$ f \f$ is the probability density function of</span></div> |
| <div class="line"><a name="l00354"></a><span class="lineno"> 354</span> <span class="comment"> * a chi-squared distributed random variable with \f$ \nu \f$ degrees of</span></div> |
| <div class="line"><a name="l00355"></a><span class="lineno"> 355</span> <span class="comment"> * freedom</span></div> |
| <div class="line"><a name="l00356"></a><span class="lineno"> 356</span> <span class="comment"> */</span></div> |
| <div class="line"><a name="l00357"></a><span class="lineno"> 357</span> CREATE FUNCTION MADLIB_SCHEMA.chi_squared_pdf(</div> |
| <div class="line"><a name="l00358"></a><span class="lineno"> 358</span>  x DOUBLE PRECISION,</div> |
| <div class="line"><a name="l00359"></a><span class="lineno"> 359</span>  df DOUBLE PRECISION</div> |
| <div class="line"><a name="l00360"></a><span class="lineno"> 360</span> ) RETURNS DOUBLE PRECISION</div> |
| <div class="line"><a name="l00361"></a><span class="lineno"> 361</span> AS 'MODULE_PATHNAME<span class="stringliteral">'</span></div> |
| <div class="line"><a name="l00362"></a><span class="lineno"><a class="code" href="prob_8sql__in.html#a230513b6b549d5b445cbacbdbab42c15"> 362</a></span> <span class="stringliteral">LANGUAGE C</span></div> |
| <div class="line"><a name="l00363"></a><span class="lineno"> 363</span> <span class="stringliteral">IMMUTABLE STRICT;</span></div> |
| <div class="line"><a name="l00364"></a><span class="lineno"> 364</span> <span class="stringliteral"></span><span class="comment"></span></div> |
| <div class="line"><a name="l00365"></a><span class="lineno"> 365</span> <span class="comment">/**</span></div> |
| <div class="line"><a name="l00366"></a><span class="lineno"> 366</span> <span class="comment"> * @brief Chi-squared distribution quantile function</span></div> |
| <div class="line"><a name="l00367"></a><span class="lineno"> 367</span> <span class="comment"> *</span></div> |
| <div class="line"><a name="l00368"></a><span class="lineno"> 368</span> <span class="comment"> * @param p Probability \f$ p \in [0,1] \f$</span></div> |
| <div class="line"><a name="l00369"></a><span class="lineno"> 369</span> <span class="comment"> * @param df Degrees of freedom \f$ \mu > 0 \f$</span></div> |
| <div class="line"><a name="l00370"></a><span class="lineno"> 370</span> <span class="comment"> * @return \f$ x \f$ such that \f$ p = \Pr[X \leq x] \f$ where \f$ X \f$ is a</span></div> |
| <div class="line"><a name="l00371"></a><span class="lineno"> 371</span> <span class="comment"> * chi-squared distributed random variable with \f$ \nu \f$ degrees of</span></div> |
| <div class="line"><a name="l00372"></a><span class="lineno"> 372</span> <span class="comment"> * freedom</span></div> |
| <div class="line"><a name="l00373"></a><span class="lineno"> 373</span> <span class="comment"> */</span></div> |
| <div class="line"><a name="l00374"></a><span class="lineno"> 374</span> CREATE FUNCTION MADLIB_SCHEMA.chi_squared_quantile(</div> |
| <div class="line"><a name="l00375"></a><span class="lineno"> 375</span>  p DOUBLE PRECISION,</div> |
| <div class="line"><a name="l00376"></a><span class="lineno"> 376</span>  df DOUBLE PRECISION</div> |
| <div class="line"><a name="l00377"></a><span class="lineno"> 377</span> ) RETURNS DOUBLE PRECISION</div> |
| <div class="line"><a name="l00378"></a><span class="lineno"> 378</span> AS 'MODULE_PATHNAME<span class="stringliteral">'</span></div> |
| <div class="line"><a name="l00379"></a><span class="lineno"><a class="code" href="prob_8sql__in.html#a90bccc717d7052e83bafd7f160a783b1"> 379</a></span> <span class="stringliteral">LANGUAGE C</span></div> |
| <div class="line"><a name="l00380"></a><span class="lineno"> 380</span> <span class="stringliteral">IMMUTABLE STRICT;</span></div> |
| <div class="line"><a name="l00381"></a><span class="lineno"> 381</span> <span class="stringliteral"></span></div> |
| <div class="line"><a name="l00382"></a><span class="lineno"> 382</span> <span class="stringliteral"></span><span class="comment"></span></div> |
| <div class="line"><a name="l00383"></a><span class="lineno"> 383</span> <span class="comment">/**</span></div> |
| <div class="line"><a name="l00384"></a><span class="lineno"> 384</span> <span class="comment"> * @brief Exponential cumulative distribution function</span></div> |
| <div class="line"><a name="l00385"></a><span class="lineno"> 385</span> <span class="comment"> *</span></div> |
| <div class="line"><a name="l00386"></a><span class="lineno"> 386</span> <span class="comment"> * @param x Random variate \f$ x \f$</span></div> |
| <div class="line"><a name="l00387"></a><span class="lineno"> 387</span> <span class="comment"> * @param lambda Rate parameter \f$ \lambda > 0 \f$</span></div> |
| <div class="line"><a name="l00388"></a><span class="lineno"> 388</span> <span class="comment"> * @return \f$ \Pr[X \leq x] \f$ where \f$ X \f$ is an exponentially distributed</span></div> |
| <div class="line"><a name="l00389"></a><span class="lineno"> 389</span> <span class="comment"> * random variable with rate parameter \f$ \lambda \f$</span></div> |
| <div class="line"><a name="l00390"></a><span class="lineno"> 390</span> <span class="comment"> */</span></div> |
| <div class="line"><a name="l00391"></a><span class="lineno"> 391</span> CREATE FUNCTION MADLIB_SCHEMA.exponential_cdf(</div> |
| <div class="line"><a name="l00392"></a><span class="lineno"> 392</span>  x DOUBLE PRECISION,</div> |
| <div class="line"><a name="l00393"></a><span class="lineno"> 393</span>  lambda DOUBLE PRECISION</div> |
| <div class="line"><a name="l00394"></a><span class="lineno"> 394</span> ) RETURNS DOUBLE PRECISION</div> |
| <div class="line"><a name="l00395"></a><span class="lineno"> 395</span> AS 'MODULE_PATHNAME<span class="stringliteral">'</span></div> |
| <div class="line"><a name="l00396"></a><span class="lineno"><a class="code" href="prob_8sql__in.html#ad125307fe65a33b60f6dd524037d4548"> 396</a></span> <span class="stringliteral">LANGUAGE C</span></div> |
| <div class="line"><a name="l00397"></a><span class="lineno"> 397</span> <span class="stringliteral">IMMUTABLE STRICT;</span></div> |
| <div class="line"><a name="l00398"></a><span class="lineno"> 398</span> <span class="stringliteral"></span><span class="comment"></span></div> |
| <div class="line"><a name="l00399"></a><span class="lineno"> 399</span> <span class="comment">/**</span></div> |
| <div class="line"><a name="l00400"></a><span class="lineno"> 400</span> <span class="comment"> * @brief Exponential probability density function</span></div> |
| <div class="line"><a name="l00401"></a><span class="lineno"> 401</span> <span class="comment"> *</span></div> |
| <div class="line"><a name="l00402"></a><span class="lineno"> 402</span> <span class="comment"> * @param x Random variate \f$ x \f$</span></div> |
| <div class="line"><a name="l00403"></a><span class="lineno"> 403</span> <span class="comment"> * @param lambda Rate parameter \f$ \lambda > 0 \f$</span></div> |
| <div class="line"><a name="l00404"></a><span class="lineno"> 404</span> <span class="comment"> * @return \f$ f(x) \f$ where \f$ f \f$ is the probability density function of</span></div> |
| <div class="line"><a name="l00405"></a><span class="lineno"> 405</span> <span class="comment"> * exponentially distributed random variable with rate parameter</span></div> |
| <div class="line"><a name="l00406"></a><span class="lineno"> 406</span> <span class="comment"> * \f$ \lambda \f$</span></div> |
| <div class="line"><a name="l00407"></a><span class="lineno"> 407</span> <span class="comment"> */</span></div> |
| <div class="line"><a name="l00408"></a><span class="lineno"> 408</span> CREATE FUNCTION MADLIB_SCHEMA.exponential_pdf(</div> |
| <div class="line"><a name="l00409"></a><span class="lineno"> 409</span>  x DOUBLE PRECISION,</div> |
| <div class="line"><a name="l00410"></a><span class="lineno"> 410</span>  lambda DOUBLE PRECISION</div> |
| <div class="line"><a name="l00411"></a><span class="lineno"> 411</span> ) RETURNS DOUBLE PRECISION</div> |
| <div class="line"><a name="l00412"></a><span class="lineno"> 412</span> AS 'MODULE_PATHNAME<span class="stringliteral">'</span></div> |
| <div class="line"><a name="l00413"></a><span class="lineno"><a class="code" href="prob_8sql__in.html#a6d1bf6816f56b8e5ba6bf6ca94752f46"> 413</a></span> <span class="stringliteral">LANGUAGE C</span></div> |
| <div class="line"><a name="l00414"></a><span class="lineno"> 414</span> <span class="stringliteral">IMMUTABLE STRICT;</span></div> |
| <div class="line"><a name="l00415"></a><span class="lineno"> 415</span> <span class="stringliteral"></span><span class="comment"></span></div> |
| <div class="line"><a name="l00416"></a><span class="lineno"> 416</span> <span class="comment">/**</span></div> |
| <div class="line"><a name="l00417"></a><span class="lineno"> 417</span> <span class="comment"> * @brief Exponential quantile function</span></div> |
| <div class="line"><a name="l00418"></a><span class="lineno"> 418</span> <span class="comment"> *</span></div> |
| <div class="line"><a name="l00419"></a><span class="lineno"> 419</span> <span class="comment"> * @param p Probability \f$ p \in [0,1] \f$</span></div> |
| <div class="line"><a name="l00420"></a><span class="lineno"> 420</span> <span class="comment"> * @param lambda Rate parameter \f$ \lambda > 0 \f$</span></div> |
| <div class="line"><a name="l00421"></a><span class="lineno"> 421</span> <span class="comment"> * @return \f$ x \f$ such that \f$ p = \Pr[X \leq x] \f$ where \f$ X \f$ is a</span></div> |
| <div class="line"><a name="l00422"></a><span class="lineno"> 422</span> <span class="comment"> * exponentially distributed random variable with rate parameter</span></div> |
| <div class="line"><a name="l00423"></a><span class="lineno"> 423</span> <span class="comment"> * \f$ \lambda \f$</span></div> |
| <div class="line"><a name="l00424"></a><span class="lineno"> 424</span> <span class="comment"> */</span></div> |
| <div class="line"><a name="l00425"></a><span class="lineno"> 425</span> CREATE FUNCTION MADLIB_SCHEMA.exponential_quantile(</div> |
| <div class="line"><a name="l00426"></a><span class="lineno"> 426</span>  p DOUBLE PRECISION,</div> |
| <div class="line"><a name="l00427"></a><span class="lineno"> 427</span>  lambda DOUBLE PRECISION</div> |
| <div class="line"><a name="l00428"></a><span class="lineno"> 428</span> ) RETURNS DOUBLE PRECISION</div> |
| <div class="line"><a name="l00429"></a><span class="lineno"> 429</span> AS 'MODULE_PATHNAME<span class="stringliteral">'</span></div> |
| <div class="line"><a name="l00430"></a><span class="lineno"><a class="code" href="prob_8sql__in.html#a18a5458c4bc85f0c4ea321317f90bdbb"> 430</a></span> <span class="stringliteral">LANGUAGE C</span></div> |
| <div class="line"><a name="l00431"></a><span class="lineno"> 431</span> <span class="stringliteral">IMMUTABLE STRICT;</span></div> |
| <div class="line"><a name="l00432"></a><span class="lineno"> 432</span> <span class="stringliteral"></span></div> |
| <div class="line"><a name="l00433"></a><span class="lineno"> 433</span> <span class="stringliteral"></span><span class="comment"></span></div> |
| <div class="line"><a name="l00434"></a><span class="lineno"> 434</span> <span class="comment">/**</span></div> |
| <div class="line"><a name="l00435"></a><span class="lineno"> 435</span> <span class="comment"> * @brief Extreme Value cumulative distribution function</span></div> |
| <div class="line"><a name="l00436"></a><span class="lineno"> 436</span> <span class="comment"> *</span></div> |
| <div class="line"><a name="l00437"></a><span class="lineno"> 437</span> <span class="comment"> * @param x Random variate \f$ x \f$</span></div> |
| <div class="line"><a name="l00438"></a><span class="lineno"> 438</span> <span class="comment"> * @param location Location \f$ \alpha \f$</span></div> |
| <div class="line"><a name="l00439"></a><span class="lineno"> 439</span> <span class="comment"> * @param scale Scale \f$ \beta > 0 \f$</span></div> |
| <div class="line"><a name="l00440"></a><span class="lineno"> 440</span> <span class="comment"> * @return \f$ \Pr[X \leq x] \f$ where \f$ X \f$ is an extreme-value distributed</span></div> |
| <div class="line"><a name="l00441"></a><span class="lineno"> 441</span> <span class="comment"> * random variable with location and scale parameters \f$ \alpha \f$ and</span></div> |
| <div class="line"><a name="l00442"></a><span class="lineno"> 442</span> <span class="comment"> * \f$ \beta \f$, respectively</span></div> |
| <div class="line"><a name="l00443"></a><span class="lineno"> 443</span> <span class="comment"> */</span></div> |
| <div class="line"><a name="l00444"></a><span class="lineno"> 444</span> CREATE FUNCTION MADLIB_SCHEMA.extreme_value_cdf(</div> |
| <div class="line"><a name="l00445"></a><span class="lineno"> 445</span>  x DOUBLE PRECISION,</div> |
| <div class="line"><a name="l00446"></a><span class="lineno"> 446</span>  location DOUBLE PRECISION,</div> |
| <div class="line"><a name="l00447"></a><span class="lineno"><a class="code" href="prob_8sql__in.html#ae3687b8e69a402154b829a6531b1b279"> 447</a></span>  scale DOUBLE PRECISION</div> |
| <div class="line"><a name="l00448"></a><span class="lineno"> 448</span> ) RETURNS DOUBLE PRECISION</div> |
| <div class="line"><a name="l00449"></a><span class="lineno"> 449</span> AS 'MODULE_PATHNAME<span class="stringliteral">'</span></div> |
| <div class="line"><a name="l00450"></a><span class="lineno"> 450</span> <span class="stringliteral">LANGUAGE C</span></div> |
| <div class="line"><a name="l00451"></a><span class="lineno"> 451</span> <span class="stringliteral">IMMUTABLE STRICT;</span></div> |
| <div class="line"><a name="l00452"></a><span class="lineno"> 452</span> <span class="stringliteral"></span><span class="comment"></span></div> |
| <div class="line"><a name="l00453"></a><span class="lineno"> 453</span> <span class="comment">/**</span></div> |
| <div class="line"><a name="l00454"></a><span class="lineno"> 454</span> <span class="comment"> * @brief Extreme Value probability density function</span></div> |
| <div class="line"><a name="l00455"></a><span class="lineno"> 455</span> <span class="comment"> *</span></div> |
| <div class="line"><a name="l00456"></a><span class="lineno"> 456</span> <span class="comment"> * @param x Random variate \f$ x \f$</span></div> |
| <div class="line"><a name="l00457"></a><span class="lineno"> 457</span> <span class="comment"> * @param location Location \f$ \alpha \f$</span></div> |
| <div class="line"><a name="l00458"></a><span class="lineno"> 458</span> <span class="comment"> * @param scale Scale \f$ \beta > 0 \f$</span></div> |
| <div class="line"><a name="l00459"></a><span class="lineno"> 459</span> <span class="comment"> * @return \f$ f(x) \f$ where \f$ f \f$ is the probability density function of</span></div> |
| <div class="line"><a name="l00460"></a><span class="lineno"> 460</span> <span class="comment"> * an extreme-value distributed random variable with location and scale</span></div> |
| <div class="line"><a name="l00461"></a><span class="lineno"> 461</span> <span class="comment"> * parameters \f$ \alpha \f$ and \f$ \beta \f$, respectively</span></div> |
| <div class="line"><a name="l00462"></a><span class="lineno"> 462</span> <span class="comment"> */</span></div> |
| <div class="line"><a name="l00463"></a><span class="lineno"> 463</span> CREATE FUNCTION MADLIB_SCHEMA.extreme_value_pdf(</div> |
| <div class="line"><a name="l00464"></a><span class="lineno"> 464</span>  x DOUBLE PRECISION,</div> |
| <div class="line"><a name="l00465"></a><span class="lineno"> 465</span>  location DOUBLE PRECISION,</div> |
| <div class="line"><a name="l00466"></a><span class="lineno"><a class="code" href="prob_8sql__in.html#acffffe04c15eccd2e88cdac250bccc68"> 466</a></span>  scale DOUBLE PRECISION</div> |
| <div class="line"><a name="l00467"></a><span class="lineno"> 467</span> ) RETURNS DOUBLE PRECISION</div> |
| <div class="line"><a name="l00468"></a><span class="lineno"> 468</span> AS 'MODULE_PATHNAME<span class="stringliteral">'</span></div> |
| <div class="line"><a name="l00469"></a><span class="lineno"> 469</span> <span class="stringliteral">LANGUAGE C</span></div> |
| <div class="line"><a name="l00470"></a><span class="lineno"> 470</span> <span class="stringliteral">IMMUTABLE STRICT;</span></div> |
| <div class="line"><a name="l00471"></a><span class="lineno"> 471</span> <span class="stringliteral"></span><span class="comment"></span></div> |
| <div class="line"><a name="l00472"></a><span class="lineno"> 472</span> <span class="comment">/**</span></div> |
| <div class="line"><a name="l00473"></a><span class="lineno"> 473</span> <span class="comment"> * @brief Extreme Value quantile function</span></div> |
| <div class="line"><a name="l00474"></a><span class="lineno"> 474</span> <span class="comment"> *</span></div> |
| <div class="line"><a name="l00475"></a><span class="lineno"> 475</span> <span class="comment"> * @param p Probability \f$ p \in [0,1] \f$</span></div> |
| <div class="line"><a name="l00476"></a><span class="lineno"> 476</span> <span class="comment"> * @param location Location \f$ \alpha \f$</span></div> |
| <div class="line"><a name="l00477"></a><span class="lineno"> 477</span> <span class="comment"> * @param scale Scale \f$ \beta > 0 \f$</span></div> |
| <div class="line"><a name="l00478"></a><span class="lineno"> 478</span> <span class="comment"> * @return \f$ x \f$ such that \f$ p = \Pr[X \leq x] \f$ where \f$ X \f$ is</span></div> |
| <div class="line"><a name="l00479"></a><span class="lineno"> 479</span> <span class="comment"> * an extreme-value distributed random variable with location and scale</span></div> |
| <div class="line"><a name="l00480"></a><span class="lineno"> 480</span> <span class="comment"> * parameters \f$ \alpha \f$ and \f$ \beta \f$, respectively</span></div> |
| <div class="line"><a name="l00481"></a><span class="lineno"> 481</span> <span class="comment"> */</span></div> |
| <div class="line"><a name="l00482"></a><span class="lineno"> 482</span> CREATE FUNCTION MADLIB_SCHEMA.extreme_value_quantile(</div> |
| <div class="line"><a name="l00483"></a><span class="lineno"> 483</span>  p DOUBLE PRECISION,</div> |
| <div class="line"><a name="l00484"></a><span class="lineno"> 484</span>  location DOUBLE PRECISION,</div> |
| <div class="line"><a name="l00485"></a><span class="lineno"><a class="code" href="prob_8sql__in.html#a03a3494462f4cb8c9fb6212e72b0b2e9"> 485</a></span>  scale DOUBLE PRECISION</div> |
| <div class="line"><a name="l00486"></a><span class="lineno"> 486</span> ) RETURNS DOUBLE PRECISION</div> |
| <div class="line"><a name="l00487"></a><span class="lineno"> 487</span> AS 'MODULE_PATHNAME<span class="stringliteral">'</span></div> |
| <div class="line"><a name="l00488"></a><span class="lineno"> 488</span> <span class="stringliteral">LANGUAGE C</span></div> |
| <div class="line"><a name="l00489"></a><span class="lineno"> 489</span> <span class="stringliteral">IMMUTABLE STRICT;</span></div> |
| <div class="line"><a name="l00490"></a><span class="lineno"> 490</span> <span class="stringliteral"></span></div> |
| <div class="line"><a name="l00491"></a><span class="lineno"> 491</span> <span class="stringliteral"></span><span class="comment"></span></div> |
| <div class="line"><a name="l00492"></a><span class="lineno"> 492</span> <span class="comment">/**</span></div> |
| <div class="line"><a name="l00493"></a><span class="lineno"> 493</span> <span class="comment"> * @brief Fisher F cumulative distribution function</span></div> |
| <div class="line"><a name="l00494"></a><span class="lineno"> 494</span> <span class="comment"> *</span></div> |
| <div class="line"><a name="l00495"></a><span class="lineno"> 495</span> <span class="comment"> * @param x Random variate \f$ x \f$</span></div> |
| <div class="line"><a name="l00496"></a><span class="lineno"> 496</span> <span class="comment"> * @param df1 Degrees of freedom in numerator \f$ \nu_1 > 0 \f$</span></div> |
| <div class="line"><a name="l00497"></a><span class="lineno"> 497</span> <span class="comment"> * @param df2 Degrees of freedom in denominator \f$ \nu_1 > 0 \f$</span></div> |
| <div class="line"><a name="l00498"></a><span class="lineno"> 498</span> <span class="comment"> * @return \f$ \Pr[X \leq x] \f$ where \f$ X \f$ is a Fisher F-distributed</span></div> |
| <div class="line"><a name="l00499"></a><span class="lineno"> 499</span> <span class="comment"> * random variable with parameters \f$ \nu_1 \f$ and \f$ \nu_2 \f$</span></div> |
| <div class="line"><a name="l00500"></a><span class="lineno"> 500</span> <span class="comment"> */</span></div> |
| <div class="line"><a name="l00501"></a><span class="lineno"> 501</span> CREATE FUNCTION MADLIB_SCHEMA.fisher_f_cdf(</div> |
| <div class="line"><a name="l00502"></a><span class="lineno"> 502</span>  x DOUBLE PRECISION,</div> |
| <div class="line"><a name="l00503"></a><span class="lineno"> 503</span>  df1 DOUBLE PRECISION,</div> |
| <div class="line"><a name="l00504"></a><span class="lineno"><a class="code" href="prob_8sql__in.html#aeb5a7d295b83a891774a4fb0ef27c458"> 504</a></span>  df2 DOUBLE PRECISION</div> |
| <div class="line"><a name="l00505"></a><span class="lineno"> 505</span> ) RETURNS DOUBLE PRECISION</div> |
| <div class="line"><a name="l00506"></a><span class="lineno"> 506</span> AS 'MODULE_PATHNAME<span class="stringliteral">'</span></div> |
| <div class="line"><a name="l00507"></a><span class="lineno"> 507</span> <span class="stringliteral">LANGUAGE C</span></div> |
| <div class="line"><a name="l00508"></a><span class="lineno"> 508</span> <span class="stringliteral">IMMUTABLE STRICT;</span></div> |
| <div class="line"><a name="l00509"></a><span class="lineno"> 509</span> <span class="stringliteral"></span><span class="comment"></span></div> |
| <div class="line"><a name="l00510"></a><span class="lineno"> 510</span> <span class="comment">/**</span></div> |
| <div class="line"><a name="l00511"></a><span class="lineno"> 511</span> <span class="comment"> * @brief Fisher F probability density function</span></div> |
| <div class="line"><a name="l00512"></a><span class="lineno"> 512</span> <span class="comment"> *</span></div> |
| <div class="line"><a name="l00513"></a><span class="lineno"> 513</span> <span class="comment"> * @param x Random variate \f$ x \f$</span></div> |
| <div class="line"><a name="l00514"></a><span class="lineno"> 514</span> <span class="comment"> * @param df1 Degrees of freedom in numerator \f$ \nu_1 > 0 \f$</span></div> |
| <div class="line"><a name="l00515"></a><span class="lineno"> 515</span> <span class="comment"> * @param df2 Degrees of freedom in denominator \f$ \nu_1 > 0 \f$</span></div> |
| <div class="line"><a name="l00516"></a><span class="lineno"> 516</span> <span class="comment"> * @return \f$ f(x) \f$ where \f$ f \f$ is the probability density function of</span></div> |
| <div class="line"><a name="l00517"></a><span class="lineno"> 517</span> <span class="comment"> * a Fisher F-distributed random variable with parameters \f$ \nu_1 \f$ and</span></div> |
| <div class="line"><a name="l00518"></a><span class="lineno"> 518</span> <span class="comment"> * \f$ \nu_2 \f$</span></div> |
| <div class="line"><a name="l00519"></a><span class="lineno"> 519</span> <span class="comment"> */</span></div> |
| <div class="line"><a name="l00520"></a><span class="lineno"> 520</span> CREATE FUNCTION MADLIB_SCHEMA.fisher_f_pdf(</div> |
| <div class="line"><a name="l00521"></a><span class="lineno"> 521</span>  x DOUBLE PRECISION,</div> |
| <div class="line"><a name="l00522"></a><span class="lineno"> 522</span>  df1 DOUBLE PRECISION,</div> |
| <div class="line"><a name="l00523"></a><span class="lineno"><a class="code" href="prob_8sql__in.html#a6c5b3e35531e44098f9d0cbef14cb8a6"> 523</a></span>  df2 DOUBLE PRECISION</div> |
| <div class="line"><a name="l00524"></a><span class="lineno"> 524</span> ) RETURNS DOUBLE PRECISION</div> |
| <div class="line"><a name="l00525"></a><span class="lineno"> 525</span> AS 'MODULE_PATHNAME<span class="stringliteral">'</span></div> |
| <div class="line"><a name="l00526"></a><span class="lineno"> 526</span> <span class="stringliteral">LANGUAGE C</span></div> |
| <div class="line"><a name="l00527"></a><span class="lineno"> 527</span> <span class="stringliteral">IMMUTABLE STRICT;</span></div> |
| <div class="line"><a name="l00528"></a><span class="lineno"> 528</span> <span class="stringliteral"></span><span class="comment"></span></div> |
| <div class="line"><a name="l00529"></a><span class="lineno"> 529</span> <span class="comment">/**</span></div> |
| <div class="line"><a name="l00530"></a><span class="lineno"> 530</span> <span class="comment"> * @brief Fisher F quantile function</span></div> |
| <div class="line"><a name="l00531"></a><span class="lineno"> 531</span> <span class="comment"> *</span></div> |
| <div class="line"><a name="l00532"></a><span class="lineno"> 532</span> <span class="comment"> * @param p Probability \f$ p \in [0,1] \f$</span></div> |
| <div class="line"><a name="l00533"></a><span class="lineno"> 533</span> <span class="comment"> * @param df1 Degrees of freedom in numerator \f$ \nu_1 > 0 \f$</span></div> |
| <div class="line"><a name="l00534"></a><span class="lineno"> 534</span> <span class="comment"> * @param df2 Degrees of freedom in denominator \f$ \nu_1 > 0 \f$</span></div> |
| <div class="line"><a name="l00535"></a><span class="lineno"> 535</span> <span class="comment"> * @return \f$ x \f$ such that \f$ p = \Pr[X \leq x] \f$ where \f$ X \f$ is a</span></div> |
| <div class="line"><a name="l00536"></a><span class="lineno"> 536</span> <span class="comment"> * Fisher F-distributed random variable with parameters \f$ \nu_1 \f$ and</span></div> |
| <div class="line"><a name="l00537"></a><span class="lineno"> 537</span> <span class="comment"> * \f$ \nu_2 \f$</span></div> |
| <div class="line"><a name="l00538"></a><span class="lineno"> 538</span> <span class="comment"> */</span></div> |
| <div class="line"><a name="l00539"></a><span class="lineno"> 539</span> CREATE FUNCTION MADLIB_SCHEMA.fisher_f_quantile(</div> |
| <div class="line"><a name="l00540"></a><span class="lineno"> 540</span>  p DOUBLE PRECISION,</div> |
| <div class="line"><a name="l00541"></a><span class="lineno"> 541</span>  df1 DOUBLE PRECISION,</div> |
| <div class="line"><a name="l00542"></a><span class="lineno"><a class="code" href="prob_8sql__in.html#a1c7937426379a8913519a6abc5a38ac2"> 542</a></span>  df2 DOUBLE PRECISION</div> |
| <div class="line"><a name="l00543"></a><span class="lineno"> 543</span> ) RETURNS DOUBLE PRECISION</div> |
| <div class="line"><a name="l00544"></a><span class="lineno"> 544</span> AS 'MODULE_PATHNAME<span class="stringliteral">'</span></div> |
| <div class="line"><a name="l00545"></a><span class="lineno"> 545</span> <span class="stringliteral">LANGUAGE C</span></div> |
| <div class="line"><a name="l00546"></a><span class="lineno"> 546</span> <span class="stringliteral">IMMUTABLE STRICT;</span></div> |
| <div class="line"><a name="l00547"></a><span class="lineno"> 547</span> <span class="stringliteral"></span></div> |
| <div class="line"><a name="l00548"></a><span class="lineno"> 548</span> <span class="stringliteral"></span><span class="comment"></span></div> |
| <div class="line"><a name="l00549"></a><span class="lineno"> 549</span> <span class="comment">/**</span></div> |
| <div class="line"><a name="l00550"></a><span class="lineno"> 550</span> <span class="comment"> * @brief Gamma cumulative distribution function</span></div> |
| <div class="line"><a name="l00551"></a><span class="lineno"> 551</span> <span class="comment"> *</span></div> |
| <div class="line"><a name="l00552"></a><span class="lineno"> 552</span> <span class="comment"> * @param x Random variate \f$ x \f$</span></div> |
| <div class="line"><a name="l00553"></a><span class="lineno"> 553</span> <span class="comment"> * @param shape Shape \f$ k > 0 \f$</span></div> |
| <div class="line"><a name="l00554"></a><span class="lineno"> 554</span> <span class="comment"> * @param scale Scale \f$ \theta > 0 \f$</span></div> |
| <div class="line"><a name="l00555"></a><span class="lineno"> 555</span> <span class="comment"> * @return \f$ \Pr[X \leq x] \f$ where \f$ X \f$ is a gamma distributed random</span></div> |
| <div class="line"><a name="l00556"></a><span class="lineno"> 556</span> <span class="comment"> * variable with shape and scale parameters \f$ k \f$ and</span></div> |
| <div class="line"><a name="l00557"></a><span class="lineno"> 557</span> <span class="comment"> * \f$ \theta \f$, respectively</span></div> |
| <div class="line"><a name="l00558"></a><span class="lineno"> 558</span> <span class="comment"> */</span></div> |
| <div class="line"><a name="l00559"></a><span class="lineno"> 559</span> CREATE FUNCTION MADLIB_SCHEMA.gamma_cdf(</div> |
| <div class="line"><a name="l00560"></a><span class="lineno"> 560</span>  x DOUBLE PRECISION,</div> |
| <div class="line"><a name="l00561"></a><span class="lineno"><a class="code" href="prob_8sql__in.html#ab6ed888a5338a0bee9c55edf4d33847f"> 561</a></span>  shape DOUBLE PRECISION,</div> |
| <div class="line"><a name="l00562"></a><span class="lineno"> 562</span>  scale DOUBLE PRECISION</div> |
| <div class="line"><a name="l00563"></a><span class="lineno"> 563</span> ) RETURNS DOUBLE PRECISION</div> |
| <div class="line"><a name="l00564"></a><span class="lineno"> 564</span> AS 'MODULE_PATHNAME<span class="stringliteral">'</span></div> |
| <div class="line"><a name="l00565"></a><span class="lineno"> 565</span> <span class="stringliteral">LANGUAGE C</span></div> |
| <div class="line"><a name="l00566"></a><span class="lineno"> 566</span> <span class="stringliteral">IMMUTABLE STRICT;</span></div> |
| <div class="line"><a name="l00567"></a><span class="lineno"> 567</span> <span class="stringliteral"></span><span class="comment"></span></div> |
| <div class="line"><a name="l00568"></a><span class="lineno"> 568</span> <span class="comment">/**</span></div> |
| <div class="line"><a name="l00569"></a><span class="lineno"> 569</span> <span class="comment"> * @brief Gamma probability density function</span></div> |
| <div class="line"><a name="l00570"></a><span class="lineno"> 570</span> <span class="comment"> *</span></div> |
| <div class="line"><a name="l00571"></a><span class="lineno"> 571</span> <span class="comment"> * @param x Random variate \f$ x \f$</span></div> |
| <div class="line"><a name="l00572"></a><span class="lineno"> 572</span> <span class="comment"> * @param shape Shape \f$ k > 0 \f$</span></div> |
| <div class="line"><a name="l00573"></a><span class="lineno"> 573</span> <span class="comment"> * @param scale Scale \f$ \theta > 0 \f$</span></div> |
| <div class="line"><a name="l00574"></a><span class="lineno"> 574</span> <span class="comment"> * @return \f$ f(x) \f$ where \f$ f \f$ is the probability density function of</span></div> |
| <div class="line"><a name="l00575"></a><span class="lineno"> 575</span> <span class="comment"> * a gamma distributed random variable with shape and scale parameters</span></div> |
| <div class="line"><a name="l00576"></a><span class="lineno"> 576</span> <span class="comment"> * \f$ k \f$ and \f$ \theta \f$, respectively</span></div> |
| <div class="line"><a name="l00577"></a><span class="lineno"> 577</span> <span class="comment"> */</span></div> |
| <div class="line"><a name="l00578"></a><span class="lineno"> 578</span> CREATE FUNCTION MADLIB_SCHEMA.gamma_pdf(</div> |
| <div class="line"><a name="l00579"></a><span class="lineno"> 579</span>  x DOUBLE PRECISION,</div> |
| <div class="line"><a name="l00580"></a><span class="lineno"> 580</span>  shape DOUBLE PRECISION,</div> |
| <div class="line"><a name="l00581"></a><span class="lineno"><a class="code" href="prob_8sql__in.html#ab6760b0486bad2f1ab0635eb59404e7c"> 581</a></span>  scale DOUBLE PRECISION</div> |
| <div class="line"><a name="l00582"></a><span class="lineno"> 582</span> ) RETURNS DOUBLE PRECISION</div> |
| <div class="line"><a name="l00583"></a><span class="lineno"> 583</span> AS 'MODULE_PATHNAME<span class="stringliteral">'</span></div> |
| <div class="line"><a name="l00584"></a><span class="lineno"> 584</span> <span class="stringliteral">LANGUAGE C</span></div> |
| <div class="line"><a name="l00585"></a><span class="lineno"> 585</span> <span class="stringliteral">IMMUTABLE STRICT;</span></div> |
| <div class="line"><a name="l00586"></a><span class="lineno"> 586</span> <span class="stringliteral"></span><span class="comment"></span></div> |
| <div class="line"><a name="l00587"></a><span class="lineno"> 587</span> <span class="comment">/**</span></div> |
| <div class="line"><a name="l00588"></a><span class="lineno"> 588</span> <span class="comment"> * @brief Gamma quantile function</span></div> |
| <div class="line"><a name="l00589"></a><span class="lineno"> 589</span> <span class="comment"> *</span></div> |
| <div class="line"><a name="l00590"></a><span class="lineno"> 590</span> <span class="comment"> * @param p Probability \f$ p \in [0,1] \f$</span></div> |
| <div class="line"><a name="l00591"></a><span class="lineno"> 591</span> <span class="comment"> * @param shape Shape \f$ k > 0 \f$</span></div> |
| <div class="line"><a name="l00592"></a><span class="lineno"> 592</span> <span class="comment"> * @param scale Scale \f$ \theta > 0 \f$</span></div> |
| <div class="line"><a name="l00593"></a><span class="lineno"> 593</span> <span class="comment"> * @return \f$ x \f$ such that \f$ p = \Pr[X \leq x] \f$ where \f$ X \f$ is</span></div> |
| <div class="line"><a name="l00594"></a><span class="lineno"> 594</span> <span class="comment"> * a gamma distributed random variable with shape and scale parameters</span></div> |
| <div class="line"><a name="l00595"></a><span class="lineno"> 595</span> <span class="comment"> * \f$ k \f$ and \f$ \theta \f$, respectively</span></div> |
| <div class="line"><a name="l00596"></a><span class="lineno"> 596</span> <span class="comment"> */</span></div> |
| <div class="line"><a name="l00597"></a><span class="lineno"> 597</span> CREATE FUNCTION MADLIB_SCHEMA.gamma_quantile(</div> |
| <div class="line"><a name="l00598"></a><span class="lineno"> 598</span>  p DOUBLE PRECISION,</div> |
| <div class="line"><a name="l00599"></a><span class="lineno"> 599</span>  shape DOUBLE PRECISION,</div> |
| <div class="line"><a name="l00600"></a><span class="lineno"><a class="code" href="prob_8sql__in.html#a6c37e3bda2596accbb46525321a328c4"> 600</a></span>  scale DOUBLE PRECISION</div> |
| <div class="line"><a name="l00601"></a><span class="lineno"> 601</span> ) RETURNS DOUBLE PRECISION</div> |
| <div class="line"><a name="l00602"></a><span class="lineno"> 602</span> AS 'MODULE_PATHNAME<span class="stringliteral">'</span></div> |
| <div class="line"><a name="l00603"></a><span class="lineno"> 603</span> <span class="stringliteral">LANGUAGE C</span></div> |
| <div class="line"><a name="l00604"></a><span class="lineno"> 604</span> <span class="stringliteral">IMMUTABLE STRICT;</span></div> |
| <div class="line"><a name="l00605"></a><span class="lineno"> 605</span> <span class="stringliteral"></span></div> |
| <div class="line"><a name="l00606"></a><span class="lineno"> 606</span> <span class="stringliteral"></span><span class="comment"></span></div> |
| <div class="line"><a name="l00607"></a><span class="lineno"> 607</span> <span class="comment">/**</span></div> |
| <div class="line"><a name="l00608"></a><span class="lineno"> 608</span> <span class="comment"> * @brief Geometric cumulative distribution function</span></div> |
| <div class="line"><a name="l00609"></a><span class="lineno"> 609</span> <span class="comment"> *</span></div> |
| <div class="line"><a name="l00610"></a><span class="lineno"> 610</span> <span class="comment"> * @param x Random variate \f$ x \f$</span></div> |
| <div class="line"><a name="l00611"></a><span class="lineno"> 611</span> <span class="comment"> * @param sp Success probability \f$ \mathit{sp} \in [0,1] \f$</span></div> |
| <div class="line"><a name="l00612"></a><span class="lineno"> 612</span> <span class="comment"> * @return \f$ \Pr[X \leq x] \f$ where \f$ X \f$ is a geometrically distributed</span></div> |
| <div class="line"><a name="l00613"></a><span class="lineno"> 613</span> <span class="comment"> * random variable with success probability \f$ \mathit{sp} \f$.</span></div> |
| <div class="line"><a name="l00614"></a><span class="lineno"> 614</span> <span class="comment"> */</span></div> |
| <div class="line"><a name="l00615"></a><span class="lineno"> 615</span> CREATE FUNCTION MADLIB_SCHEMA.geometric_cdf(</div> |
| <div class="line"><a name="l00616"></a><span class="lineno"> 616</span>  x DOUBLE PRECISION,</div> |
| <div class="line"><a name="l00617"></a><span class="lineno"> 617</span>  sp DOUBLE PRECISION</div> |
| <div class="line"><a name="l00618"></a><span class="lineno"> 618</span> ) RETURNS DOUBLE PRECISION</div> |
| <div class="line"><a name="l00619"></a><span class="lineno"><a class="code" href="prob_8sql__in.html#ac48bbd491bd34831415705c3a0b7bf29"> 619</a></span> AS 'MODULE_PATHNAME<span class="stringliteral">'</span></div> |
| <div class="line"><a name="l00620"></a><span class="lineno"> 620</span> <span class="stringliteral">LANGUAGE C</span></div> |
| <div class="line"><a name="l00621"></a><span class="lineno"> 621</span> <span class="stringliteral">IMMUTABLE STRICT;</span></div> |
| <div class="line"><a name="l00622"></a><span class="lineno"> 622</span> <span class="stringliteral"></span><span class="comment"></span></div> |
| <div class="line"><a name="l00623"></a><span class="lineno"> 623</span> <span class="comment">/**</span></div> |
| <div class="line"><a name="l00624"></a><span class="lineno"> 624</span> <span class="comment"> * @brief Geometric probability mass function</span></div> |
| <div class="line"><a name="l00625"></a><span class="lineno"> 625</span> <span class="comment"> *</span></div> |
| <div class="line"><a name="l00626"></a><span class="lineno"> 626</span> <span class="comment"> * @param x Random variate \f$ x \f$</span></div> |
| <div class="line"><a name="l00627"></a><span class="lineno"> 627</span> <span class="comment"> * @param sp Success probability \f$ \mathit{sp} \in [0,1] \f$</span></div> |
| <div class="line"><a name="l00628"></a><span class="lineno"> 628</span> <span class="comment"> * @return \f$ f(x) \f$ where \f$ f \f$ is the probability mass function of a</span></div> |
| <div class="line"><a name="l00629"></a><span class="lineno"> 629</span> <span class="comment"> * geometrically distributed random variable with success probability</span></div> |
| <div class="line"><a name="l00630"></a><span class="lineno"> 630</span> <span class="comment"> * \f$ \mathit{sp} \f$</span></div> |
| <div class="line"><a name="l00631"></a><span class="lineno"> 631</span> <span class="comment"> */</span></div> |
| <div class="line"><a name="l00632"></a><span class="lineno"> 632</span> CREATE FUNCTION MADLIB_SCHEMA.geometric_pmf(</div> |
| <div class="line"><a name="l00633"></a><span class="lineno"> 633</span>  x INT4,</div> |
| <div class="line"><a name="l00634"></a><span class="lineno"> 634</span>  sp DOUBLE PRECISION</div> |
| <div class="line"><a name="l00635"></a><span class="lineno"> 635</span> ) RETURNS DOUBLE PRECISION</div> |
| <div class="line"><a name="l00636"></a><span class="lineno"> 636</span> AS 'MODULE_PATHNAME<span class="stringliteral">'</span></div> |
| <div class="line"><a name="l00637"></a><span class="lineno"><a class="code" href="prob_8sql__in.html#a00879bdf7d48ceddedb3b4cc33511497"> 637</a></span> <span class="stringliteral">LANGUAGE C</span></div> |
| <div class="line"><a name="l00638"></a><span class="lineno"> 638</span> <span class="stringliteral">IMMUTABLE STRICT;</span></div> |
| <div class="line"><a name="l00639"></a><span class="lineno"> 639</span> <span class="stringliteral"></span><span class="comment"></span></div> |
| <div class="line"><a name="l00640"></a><span class="lineno"> 640</span> <span class="comment">/**</span></div> |
| <div class="line"><a name="l00641"></a><span class="lineno"> 641</span> <span class="comment"> * @brief Geometric quantile function</span></div> |
| <div class="line"><a name="l00642"></a><span class="lineno"> 642</span> <span class="comment"> *</span></div> |
| <div class="line"><a name="l00643"></a><span class="lineno"> 643</span> <span class="comment"> * @param p Probability \f$ p \in [0,1] \f$</span></div> |
| <div class="line"><a name="l00644"></a><span class="lineno"> 644</span> <span class="comment"> * @param sp Success probability \f$ \mathit{sp} \in [0,1] \f$</span></div> |
| <div class="line"><a name="l00645"></a><span class="lineno"> 645</span> <span class="comment"> * @return If \f$ p < 0.5 \f$ the maximum \f$ x \f$ such that</span></div> |
| <div class="line"><a name="l00646"></a><span class="lineno"> 646</span> <span class="comment"> * \f$ p \geq \Pr[X \leq x] \f$. If \f$ p \geq 0.5 \f$ the minimum \f$ x \f$</span></div> |
| <div class="line"><a name="l00647"></a><span class="lineno"> 647</span> <span class="comment"> * such that \f$ p \leq \Pr[X \leq x] \f$. Here, \f$ X \f$ is a</span></div> |
| <div class="line"><a name="l00648"></a><span class="lineno"> 648</span> <span class="comment"> * geometrically distributed random variable with success probability</span></div> |
| <div class="line"><a name="l00649"></a><span class="lineno"> 649</span> <span class="comment"> * \f$ \mathit{sp} \f$.</span></div> |
| <div class="line"><a name="l00650"></a><span class="lineno"> 650</span> <span class="comment"> */</span></div> |
| <div class="line"><a name="l00651"></a><span class="lineno"> 651</span> CREATE FUNCTION MADLIB_SCHEMA.geometric_quantile(</div> |
| <div class="line"><a name="l00652"></a><span class="lineno"> 652</span>  p DOUBLE PRECISION,</div> |
| <div class="line"><a name="l00653"></a><span class="lineno"> 653</span>  sp DOUBLE PRECISION</div> |
| <div class="line"><a name="l00654"></a><span class="lineno"><a class="code" href="prob_8sql__in.html#a5e08db93bd448a1e2164e106ce5781a4"> 654</a></span> ) RETURNS DOUBLE PRECISION</div> |
| <div class="line"><a name="l00655"></a><span class="lineno"> 655</span> AS 'MODULE_PATHNAME<span class="stringliteral">'</span></div> |
| <div class="line"><a name="l00656"></a><span class="lineno"> 656</span> <span class="stringliteral">LANGUAGE C</span></div> |
| <div class="line"><a name="l00657"></a><span class="lineno"> 657</span> <span class="stringliteral">IMMUTABLE STRICT;</span></div> |
| <div class="line"><a name="l00658"></a><span class="lineno"> 658</span> <span class="stringliteral"></span></div> |
| <div class="line"><a name="l00659"></a><span class="lineno"> 659</span> <span class="stringliteral"></span><span class="comment"></span></div> |
| <div class="line"><a name="l00660"></a><span class="lineno"> 660</span> <span class="comment">/**</span></div> |
| <div class="line"><a name="l00661"></a><span class="lineno"> 661</span> <span class="comment"> * @brief Hypergeometric cumulative distribution function</span></div> |
| <div class="line"><a name="l00662"></a><span class="lineno"> 662</span> <span class="comment"> *</span></div> |
| <div class="line"><a name="l00663"></a><span class="lineno"> 663</span> <span class="comment"> * @param x Random variate \f$ x \f$</span></div> |
| <div class="line"><a name="l00664"></a><span class="lineno"> 664</span> <span class="comment"> * @param r Number \f$ r \in \{ 0, 1, \dots, N \} \f$ of items with</span></div> |
| <div class="line"><a name="l00665"></a><span class="lineno"> 665</span> <span class="comment"> * distinct property (sometimes called the number of <em>success states</em></span></div> |
| <div class="line"><a name="l00666"></a><span class="lineno"> 666</span> <span class="comment"> * in population)</span></div> |
| <div class="line"><a name="l00667"></a><span class="lineno"> 667</span> <span class="comment"> * @param n Number \f$ n \in \{ 0, 1, \dots, N \} \f$ of draws (without</span></div> |
| <div class="line"><a name="l00668"></a><span class="lineno"> 668</span> <span class="comment"> * replacement)</span></div> |
| <div class="line"><a name="l00669"></a><span class="lineno"> 669</span> <span class="comment"> * @param N Total number \f$ N \in \mathbb N \f$ of items</span></div> |
| <div class="line"><a name="l00670"></a><span class="lineno"> 670</span> <span class="comment"> * @return \f$ \Pr[X \leq x] \f$ where \f$ X \f$ is a hypergeometrically</span></div> |
| <div class="line"><a name="l00671"></a><span class="lineno"> 671</span> <span class="comment"> * distributed random variable with parameters \f$ r, n, N \f$</span></div> |
| <div class="line"><a name="l00672"></a><span class="lineno"> 672</span> <span class="comment"> *</span></div> |
| <div class="line"><a name="l00673"></a><span class="lineno"><a class="code" href="prob_8sql__in.html#a62674ca958aec0533cdf0a74a1dadea9"> 673</a></span> <span class="comment"> * @internal Boost error messages refer to parameters 'r', 'n', 'N', so for now</span></div> |
| <div class="line"><a name="l00674"></a><span class="lineno"> 674</span> <span class="comment"> * we use the same identifiers for our function definition.</span></div> |
| <div class="line"><a name="l00675"></a><span class="lineno"> 675</span> <span class="comment"> */</span></div> |
| <div class="line"><a name="l00676"></a><span class="lineno"> 676</span> CREATE FUNCTION MADLIB_SCHEMA.hypergeometric_cdf(</div> |
| <div class="line"><a name="l00677"></a><span class="lineno"> 677</span>  x DOUBLE PRECISION,</div> |
| <div class="line"><a name="l00678"></a><span class="lineno"> 678</span>  r INT4,</div> |
| <div class="line"><a name="l00679"></a><span class="lineno"> 679</span>  n INT4,</div> |
| <div class="line"><a name="l00680"></a><span class="lineno"> 680</span>  "N" INT4</div> |
| <div class="line"><a name="l00681"></a><span class="lineno"> 681</span> ) RETURNS DOUBLE PRECISION</div> |
| <div class="line"><a name="l00682"></a><span class="lineno"> 682</span> AS 'MODULE_PATHNAME<span class="stringliteral">'</span></div> |
| <div class="line"><a name="l00683"></a><span class="lineno"> 683</span> <span class="stringliteral">LANGUAGE C</span></div> |
| <div class="line"><a name="l00684"></a><span class="lineno"> 684</span> <span class="stringliteral">IMMUTABLE STRICT;</span></div> |
| <div class="line"><a name="l00685"></a><span class="lineno"> 685</span> <span class="stringliteral"></span><span class="comment"></span></div> |
| <div class="line"><a name="l00686"></a><span class="lineno"> 686</span> <span class="comment">/**</span></div> |
| <div class="line"><a name="l00687"></a><span class="lineno"> 687</span> <span class="comment"> * @brief Hypergeometric probability mass function</span></div> |
| <div class="line"><a name="l00688"></a><span class="lineno"> 688</span> <span class="comment"> *</span></div> |
| <div class="line"><a name="l00689"></a><span class="lineno"> 689</span> <span class="comment"> * @param x Random variate \f$ x \f$</span></div> |
| <div class="line"><a name="l00690"></a><span class="lineno"> 690</span> <span class="comment"> * @param r Number \f$ r \in \{ 0, 1, \dots, N \} \f$ of items with</span></div> |
| <div class="line"><a name="l00691"></a><span class="lineno"> 691</span> <span class="comment"> * distinct property (sometimes called the number of <em>success states</em></span></div> |
| <div class="line"><a name="l00692"></a><span class="lineno"> 692</span> <span class="comment"> * in population)</span></div> |
| <div class="line"><a name="l00693"></a><span class="lineno"> 693</span> <span class="comment"> * @param n Number \f$ n \in \{ 0, 1, \dots, N \} \f$ of draws (without</span></div> |
| <div class="line"><a name="l00694"></a><span class="lineno"> 694</span> <span class="comment"> * replacement)</span></div> |
| <div class="line"><a name="l00695"></a><span class="lineno"> 695</span> <span class="comment"> * @param N Total number \f$ N \in \mathbb N \f$ of items</span></div> |
| <div class="line"><a name="l00696"></a><span class="lineno"> 696</span> <span class="comment"> * @return \f$ f(x) \f$ where \f$ f \f$ is the probability mass function of</span></div> |
| <div class="line"><a name="l00697"></a><span class="lineno"> 697</span> <span class="comment"> * a hypergeometrically distributed random variable with parameters</span></div> |
| <div class="line"><a name="l00698"></a><span class="lineno"><a class="code" href="prob_8sql__in.html#a5c48e7fa2fc7bcbc69c7f4da663d457f"> 698</a></span> <span class="comment"> * \f$ r, n, N \f$</span></div> |
| <div class="line"><a name="l00699"></a><span class="lineno"> 699</span> <span class="comment"> */</span></div> |
| <div class="line"><a name="l00700"></a><span class="lineno"> 700</span> CREATE FUNCTION MADLIB_SCHEMA.hypergeometric_pmf(</div> |
| <div class="line"><a name="l00701"></a><span class="lineno"> 701</span>  x INT4,</div> |
| <div class="line"><a name="l00702"></a><span class="lineno"> 702</span>  r INT4,</div> |
| <div class="line"><a name="l00703"></a><span class="lineno"> 703</span>  n INT4,</div> |
| <div class="line"><a name="l00704"></a><span class="lineno"> 704</span>  "N" INT4</div> |
| <div class="line"><a name="l00705"></a><span class="lineno"> 705</span> ) RETURNS DOUBLE PRECISION</div> |
| <div class="line"><a name="l00706"></a><span class="lineno"> 706</span> AS 'MODULE_PATHNAME<span class="stringliteral">'</span></div> |
| <div class="line"><a name="l00707"></a><span class="lineno"> 707</span> <span class="stringliteral">LANGUAGE C</span></div> |
| <div class="line"><a name="l00708"></a><span class="lineno"> 708</span> <span class="stringliteral">IMMUTABLE STRICT;</span></div> |
| <div class="line"><a name="l00709"></a><span class="lineno"> 709</span> <span class="stringliteral"></span></div> |
| <div class="line"><a name="l00710"></a><span class="lineno"> 710</span> <span class="stringliteral"></span><span class="comment"></span></div> |
| <div class="line"><a name="l00711"></a><span class="lineno"> 711</span> <span class="comment">/**</span></div> |
| <div class="line"><a name="l00712"></a><span class="lineno"> 712</span> <span class="comment"> * @brief Hypergeometric quantile function</span></div> |
| <div class="line"><a name="l00713"></a><span class="lineno"> 713</span> <span class="comment"> *</span></div> |
| <div class="line"><a name="l00714"></a><span class="lineno"> 714</span> <span class="comment"> * @param p Probability \f$ p \in [0,1] \f$</span></div> |
| <div class="line"><a name="l00715"></a><span class="lineno"> 715</span> <span class="comment"> * @param r Number \f$ r \in \{ 0, 1, \dots, N \} \f$ of items with</span></div> |
| <div class="line"><a name="l00716"></a><span class="lineno"> 716</span> <span class="comment"> * distinct property (sometimes called the number of <em>success states</em></span></div> |
| <div class="line"><a name="l00717"></a><span class="lineno"> 717</span> <span class="comment"> * in population)</span></div> |
| <div class="line"><a name="l00718"></a><span class="lineno"> 718</span> <span class="comment"> * @param n Number \f$ n \in \{ 0, 1, \dots, N \} \f$ of draws (without</span></div> |
| <div class="line"><a name="l00719"></a><span class="lineno"> 719</span> <span class="comment"> * replacement)</span></div> |
| <div class="line"><a name="l00720"></a><span class="lineno"> 720</span> <span class="comment"> * @param N Total number \f$ N \in \mathbb N \f$ of items</span></div> |
| <div class="line"><a name="l00721"></a><span class="lineno"> 721</span> <span class="comment"> * @return \f$ x \f$ such that \f$ p = \Pr[X \leq x] \f$ where \f$ X \f$ is</span></div> |
| <div class="line"><a name="l00722"></a><span class="lineno"><a class="code" href="prob_8sql__in.html#afbd2f8d9fb30fb179f59cc14f1fd8d6d"> 722</a></span> <span class="comment"> * a hypergeometrically distributed random variable with parameters</span></div> |
| <div class="line"><a name="l00723"></a><span class="lineno"> 723</span> <span class="comment"> * \f$ r, n, N \f$</span></div> |
| <div class="line"><a name="l00724"></a><span class="lineno"> 724</span> <span class="comment"> */</span></div> |
| <div class="line"><a name="l00725"></a><span class="lineno"> 725</span> CREATE FUNCTION MADLIB_SCHEMA.hypergeometric_quantile(</div> |
| <div class="line"><a name="l00726"></a><span class="lineno"> 726</span>  p DOUBLE PRECISION,</div> |
| <div class="line"><a name="l00727"></a><span class="lineno"> 727</span>  r INT4,</div> |
| <div class="line"><a name="l00728"></a><span class="lineno"> 728</span>  n INT4,</div> |
| <div class="line"><a name="l00729"></a><span class="lineno"> 729</span>  "N" INT4</div> |
| <div class="line"><a name="l00730"></a><span class="lineno"> 730</span> ) RETURNS DOUBLE PRECISION</div> |
| <div class="line"><a name="l00731"></a><span class="lineno"> 731</span> AS 'MODULE_PATHNAME<span class="stringliteral">'</span></div> |
| <div class="line"><a name="l00732"></a><span class="lineno"> 732</span> <span class="stringliteral">LANGUAGE C</span></div> |
| <div class="line"><a name="l00733"></a><span class="lineno"> 733</span> <span class="stringliteral">IMMUTABLE STRICT;</span></div> |
| <div class="line"><a name="l00734"></a><span class="lineno"> 734</span> <span class="stringliteral"></span></div> |
| <div class="line"><a name="l00735"></a><span class="lineno"> 735</span> <span class="stringliteral"></span><span class="comment"></span></div> |
| <div class="line"><a name="l00736"></a><span class="lineno"> 736</span> <span class="comment">/**</span></div> |
| <div class="line"><a name="l00737"></a><span class="lineno"> 737</span> <span class="comment"> * @brief Inverse Gamma cumulative distribution function</span></div> |
| <div class="line"><a name="l00738"></a><span class="lineno"> 738</span> <span class="comment"> *</span></div> |
| <div class="line"><a name="l00739"></a><span class="lineno"> 739</span> <span class="comment"> * @param x Random variate \f$ x \f$</span></div> |
| <div class="line"><a name="l00740"></a><span class="lineno"> 740</span> <span class="comment"> * @param shape Shape \f$ \alpha > 0 \f$</span></div> |
| <div class="line"><a name="l00741"></a><span class="lineno"> 741</span> <span class="comment"> * @param scale Scale \f$ \beta > 0 \f$</span></div> |
| <div class="line"><a name="l00742"></a><span class="lineno"> 742</span> <span class="comment"> * @return \f$ \Pr[X \leq x] \f$ where \f$ X \f$ is an inverse-gamma distributed</span></div> |
| <div class="line"><a name="l00743"></a><span class="lineno"> 743</span> <span class="comment"> * random variable with shape and scale parameters \f$ \alpha \f$ and</span></div> |
| <div class="line"><a name="l00744"></a><span class="lineno"> 744</span> <span class="comment"> * \f$ \beta \f$, respectively</span></div> |
| <div class="line"><a name="l00745"></a><span class="lineno"> 745</span> <span class="comment"> */</span></div> |
| <div class="line"><a name="l00746"></a><span class="lineno"> 746</span> CREATE FUNCTION MADLIB_SCHEMA.inverse_gamma_cdf(</div> |
| <div class="line"><a name="l00747"></a><span class="lineno"><a class="code" href="prob_8sql__in.html#a813cc27fe097e797ed0fb6022c7bb79a"> 747</a></span>  x DOUBLE PRECISION,</div> |
| <div class="line"><a name="l00748"></a><span class="lineno"> 748</span>  shape DOUBLE PRECISION,</div> |
| <div class="line"><a name="l00749"></a><span class="lineno"> 749</span>  scale DOUBLE PRECISION</div> |
| <div class="line"><a name="l00750"></a><span class="lineno"> 750</span> ) RETURNS DOUBLE PRECISION</div> |
| <div class="line"><a name="l00751"></a><span class="lineno"> 751</span> AS 'MODULE_PATHNAME<span class="stringliteral">'</span></div> |
| <div class="line"><a name="l00752"></a><span class="lineno"> 752</span> <span class="stringliteral">LANGUAGE C</span></div> |
| <div class="line"><a name="l00753"></a><span class="lineno"> 753</span> <span class="stringliteral">IMMUTABLE STRICT;</span></div> |
| <div class="line"><a name="l00754"></a><span class="lineno"> 754</span> <span class="stringliteral"></span><span class="comment"></span></div> |
| <div class="line"><a name="l00755"></a><span class="lineno"> 755</span> <span class="comment">/**</span></div> |
| <div class="line"><a name="l00756"></a><span class="lineno"> 756</span> <span class="comment"> * @brief Inverse Gamma probability density function</span></div> |
| <div class="line"><a name="l00757"></a><span class="lineno"> 757</span> <span class="comment"> *</span></div> |
| <div class="line"><a name="l00758"></a><span class="lineno"> 758</span> <span class="comment"> * @param x Random variate \f$ x \f$</span></div> |
| <div class="line"><a name="l00759"></a><span class="lineno"> 759</span> <span class="comment"> * @param shape Shape \f$ \alpha > 0 \f$</span></div> |
| <div class="line"><a name="l00760"></a><span class="lineno"> 760</span> <span class="comment"> * @param scale Scale \f$ \beta > 0 \f$</span></div> |
| <div class="line"><a name="l00761"></a><span class="lineno"> 761</span> <span class="comment"> * @return \f$ f(x) \f$ where \f$ f \f$ is the probability density function of</span></div> |
| <div class="line"><a name="l00762"></a><span class="lineno"> 762</span> <span class="comment"> * an inverse-gamma distributed random variable with shape and scale</span></div> |
| <div class="line"><a name="l00763"></a><span class="lineno"> 763</span> <span class="comment"> * parameters \f$ \alpha \f$ and \f$ \beta \f$, respectively</span></div> |
| <div class="line"><a name="l00764"></a><span class="lineno"> 764</span> <span class="comment"> */</span></div> |
| <div class="line"><a name="l00765"></a><span class="lineno"> 765</span> CREATE FUNCTION MADLIB_SCHEMA.inverse_gamma_pdf(</div> |
| <div class="line"><a name="l00766"></a><span class="lineno"> 766</span>  x DOUBLE PRECISION,</div> |
| <div class="line"><a name="l00767"></a><span class="lineno"> 767</span>  shape DOUBLE PRECISION,</div> |
| <div class="line"><a name="l00768"></a><span class="lineno"><a class="code" href="prob_8sql__in.html#a85e9c16aa2c6973ddeb7883a5f153d93"> 768</a></span>  scale DOUBLE PRECISION</div> |
| <div class="line"><a name="l00769"></a><span class="lineno"> 769</span> ) RETURNS DOUBLE PRECISION</div> |
| <div class="line"><a name="l00770"></a><span class="lineno"> 770</span> AS 'MODULE_PATHNAME<span class="stringliteral">'</span></div> |
| <div class="line"><a name="l00771"></a><span class="lineno"> 771</span> <span class="stringliteral">LANGUAGE C</span></div> |
| <div class="line"><a name="l00772"></a><span class="lineno"> 772</span> <span class="stringliteral">IMMUTABLE STRICT;</span></div> |
| <div class="line"><a name="l00773"></a><span class="lineno"> 773</span> <span class="stringliteral"></span><span class="comment"></span></div> |
| <div class="line"><a name="l00774"></a><span class="lineno"> 774</span> <span class="comment">/**</span></div> |
| <div class="line"><a name="l00775"></a><span class="lineno"> 775</span> <span class="comment"> * @brief Inverse Gamma quantile function</span></div> |
| <div class="line"><a name="l00776"></a><span class="lineno"> 776</span> <span class="comment"> *</span></div> |
| <div class="line"><a name="l00777"></a><span class="lineno"> 777</span> <span class="comment"> * @param p Probability \f$ p \in [0,1] \f$</span></div> |
| <div class="line"><a name="l00778"></a><span class="lineno"> 778</span> <span class="comment"> * @param shape Shape \f$ \alpha > 0 \f$</span></div> |
| <div class="line"><a name="l00779"></a><span class="lineno"> 779</span> <span class="comment"> * @param scale Scale \f$ \beta > 0 \f$</span></div> |
| <div class="line"><a name="l00780"></a><span class="lineno"> 780</span> <span class="comment"> * @return \f$ x \f$ such that \f$ p = \Pr[X \leq x] \f$ where \f$ X \f$ is</span></div> |
| <div class="line"><a name="l00781"></a><span class="lineno"> 781</span> <span class="comment"> * an inverse-gamma distributed random variable with shape and scale</span></div> |
| <div class="line"><a name="l00782"></a><span class="lineno"> 782</span> <span class="comment"> * parameters \f$ \alpha \f$ and \f$ \beta \f$, respectively</span></div> |
| <div class="line"><a name="l00783"></a><span class="lineno"> 783</span> <span class="comment"> */</span></div> |
| <div class="line"><a name="l00784"></a><span class="lineno"> 784</span> CREATE FUNCTION MADLIB_SCHEMA.inverse_gamma_quantile(</div> |
| <div class="line"><a name="l00785"></a><span class="lineno"> 785</span>  p DOUBLE PRECISION,</div> |
| <div class="line"><a name="l00786"></a><span class="lineno"> 786</span>  shape DOUBLE PRECISION,</div> |
| <div class="line"><a name="l00787"></a><span class="lineno"><a class="code" href="prob_8sql__in.html#a126211c2172a43a654288fa72a2349f9"> 787</a></span>  scale DOUBLE PRECISION</div> |
| <div class="line"><a name="l00788"></a><span class="lineno"> 788</span> ) RETURNS DOUBLE PRECISION</div> |
| <div class="line"><a name="l00789"></a><span class="lineno"> 789</span> AS 'MODULE_PATHNAME<span class="stringliteral">'</span></div> |
| <div class="line"><a name="l00790"></a><span class="lineno"> 790</span> <span class="stringliteral">LANGUAGE C</span></div> |
| <div class="line"><a name="l00791"></a><span class="lineno"> 791</span> <span class="stringliteral">IMMUTABLE STRICT;</span></div> |
| <div class="line"><a name="l00792"></a><span class="lineno"> 792</span> <span class="stringliteral"></span></div> |
| <div class="line"><a name="l00793"></a><span class="lineno"> 793</span> <span class="stringliteral"></span><span class="comment"></span></div> |
| <div class="line"><a name="l00794"></a><span class="lineno"> 794</span> <span class="comment">/**</span></div> |
| <div class="line"><a name="l00795"></a><span class="lineno"> 795</span> <span class="comment"> * @brief Kolmogorov cumulative distribution function</span></div> |
| <div class="line"><a name="l00796"></a><span class="lineno"> 796</span> <span class="comment"> *</span></div> |
| <div class="line"><a name="l00797"></a><span class="lineno"> 797</span> <span class="comment"> * @param x Random variate \f$ x \f$</span></div> |
| <div class="line"><a name="l00798"></a><span class="lineno"> 798</span> <span class="comment"> * @return \f$ \Pr[X \leq x] \f$ where \f$ X \f$ is a Kolmogorov distributed</span></div> |
| <div class="line"><a name="l00799"></a><span class="lineno"> 799</span> <span class="comment"> * random variable</span></div> |
| <div class="line"><a name="l00800"></a><span class="lineno"> 800</span> <span class="comment"> *</span></div> |
| <div class="line"><a name="l00801"></a><span class="lineno"> 801</span> <span class="comment"> * @sa Kolmogorov-Smirnov test: ks_test()</span></div> |
| <div class="line"><a name="l00802"></a><span class="lineno"> 802</span> <span class="comment"> */</span></div> |
| <div class="line"><a name="l00803"></a><span class="lineno"> 803</span> CREATE FUNCTION MADLIB_SCHEMA.kolmogorov_cdf(</div> |
| <div class="line"><a name="l00804"></a><span class="lineno"> 804</span>  x DOUBLE PRECISION</div> |
| <div class="line"><a name="l00805"></a><span class="lineno"> 805</span> ) RETURNS DOUBLE PRECISION</div> |
| <div class="line"><a name="l00806"></a><span class="lineno"><a class="code" href="prob_8sql__in.html#a5876aae01f14729866d4fd52918a65ba"> 806</a></span> AS 'MODULE_PATHNAME<span class="stringliteral">'</span></div> |
| <div class="line"><a name="l00807"></a><span class="lineno"> 807</span> <span class="stringliteral">LANGUAGE C</span></div> |
| <div class="line"><a name="l00808"></a><span class="lineno"> 808</span> <span class="stringliteral">IMMUTABLE STRICT;</span></div> |
| <div class="line"><a name="l00809"></a><span class="lineno"> 809</span> <span class="stringliteral"></span></div> |
| <div class="line"><a name="l00810"></a><span class="lineno"> 810</span> <span class="stringliteral"></span><span class="comment"></span></div> |
| <div class="line"><a name="l00811"></a><span class="lineno"> 811</span> <span class="comment">/**</span></div> |
| <div class="line"><a name="l00812"></a><span class="lineno"> 812</span> <span class="comment"> * @brief Laplace cumulative distribution function</span></div> |
| <div class="line"><a name="l00813"></a><span class="lineno"> 813</span> <span class="comment"> *</span></div> |
| <div class="line"><a name="l00814"></a><span class="lineno"> 814</span> <span class="comment"> * @param x Random variate \f$ x \f$</span></div> |
| <div class="line"><a name="l00815"></a><span class="lineno"> 815</span> <span class="comment"> * @param mean Mean \f$ \mu \f$</span></div> |
| <div class="line"><a name="l00816"></a><span class="lineno"> 816</span> <span class="comment"> * @param scale Scale \f$ b > 0 \f$</span></div> |
| <div class="line"><a name="l00817"></a><span class="lineno"> 817</span> <span class="comment"> * @return \f$ \Pr[X \leq x] \f$ where \f$ X \f$ is a Laplace-distributed random</span></div> |
| <div class="line"><a name="l00818"></a><span class="lineno"> 818</span> <span class="comment"> * variable with mean \f$ \mu \f$ and variance \f$ 2 b^2 \f$</span></div> |
| <div class="line"><a name="l00819"></a><span class="lineno"> 819</span> <span class="comment"> */</span></div> |
| <div class="line"><a name="l00820"></a><span class="lineno"> 820</span> CREATE FUNCTION MADLIB_SCHEMA.laplace_cdf(</div> |
| <div class="line"><a name="l00821"></a><span class="lineno"> 821</span>  x DOUBLE PRECISION,</div> |
| <div class="line"><a name="l00822"></a><span class="lineno"> 822</span>  mean DOUBLE PRECISION,</div> |
| <div class="line"><a name="l00823"></a><span class="lineno"> 823</span>  scale DOUBLE PRECISION</div> |
| <div class="line"><a name="l00824"></a><span class="lineno"> 824</span> ) RETURNS DOUBLE PRECISION</div> |
| <div class="line"><a name="l00825"></a><span class="lineno"><a class="code" href="prob_8sql__in.html#aeef43f74f583bdff17bd074d9c0d9607"> 825</a></span> AS 'MODULE_PATHNAME<span class="stringliteral">'</span></div> |
| <div class="line"><a name="l00826"></a><span class="lineno"> 826</span> <span class="stringliteral">LANGUAGE C</span></div> |
| <div class="line"><a name="l00827"></a><span class="lineno"> 827</span> <span class="stringliteral">IMMUTABLE STRICT;</span></div> |
| <div class="line"><a name="l00828"></a><span class="lineno"> 828</span> <span class="stringliteral"></span><span class="comment"></span></div> |
| <div class="line"><a name="l00829"></a><span class="lineno"> 829</span> <span class="comment">/**</span></div> |
| <div class="line"><a name="l00830"></a><span class="lineno"> 830</span> <span class="comment"> * @brief Laplace probability density function</span></div> |
| <div class="line"><a name="l00831"></a><span class="lineno"> 831</span> <span class="comment"> *</span></div> |
| <div class="line"><a name="l00832"></a><span class="lineno"> 832</span> <span class="comment"> * @param x Random variate \f$ x \f$</span></div> |
| <div class="line"><a name="l00833"></a><span class="lineno"> 833</span> <span class="comment"> * @param mean Mean \f$ \mu \f$</span></div> |
| <div class="line"><a name="l00834"></a><span class="lineno"> 834</span> <span class="comment"> * @param scale Scale \f$ b > 0 \f$</span></div> |
| <div class="line"><a name="l00835"></a><span class="lineno"> 835</span> <span class="comment"> * @return \f$ f(x) \f$ where \f$ f \f$ is the probability density function of</span></div> |
| <div class="line"><a name="l00836"></a><span class="lineno"> 836</span> <span class="comment"> * a Laplace-distributed random variable with mean \f$ \mu \f$ and variance</span></div> |
| <div class="line"><a name="l00837"></a><span class="lineno"> 837</span> <span class="comment"> * \f$ 2 b^2 \f$</span></div> |
| <div class="line"><a name="l00838"></a><span class="lineno"> 838</span> <span class="comment"> */</span></div> |
| <div class="line"><a name="l00839"></a><span class="lineno"> 839</span> CREATE FUNCTION MADLIB_SCHEMA.laplace_pdf(</div> |
| <div class="line"><a name="l00840"></a><span class="lineno"> 840</span>  x DOUBLE PRECISION,</div> |
| <div class="line"><a name="l00841"></a><span class="lineno"> 841</span>  mean DOUBLE PRECISION,</div> |
| <div class="line"><a name="l00842"></a><span class="lineno"><a class="code" href="prob_8sql__in.html#a64e197de8da3761acdeec9db7e211703"> 842</a></span>  scale DOUBLE PRECISION</div> |
| <div class="line"><a name="l00843"></a><span class="lineno"> 843</span> ) RETURNS DOUBLE PRECISION</div> |
| <div class="line"><a name="l00844"></a><span class="lineno"> 844</span> AS 'MODULE_PATHNAME<span class="stringliteral">'</span></div> |
| <div class="line"><a name="l00845"></a><span class="lineno"> 845</span> <span class="stringliteral">LANGUAGE C</span></div> |
| <div class="line"><a name="l00846"></a><span class="lineno"> 846</span> <span class="stringliteral">IMMUTABLE STRICT;</span></div> |
| <div class="line"><a name="l00847"></a><span class="lineno"> 847</span> <span class="stringliteral"></span><span class="comment"></span></div> |
| <div class="line"><a name="l00848"></a><span class="lineno"> 848</span> <span class="comment">/**</span></div> |
| <div class="line"><a name="l00849"></a><span class="lineno"> 849</span> <span class="comment"> * @brief Laplace quantile function</span></div> |
| <div class="line"><a name="l00850"></a><span class="lineno"> 850</span> <span class="comment"> *</span></div> |
| <div class="line"><a name="l00851"></a><span class="lineno"> 851</span> <span class="comment"> * @param p Probability \f$ p \in [0,1] \f$</span></div> |
| <div class="line"><a name="l00852"></a><span class="lineno"> 852</span> <span class="comment"> * @param mean Mean \f$ \mu \f$</span></div> |
| <div class="line"><a name="l00853"></a><span class="lineno"> 853</span> <span class="comment"> * @param scale Scale \f$ b > 0 \f$</span></div> |
| <div class="line"><a name="l00854"></a><span class="lineno"> 854</span> <span class="comment"> * @return \f$ x \f$ such that \f$ p = \Pr[X \leq x] \f$ where \f$ X \f$ is a</span></div> |
| <div class="line"><a name="l00855"></a><span class="lineno"> 855</span> <span class="comment"> * Laplace-distributed random variable with mean \f$ \mu \f$ and variance</span></div> |
| <div class="line"><a name="l00856"></a><span class="lineno"> 856</span> <span class="comment"> * \f$ 2 b^2 \f$</span></div> |
| <div class="line"><a name="l00857"></a><span class="lineno"> 857</span> <span class="comment"> */</span></div> |
| <div class="line"><a name="l00858"></a><span class="lineno"> 858</span> CREATE FUNCTION MADLIB_SCHEMA.laplace_quantile(</div> |
| <div class="line"><a name="l00859"></a><span class="lineno"> 859</span>  p DOUBLE PRECISION,</div> |
| <div class="line"><a name="l00860"></a><span class="lineno"> 860</span>  mean DOUBLE PRECISION,</div> |
| <div class="line"><a name="l00861"></a><span class="lineno"><a class="code" href="prob_8sql__in.html#a750278ad29d514793f76e159b773f410"> 861</a></span>  scale DOUBLE PRECISION</div> |
| <div class="line"><a name="l00862"></a><span class="lineno"> 862</span> ) RETURNS DOUBLE PRECISION</div> |
| <div class="line"><a name="l00863"></a><span class="lineno"> 863</span> AS 'MODULE_PATHNAME<span class="stringliteral">'</span></div> |
| <div class="line"><a name="l00864"></a><span class="lineno"> 864</span> <span class="stringliteral">LANGUAGE C</span></div> |
| <div class="line"><a name="l00865"></a><span class="lineno"> 865</span> <span class="stringliteral">IMMUTABLE STRICT;</span></div> |
| <div class="line"><a name="l00866"></a><span class="lineno"> 866</span> <span class="stringliteral"></span></div> |
| <div class="line"><a name="l00867"></a><span class="lineno"> 867</span> <span class="stringliteral"></span><span class="comment"></span></div> |
| <div class="line"><a name="l00868"></a><span class="lineno"> 868</span> <span class="comment">/**</span></div> |
| <div class="line"><a name="l00869"></a><span class="lineno"> 869</span> <span class="comment"> * @brief Logistic cumulative distribution function</span></div> |
| <div class="line"><a name="l00870"></a><span class="lineno"> 870</span> <span class="comment"> *</span></div> |
| <div class="line"><a name="l00871"></a><span class="lineno"> 871</span> <span class="comment"> * @param x Random variate \f$ x \f$</span></div> |
| <div class="line"><a name="l00872"></a><span class="lineno"> 872</span> <span class="comment"> * @param mean Mean \f$ \mu \f$</span></div> |
| <div class="line"><a name="l00873"></a><span class="lineno"> 873</span> <span class="comment"> * @param scale Scale \f$ s > 0 \f$</span></div> |
| <div class="line"><a name="l00874"></a><span class="lineno"> 874</span> <span class="comment"> * @return \f$ \Pr[X \leq x] \f$ where \f$ X \f$ is a logistically distributed</span></div> |
| <div class="line"><a name="l00875"></a><span class="lineno"> 875</span> <span class="comment"> * random variable with mean \f$ \mu \f$ and scale parameter \f$ s \f$</span></div> |
| <div class="line"><a name="l00876"></a><span class="lineno"> 876</span> <span class="comment"> */</span></div> |
| <div class="line"><a name="l00877"></a><span class="lineno"> 877</span> CREATE FUNCTION MADLIB_SCHEMA.logistic_cdf(</div> |
| <div class="line"><a name="l00878"></a><span class="lineno"> 878</span>  x DOUBLE PRECISION,</div> |
| <div class="line"><a name="l00879"></a><span class="lineno"> 879</span>  mean DOUBLE PRECISION,</div> |
| <div class="line"><a name="l00880"></a><span class="lineno"><a class="code" href="prob_8sql__in.html#a77f94fc43d4777fc4f68d18e29454a81"> 880</a></span>  scale DOUBLE PRECISION</div> |
| <div class="line"><a name="l00881"></a><span class="lineno"> 881</span> ) RETURNS DOUBLE PRECISION</div> |
| <div class="line"><a name="l00882"></a><span class="lineno"> 882</span> AS 'MODULE_PATHNAME<span class="stringliteral">'</span></div> |
| <div class="line"><a name="l00883"></a><span class="lineno"> 883</span> <span class="stringliteral">LANGUAGE C</span></div> |
| <div class="line"><a name="l00884"></a><span class="lineno"> 884</span> <span class="stringliteral">IMMUTABLE STRICT;</span></div> |
| <div class="line"><a name="l00885"></a><span class="lineno"> 885</span> <span class="stringliteral"></span><span class="comment"></span></div> |
| <div class="line"><a name="l00886"></a><span class="lineno"> 886</span> <span class="comment">/**</span></div> |
| <div class="line"><a name="l00887"></a><span class="lineno"> 887</span> <span class="comment"> * @brief Logistic probability density function</span></div> |
| <div class="line"><a name="l00888"></a><span class="lineno"> 888</span> <span class="comment"> *</span></div> |
| <div class="line"><a name="l00889"></a><span class="lineno"> 889</span> <span class="comment"> * @param x Random variate \f$ x \f$</span></div> |
| <div class="line"><a name="l00890"></a><span class="lineno"> 890</span> <span class="comment"> * @param mean Mean \f$ \mu \f$</span></div> |
| <div class="line"><a name="l00891"></a><span class="lineno"> 891</span> <span class="comment"> * @param scale Scale \f$ s > 0 \f$</span></div> |
| <div class="line"><a name="l00892"></a><span class="lineno"> 892</span> <span class="comment"> * @return \f$ f(x) \f$ where \f$ f \f$ is the probability density function of</span></div> |
| <div class="line"><a name="l00893"></a><span class="lineno"> 893</span> <span class="comment"> * a logistically distributed random variable with mean \f$ \mu \f$ and</span></div> |
| <div class="line"><a name="l00894"></a><span class="lineno"> 894</span> <span class="comment"> * scale parameter \f$ s \f$</span></div> |
| <div class="line"><a name="l00895"></a><span class="lineno"> 895</span> <span class="comment"> */</span></div> |
| <div class="line"><a name="l00896"></a><span class="lineno"> 896</span> CREATE FUNCTION MADLIB_SCHEMA.logistic_pdf(</div> |
| <div class="line"><a name="l00897"></a><span class="lineno"> 897</span>  x DOUBLE PRECISION,</div> |
| <div class="line"><a name="l00898"></a><span class="lineno"> 898</span>  mean DOUBLE PRECISION,</div> |
| <div class="line"><a name="l00899"></a><span class="lineno"><a class="code" href="prob_8sql__in.html#a140f674876813d5e786a4d8ba8d75c87"> 899</a></span>  scale DOUBLE PRECISION</div> |
| <div class="line"><a name="l00900"></a><span class="lineno"> 900</span> ) RETURNS DOUBLE PRECISION</div> |
| <div class="line"><a name="l00901"></a><span class="lineno"> 901</span> AS 'MODULE_PATHNAME<span class="stringliteral">'</span></div> |
| <div class="line"><a name="l00902"></a><span class="lineno"> 902</span> <span class="stringliteral">LANGUAGE C</span></div> |
| <div class="line"><a name="l00903"></a><span class="lineno"> 903</span> <span class="stringliteral">IMMUTABLE STRICT;</span></div> |
| <div class="line"><a name="l00904"></a><span class="lineno"> 904</span> <span class="stringliteral"></span><span class="comment"></span></div> |
| <div class="line"><a name="l00905"></a><span class="lineno"> 905</span> <span class="comment">/**</span></div> |
| <div class="line"><a name="l00906"></a><span class="lineno"> 906</span> <span class="comment"> * @brief Logistic quantile function</span></div> |
| <div class="line"><a name="l00907"></a><span class="lineno"> 907</span> <span class="comment"> *</span></div> |
| <div class="line"><a name="l00908"></a><span class="lineno"> 908</span> <span class="comment"> * @param p Probability \f$ p \in [0,1] \f$</span></div> |
| <div class="line"><a name="l00909"></a><span class="lineno"> 909</span> <span class="comment"> * @param mean Mean \f$ \mu \f$</span></div> |
| <div class="line"><a name="l00910"></a><span class="lineno"> 910</span> <span class="comment"> * @param scale Scale \f$ s > 0 \f$</span></div> |
| <div class="line"><a name="l00911"></a><span class="lineno"> 911</span> <span class="comment"> * @return \f$ x \f$ such that \f$ p = \Pr[X \leq x] \f$ where \f$ X \f$ is</span></div> |
| <div class="line"><a name="l00912"></a><span class="lineno"> 912</span> <span class="comment"> * a logistically distributed random variable with mean \f$ \mu \f$ and</span></div> |
| <div class="line"><a name="l00913"></a><span class="lineno"> 913</span> <span class="comment"> * scale parameter \f$ s \f$</span></div> |
| <div class="line"><a name="l00914"></a><span class="lineno"> 914</span> <span class="comment"> */</span></div> |
| <div class="line"><a name="l00915"></a><span class="lineno"> 915</span> CREATE FUNCTION MADLIB_SCHEMA.logistic_quantile(</div> |
| <div class="line"><a name="l00916"></a><span class="lineno"> 916</span>  p DOUBLE PRECISION,</div> |
| <div class="line"><a name="l00917"></a><span class="lineno"> 917</span>  mean DOUBLE PRECISION,</div> |
| <div class="line"><a name="l00918"></a><span class="lineno"><a class="code" href="prob_8sql__in.html#afa38eb6c61d3c9825d5c172e6c17dbf7"> 918</a></span>  scale DOUBLE PRECISION</div> |
| <div class="line"><a name="l00919"></a><span class="lineno"> 919</span> ) RETURNS DOUBLE PRECISION</div> |
| <div class="line"><a name="l00920"></a><span class="lineno"> 920</span> AS 'MODULE_PATHNAME<span class="stringliteral">'</span></div> |
| <div class="line"><a name="l00921"></a><span class="lineno"> 921</span> <span class="stringliteral">LANGUAGE C</span></div> |
| <div class="line"><a name="l00922"></a><span class="lineno"> 922</span> <span class="stringliteral">IMMUTABLE STRICT;</span></div> |
| <div class="line"><a name="l00923"></a><span class="lineno"> 923</span> <span class="stringliteral"></span></div> |
| <div class="line"><a name="l00924"></a><span class="lineno"> 924</span> <span class="stringliteral"></span><span class="comment"></span></div> |
| <div class="line"><a name="l00925"></a><span class="lineno"> 925</span> <span class="comment">/**</span></div> |
| <div class="line"><a name="l00926"></a><span class="lineno"> 926</span> <span class="comment"> * @brief Log-normal cumulative distribution function</span></div> |
| <div class="line"><a name="l00927"></a><span class="lineno"> 927</span> <span class="comment"> *</span></div> |
| <div class="line"><a name="l00928"></a><span class="lineno"> 928</span> <span class="comment"> * @param x Random variate \f$ x \f$</span></div> |
| <div class="line"><a name="l00929"></a><span class="lineno"> 929</span> <span class="comment"> * @param location Location \f$ m \f$</span></div> |
| <div class="line"><a name="l00930"></a><span class="lineno"> 930</span> <span class="comment"> * @param scale Scale \f$ s > 0 \f$</span></div> |
| <div class="line"><a name="l00931"></a><span class="lineno"> 931</span> <span class="comment"> * @return \f$ \Pr[X \leq x] \f$ where \f$ X \f$ is a lognormally distributed</span></div> |
| <div class="line"><a name="l00932"></a><span class="lineno"> 932</span> <span class="comment"> * random variable with location and scale parameters \f$ m \f$ and</span></div> |
| <div class="line"><a name="l00933"></a><span class="lineno"> 933</span> <span class="comment"> * \f$ s \f$, respectively</span></div> |
| <div class="line"><a name="l00934"></a><span class="lineno"> 934</span> <span class="comment"> */</span></div> |
| <div class="line"><a name="l00935"></a><span class="lineno"> 935</span> CREATE FUNCTION MADLIB_SCHEMA.lognormal_cdf(</div> |
| <div class="line"><a name="l00936"></a><span class="lineno"> 936</span>  x DOUBLE PRECISION,</div> |
| <div class="line"><a name="l00937"></a><span class="lineno"><a class="code" href="prob_8sql__in.html#a5a77a0bc5884af2a914a955174892ae2"> 937</a></span>  location DOUBLE PRECISION,</div> |
| <div class="line"><a name="l00938"></a><span class="lineno"> 938</span>  scale DOUBLE PRECISION</div> |
| <div class="line"><a name="l00939"></a><span class="lineno"> 939</span> ) RETURNS DOUBLE PRECISION</div> |
| <div class="line"><a name="l00940"></a><span class="lineno"> 940</span> AS 'MODULE_PATHNAME<span class="stringliteral">'</span></div> |
| <div class="line"><a name="l00941"></a><span class="lineno"> 941</span> <span class="stringliteral">LANGUAGE C</span></div> |
| <div class="line"><a name="l00942"></a><span class="lineno"> 942</span> <span class="stringliteral">IMMUTABLE STRICT;</span></div> |
| <div class="line"><a name="l00943"></a><span class="lineno"> 943</span> <span class="stringliteral"></span><span class="comment"></span></div> |
| <div class="line"><a name="l00944"></a><span class="lineno"> 944</span> <span class="comment">/**</span></div> |
| <div class="line"><a name="l00945"></a><span class="lineno"> 945</span> <span class="comment"> * @brief Log-normal probability density function</span></div> |
| <div class="line"><a name="l00946"></a><span class="lineno"> 946</span> <span class="comment"> *</span></div> |
| <div class="line"><a name="l00947"></a><span class="lineno"> 947</span> <span class="comment"> * @param x Random variate \f$ x \f$</span></div> |
| <div class="line"><a name="l00948"></a><span class="lineno"> 948</span> <span class="comment"> * @param location Location \f$ m \f$</span></div> |
| <div class="line"><a name="l00949"></a><span class="lineno"> 949</span> <span class="comment"> * @param scale Scale \f$ s > 0 \f$</span></div> |
| <div class="line"><a name="l00950"></a><span class="lineno"> 950</span> <span class="comment"> * @return \f$ f(x) \f$ where \f$ f \f$ is the probability density function of</span></div> |
| <div class="line"><a name="l00951"></a><span class="lineno"> 951</span> <span class="comment"> * a lognormally distributed random variable with location and scale</span></div> |
| <div class="line"><a name="l00952"></a><span class="lineno"> 952</span> <span class="comment"> * parameters \f$ m \f$ and \f$ s \f$, respectively</span></div> |
| <div class="line"><a name="l00953"></a><span class="lineno"> 953</span> <span class="comment"> */</span></div> |
| <div class="line"><a name="l00954"></a><span class="lineno"> 954</span> CREATE FUNCTION MADLIB_SCHEMA.lognormal_pdf(</div> |
| <div class="line"><a name="l00955"></a><span class="lineno"> 955</span>  x DOUBLE PRECISION,</div> |
| <div class="line"><a name="l00956"></a><span class="lineno"> 956</span>  location DOUBLE PRECISION,</div> |
| <div class="line"><a name="l00957"></a><span class="lineno"><a class="code" href="prob_8sql__in.html#a4c05b347f8feb64e1236d21b850af61e"> 957</a></span>  scale DOUBLE PRECISION</div> |
| <div class="line"><a name="l00958"></a><span class="lineno"> 958</span> ) RETURNS DOUBLE PRECISION</div> |
| <div class="line"><a name="l00959"></a><span class="lineno"> 959</span> AS 'MODULE_PATHNAME<span class="stringliteral">'</span></div> |
| <div class="line"><a name="l00960"></a><span class="lineno"> 960</span> <span class="stringliteral">LANGUAGE C</span></div> |
| <div class="line"><a name="l00961"></a><span class="lineno"> 961</span> <span class="stringliteral">IMMUTABLE STRICT;</span></div> |
| <div class="line"><a name="l00962"></a><span class="lineno"> 962</span> <span class="stringliteral"></span><span class="comment"></span></div> |
| <div class="line"><a name="l00963"></a><span class="lineno"> 963</span> <span class="comment">/**</span></div> |
| <div class="line"><a name="l00964"></a><span class="lineno"> 964</span> <span class="comment"> * @brief Log-normal quantile function</span></div> |
| <div class="line"><a name="l00965"></a><span class="lineno"> 965</span> <span class="comment"> *</span></div> |
| <div class="line"><a name="l00966"></a><span class="lineno"> 966</span> <span class="comment"> * @param p Probability \f$ p \in [0,1] \f$</span></div> |
| <div class="line"><a name="l00967"></a><span class="lineno"> 967</span> <span class="comment"> * @param location Location \f$ m \f$</span></div> |
| <div class="line"><a name="l00968"></a><span class="lineno"> 968</span> <span class="comment"> * @param scale Scale \f$ s > 0 \f$</span></div> |
| <div class="line"><a name="l00969"></a><span class="lineno"> 969</span> <span class="comment"> * @return \f$ x \f$ such that \f$ p = \Pr[X \leq x] \f$ where \f$ X \f$ is</span></div> |
| <div class="line"><a name="l00970"></a><span class="lineno"> 970</span> <span class="comment"> * a lognormally distributed random variable with location and scale</span></div> |
| <div class="line"><a name="l00971"></a><span class="lineno"> 971</span> <span class="comment"> * parameters \f$ m \f$ and \f$ s \f$, respectively</span></div> |
| <div class="line"><a name="l00972"></a><span class="lineno"> 972</span> <span class="comment"> */</span></div> |
| <div class="line"><a name="l00973"></a><span class="lineno"> 973</span> CREATE FUNCTION MADLIB_SCHEMA.lognormal_quantile(</div> |
| <div class="line"><a name="l00974"></a><span class="lineno"> 974</span>  p DOUBLE PRECISION,</div> |
| <div class="line"><a name="l00975"></a><span class="lineno"> 975</span>  location DOUBLE PRECISION,</div> |
| <div class="line"><a name="l00976"></a><span class="lineno"><a class="code" href="prob_8sql__in.html#a7370b797bf450f9aa54d4fea4d64d611"> 976</a></span>  scale DOUBLE PRECISION</div> |
| <div class="line"><a name="l00977"></a><span class="lineno"> 977</span> ) RETURNS DOUBLE PRECISION</div> |
| <div class="line"><a name="l00978"></a><span class="lineno"> 978</span> AS 'MODULE_PATHNAME<span class="stringliteral">'</span></div> |
| <div class="line"><a name="l00979"></a><span class="lineno"> 979</span> <span class="stringliteral">LANGUAGE C</span></div> |
| <div class="line"><a name="l00980"></a><span class="lineno"> 980</span> <span class="stringliteral">IMMUTABLE STRICT;</span></div> |
| <div class="line"><a name="l00981"></a><span class="lineno"> 981</span> <span class="stringliteral"></span></div> |
| <div class="line"><a name="l00982"></a><span class="lineno"> 982</span> <span class="stringliteral"></span><span class="comment"></span></div> |
| <div class="line"><a name="l00983"></a><span class="lineno"> 983</span> <span class="comment">/**</span></div> |
| <div class="line"><a name="l00984"></a><span class="lineno"> 984</span> <span class="comment"> * @brief Negative binomial cumulative distribution function</span></div> |
| <div class="line"><a name="l00985"></a><span class="lineno"> 985</span> <span class="comment"> *</span></div> |
| <div class="line"><a name="l00986"></a><span class="lineno"> 986</span> <span class="comment"> * @param x Random variate \f$ x \f$</span></div> |
| <div class="line"><a name="l00987"></a><span class="lineno"> 987</span> <span class="comment"> * @param r Total number \f$ r > 0 \f$ of successes in \f$ x + r \f$ trials</span></div> |
| <div class="line"><a name="l00988"></a><span class="lineno"> 988</span> <span class="comment"> * (assuming success in the last trial)</span></div> |
| <div class="line"><a name="l00989"></a><span class="lineno"> 989</span> <span class="comment"> * @param sp Success probability \f$ \mathit{sp} \in (0,1] \f$ in each trial</span></div> |
| <div class="line"><a name="l00990"></a><span class="lineno"> 990</span> <span class="comment"> * @return \f$ \Pr[X \leq x] \f$ where \f$ X \f$ is a negative-binomially</span></div> |
| <div class="line"><a name="l00991"></a><span class="lineno"> 991</span> <span class="comment"> * distributed random variable with parameters \f$ r, \mathit{sp} \f$</span></div> |
| <div class="line"><a name="l00992"></a><span class="lineno"> 992</span> <span class="comment"> */</span></div> |
| <div class="line"><a name="l00993"></a><span class="lineno"> 993</span> CREATE FUNCTION MADLIB_SCHEMA.negative_binomial_cdf(</div> |
| <div class="line"><a name="l00994"></a><span class="lineno"> 994</span>  x DOUBLE PRECISION,</div> |
| <div class="line"><a name="l00995"></a><span class="lineno"><a class="code" href="prob_8sql__in.html#aab3a6de990ae5a81834274a1cf9cad8f"> 995</a></span>  r DOUBLE PRECISION,</div> |
| <div class="line"><a name="l00996"></a><span class="lineno"> 996</span>  sp DOUBLE PRECISION</div> |
| <div class="line"><a name="l00997"></a><span class="lineno"> 997</span> ) RETURNS DOUBLE PRECISION</div> |
| <div class="line"><a name="l00998"></a><span class="lineno"> 998</span> AS 'MODULE_PATHNAME<span class="stringliteral">'</span></div> |
| <div class="line"><a name="l00999"></a><span class="lineno"> 999</span> <span class="stringliteral">LANGUAGE C</span></div> |
| <div class="line"><a name="l01000"></a><span class="lineno"> 1000</span> <span class="stringliteral">IMMUTABLE STRICT;</span></div> |
| <div class="line"><a name="l01001"></a><span class="lineno"> 1001</span> <span class="stringliteral"></span><span class="comment"></span></div> |
| <div class="line"><a name="l01002"></a><span class="lineno"> 1002</span> <span class="comment">/**</span></div> |
| <div class="line"><a name="l01003"></a><span class="lineno"> 1003</span> <span class="comment"> * @brief Negative binomial probability mass function</span></div> |
| <div class="line"><a name="l01004"></a><span class="lineno"> 1004</span> <span class="comment"> *</span></div> |
| <div class="line"><a name="l01005"></a><span class="lineno"> 1005</span> <span class="comment"> * @param x Random variate \f$ x \f$</span></div> |
| <div class="line"><a name="l01006"></a><span class="lineno"> 1006</span> <span class="comment"> * @param r Total number \f$ r > 0 \f$ of successes in \f$ x + r \f$ trials</span></div> |
| <div class="line"><a name="l01007"></a><span class="lineno"> 1007</span> <span class="comment"> * (assuming success in the last trial)</span></div> |
| <div class="line"><a name="l01008"></a><span class="lineno"> 1008</span> <span class="comment"> * @param sp Success probability \f$ \mathit{sp} \in (0,1] \f$ in each trial</span></div> |
| <div class="line"><a name="l01009"></a><span class="lineno"> 1009</span> <span class="comment"> * @return \f$ f(x) \f$ where \f$ f \f$ is the probability mass function of</span></div> |
| <div class="line"><a name="l01010"></a><span class="lineno"> 1010</span> <span class="comment"> * a negative-binomially distributed random variable with parameters</span></div> |
| <div class="line"><a name="l01011"></a><span class="lineno"> 1011</span> <span class="comment"> * \f$ r, \mathit{sp} \f$</span></div> |
| <div class="line"><a name="l01012"></a><span class="lineno"> 1012</span> <span class="comment"> */</span></div> |
| <div class="line"><a name="l01013"></a><span class="lineno"> 1013</span> CREATE FUNCTION MADLIB_SCHEMA.negative_binomial_pmf(</div> |
| <div class="line"><a name="l01014"></a><span class="lineno"> 1014</span>  x INT4,</div> |
| <div class="line"><a name="l01015"></a><span class="lineno"><a class="code" href="prob_8sql__in.html#ad0a7e4474f828869fb90e62f8e6f04d7"> 1015</a></span>  r DOUBLE PRECISION,</div> |
| <div class="line"><a name="l01016"></a><span class="lineno"> 1016</span>  sp DOUBLE PRECISION</div> |
| <div class="line"><a name="l01017"></a><span class="lineno"> 1017</span> ) RETURNS DOUBLE PRECISION</div> |
| <div class="line"><a name="l01018"></a><span class="lineno"> 1018</span> AS 'MODULE_PATHNAME<span class="stringliteral">'</span></div> |
| <div class="line"><a name="l01019"></a><span class="lineno"> 1019</span> <span class="stringliteral">LANGUAGE C</span></div> |
| <div class="line"><a name="l01020"></a><span class="lineno"> 1020</span> <span class="stringliteral">IMMUTABLE STRICT;</span></div> |
| <div class="line"><a name="l01021"></a><span class="lineno"> 1021</span> <span class="stringliteral"></span><span class="comment"></span></div> |
| <div class="line"><a name="l01022"></a><span class="lineno"> 1022</span> <span class="comment">/**</span></div> |
| <div class="line"><a name="l01023"></a><span class="lineno"> 1023</span> <span class="comment"> * @brief Negative binomial quantile function</span></div> |
| <div class="line"><a name="l01024"></a><span class="lineno"> 1024</span> <span class="comment"> *</span></div> |
| <div class="line"><a name="l01025"></a><span class="lineno"> 1025</span> <span class="comment"> * @param p Probability \f$ p \in [0,1] \f$</span></div> |
| <div class="line"><a name="l01026"></a><span class="lineno"> 1026</span> <span class="comment"> * @param r Total number \f$ r > 0 \f$ of successes in \f$ x + r \f$ trials</span></div> |
| <div class="line"><a name="l01027"></a><span class="lineno"> 1027</span> <span class="comment"> * (assuming success in the last trial)</span></div> |
| <div class="line"><a name="l01028"></a><span class="lineno"> 1028</span> <span class="comment"> * @param sp Success probability \f$ \mathit{sp} \in (0,1] \f$ in each trial</span></div> |
| <div class="line"><a name="l01029"></a><span class="lineno"> 1029</span> <span class="comment"> * @return If \f$ p < 0.5 \f$ the maximum \f$ x \f$ such that</span></div> |
| <div class="line"><a name="l01030"></a><span class="lineno"> 1030</span> <span class="comment"> * \f$ p \geq \Pr[X \leq x] \f$. If \f$ p \geq 0.5 \f$ the minimum \f$ x \f$</span></div> |
| <div class="line"><a name="l01031"></a><span class="lineno"> 1031</span> <span class="comment"> * such that \f$ p \leq \Pr[X \leq x] \f$. Here, \f$ X \f$ is</span></div> |
| <div class="line"><a name="l01032"></a><span class="lineno"> 1032</span> <span class="comment"> * a negative-binomially distributed random variable with parameters</span></div> |
| <div class="line"><a name="l01033"></a><span class="lineno"> 1033</span> <span class="comment"> * \f$ r, \mathit{sp} \f$</span></div> |
| <div class="line"><a name="l01034"></a><span class="lineno"> 1034</span> <span class="comment"> */</span></div> |
| <div class="line"><a name="l01035"></a><span class="lineno"><a class="code" href="prob_8sql__in.html#ab9cbc30424eba30f2df2a32a7e45f138"> 1035</a></span> CREATE FUNCTION MADLIB_SCHEMA.negative_binomial_quantile(</div> |
| <div class="line"><a name="l01036"></a><span class="lineno"> 1036</span>  p DOUBLE PRECISION,</div> |
| <div class="line"><a name="l01037"></a><span class="lineno"> 1037</span>  r DOUBLE PRECISION,</div> |
| <div class="line"><a name="l01038"></a><span class="lineno"> 1038</span>  sp DOUBLE PRECISION</div> |
| <div class="line"><a name="l01039"></a><span class="lineno"> 1039</span> ) RETURNS DOUBLE PRECISION</div> |
| <div class="line"><a name="l01040"></a><span class="lineno"> 1040</span> AS 'MODULE_PATHNAME<span class="stringliteral">'</span></div> |
| <div class="line"><a name="l01041"></a><span class="lineno"> 1041</span> <span class="stringliteral">LANGUAGE C</span></div> |
| <div class="line"><a name="l01042"></a><span class="lineno"> 1042</span> <span class="stringliteral">IMMUTABLE STRICT;</span></div> |
| <div class="line"><a name="l01043"></a><span class="lineno"> 1043</span> <span class="stringliteral"></span></div> |
| <div class="line"><a name="l01044"></a><span class="lineno"> 1044</span> <span class="stringliteral"></span><span class="comment"></span></div> |
| <div class="line"><a name="l01045"></a><span class="lineno"> 1045</span> <span class="comment">/**</span></div> |
| <div class="line"><a name="l01046"></a><span class="lineno"> 1046</span> <span class="comment"> * @brief Noncentral beta cumulative distribution function</span></div> |
| <div class="line"><a name="l01047"></a><span class="lineno"> 1047</span> <span class="comment"> *</span></div> |
| <div class="line"><a name="l01048"></a><span class="lineno"> 1048</span> <span class="comment"> * @param x Random variate \f$ x \f$</span></div> |
| <div class="line"><a name="l01049"></a><span class="lineno"> 1049</span> <span class="comment"> * @param alpha Shape \f$ \alpha > 0 \f$</span></div> |
| <div class="line"><a name="l01050"></a><span class="lineno"> 1050</span> <span class="comment"> * @param beta Shape \f$ \beta > 0 \f$</span></div> |
| <div class="line"><a name="l01051"></a><span class="lineno"> 1051</span> <span class="comment"> * @param ncp Noncentrality parameter \f$ \delta \geq 0 \f$</span></div> |
| <div class="line"><a name="l01052"></a><span class="lineno"> 1052</span> <span class="comment"> * @return \f$ \Pr[X \leq x] \f$ where \f$ X \f$ is a noncentral-beta</span></div> |
| <div class="line"><a name="l01053"></a><span class="lineno"> 1053</span> <span class="comment"> * distributed random variable with shape parameters \f$ shape_1 \f$ and</span></div> |
| <div class="line"><a name="l01054"></a><span class="lineno"> 1054</span> <span class="comment"> * \f$ shape_2 \f$ and noncentrality parameter \f$ \delta \f$</span></div> |
| <div class="line"><a name="l01055"></a><span class="lineno"> 1055</span> <span class="comment"> */</span></div> |
| <div class="line"><a name="l01056"></a><span class="lineno"> 1056</span> CREATE FUNCTION MADLIB_SCHEMA.non_central_beta_cdf(</div> |
| <div class="line"><a name="l01057"></a><span class="lineno"><a class="code" href="prob_8sql__in.html#ad9e541de8b41da2e7b7434f862db4845"> 1057</a></span>  x DOUBLE PRECISION,</div> |
| <div class="line"><a name="l01058"></a><span class="lineno"> 1058</span>  alpha DOUBLE PRECISION,</div> |
| <div class="line"><a name="l01059"></a><span class="lineno"> 1059</span>  beta DOUBLE PRECISION,</div> |
| <div class="line"><a name="l01060"></a><span class="lineno"> 1060</span>  ncp DOUBLE PRECISION</div> |
| <div class="line"><a name="l01061"></a><span class="lineno"> 1061</span> ) RETURNS DOUBLE PRECISION</div> |
| <div class="line"><a name="l01062"></a><span class="lineno"> 1062</span> AS 'MODULE_PATHNAME<span class="stringliteral">'</span></div> |
| <div class="line"><a name="l01063"></a><span class="lineno"> 1063</span> <span class="stringliteral">LANGUAGE C</span></div> |
| <div class="line"><a name="l01064"></a><span class="lineno"> 1064</span> <span class="stringliteral">IMMUTABLE STRICT;</span></div> |
| <div class="line"><a name="l01065"></a><span class="lineno"> 1065</span> <span class="stringliteral"></span><span class="comment"></span></div> |
| <div class="line"><a name="l01066"></a><span class="lineno"> 1066</span> <span class="comment">/**</span></div> |
| <div class="line"><a name="l01067"></a><span class="lineno"> 1067</span> <span class="comment"> * @brief Noncentral beta probability density function</span></div> |
| <div class="line"><a name="l01068"></a><span class="lineno"> 1068</span> <span class="comment"> *</span></div> |
| <div class="line"><a name="l01069"></a><span class="lineno"> 1069</span> <span class="comment"> * @param x Random variate \f$ x \f$</span></div> |
| <div class="line"><a name="l01070"></a><span class="lineno"> 1070</span> <span class="comment"> * @param alpha Shape \f$ \alpha > 0 \f$</span></div> |
| <div class="line"><a name="l01071"></a><span class="lineno"> 1071</span> <span class="comment"> * @param beta Shape \f$ \beta > 0 \f$</span></div> |
| <div class="line"><a name="l01072"></a><span class="lineno"> 1072</span> <span class="comment"> * @param ncp Noncentrality parameter \f$ \delta \geq 0 \f$</span></div> |
| <div class="line"><a name="l01073"></a><span class="lineno"> 1073</span> <span class="comment"> * @return \f$ f(x) \f$ where \f$ f \f$ is the probability density function of</span></div> |
| <div class="line"><a name="l01074"></a><span class="lineno"> 1074</span> <span class="comment"> * a noncentral-beta distributed random variable with shape parameters</span></div> |
| <div class="line"><a name="l01075"></a><span class="lineno"> 1075</span> <span class="comment"> * \f$ shape_1 \f$ and \f$ shape_2 \f$ and noncentrality parameter</span></div> |
| <div class="line"><a name="l01076"></a><span class="lineno"> 1076</span> <span class="comment"> * \f$ \delta \f$</span></div> |
| <div class="line"><a name="l01077"></a><span class="lineno"> 1077</span> <span class="comment"> */</span></div> |
| <div class="line"><a name="l01078"></a><span class="lineno"><a class="code" href="prob_8sql__in.html#a1361569bd86e41f796c70f8cb277010e"> 1078</a></span> CREATE FUNCTION MADLIB_SCHEMA.non_central_beta_pdf(</div> |
| <div class="line"><a name="l01079"></a><span class="lineno"> 1079</span>  x DOUBLE PRECISION,</div> |
| <div class="line"><a name="l01080"></a><span class="lineno"> 1080</span>  alpha DOUBLE PRECISION,</div> |
| <div class="line"><a name="l01081"></a><span class="lineno"> 1081</span>  beta DOUBLE PRECISION,</div> |
| <div class="line"><a name="l01082"></a><span class="lineno"> 1082</span>  ncp DOUBLE PRECISION</div> |
| <div class="line"><a name="l01083"></a><span class="lineno"> 1083</span> ) RETURNS DOUBLE PRECISION</div> |
| <div class="line"><a name="l01084"></a><span class="lineno"> 1084</span> AS 'MODULE_PATHNAME<span class="stringliteral">'</span></div> |
| <div class="line"><a name="l01085"></a><span class="lineno"> 1085</span> <span class="stringliteral">LANGUAGE C</span></div> |
| <div class="line"><a name="l01086"></a><span class="lineno"> 1086</span> <span class="stringliteral">IMMUTABLE STRICT;</span></div> |
| <div class="line"><a name="l01087"></a><span class="lineno"> 1087</span> <span class="stringliteral"></span><span class="comment"></span></div> |
| <div class="line"><a name="l01088"></a><span class="lineno"> 1088</span> <span class="comment">/**</span></div> |
| <div class="line"><a name="l01089"></a><span class="lineno"> 1089</span> <span class="comment"> * @brief Noncentral beta quantile function</span></div> |
| <div class="line"><a name="l01090"></a><span class="lineno"> 1090</span> <span class="comment"> *</span></div> |
| <div class="line"><a name="l01091"></a><span class="lineno"> 1091</span> <span class="comment"> * @param p Probability \f$ p \in [0,1] \f$</span></div> |
| <div class="line"><a name="l01092"></a><span class="lineno"> 1092</span> <span class="comment"> * @param alpha Shape \f$ \alpha > 0 \f$</span></div> |
| <div class="line"><a name="l01093"></a><span class="lineno"> 1093</span> <span class="comment"> * @param beta Shape \f$ \beta > 0 \f$</span></div> |
| <div class="line"><a name="l01094"></a><span class="lineno"> 1094</span> <span class="comment"> * @param ncp Noncentrality parameter \f$ \delta \geq 0 \f$</span></div> |
| <div class="line"><a name="l01095"></a><span class="lineno"> 1095</span> <span class="comment"> * @return \f$ x \f$ such that \f$ p = \Pr[X \leq x] \f$ where \f$ X \f$ is</span></div> |
| <div class="line"><a name="l01096"></a><span class="lineno"> 1096</span> <span class="comment"> * a noncentral-beta distributed random variable with shape parameters</span></div> |
| <div class="line"><a name="l01097"></a><span class="lineno"> 1097</span> <span class="comment"> * \f$ shape_1 \f$ and \f$ shape_2 \f$ and noncentrality parameter</span></div> |
| <div class="line"><a name="l01098"></a><span class="lineno"> 1098</span> <span class="comment"> * \f$ \delta \f$</span></div> |
| <div class="line"><a name="l01099"></a><span class="lineno"> 1099</span> <span class="comment"> */</span></div> |
| <div class="line"><a name="l01100"></a><span class="lineno"><a class="code" href="prob_8sql__in.html#ad4a12c083054f0e2d316ae76c9aaeef7"> 1100</a></span> CREATE FUNCTION MADLIB_SCHEMA.non_central_beta_quantile(</div> |
| <div class="line"><a name="l01101"></a><span class="lineno"> 1101</span>  p DOUBLE PRECISION,</div> |
| <div class="line"><a name="l01102"></a><span class="lineno"> 1102</span>  alpha DOUBLE PRECISION,</div> |
| <div class="line"><a name="l01103"></a><span class="lineno"> 1103</span>  beta DOUBLE PRECISION,</div> |
| <div class="line"><a name="l01104"></a><span class="lineno"> 1104</span>  ncp DOUBLE PRECISION</div> |
| <div class="line"><a name="l01105"></a><span class="lineno"> 1105</span> ) RETURNS DOUBLE PRECISION</div> |
| <div class="line"><a name="l01106"></a><span class="lineno"> 1106</span> AS 'MODULE_PATHNAME<span class="stringliteral">'</span></div> |
| <div class="line"><a name="l01107"></a><span class="lineno"> 1107</span> <span class="stringliteral">LANGUAGE C</span></div> |
| <div class="line"><a name="l01108"></a><span class="lineno"> 1108</span> <span class="stringliteral">IMMUTABLE STRICT;</span></div> |
| <div class="line"><a name="l01109"></a><span class="lineno"> 1109</span> <span class="stringliteral"></span></div> |
| <div class="line"><a name="l01110"></a><span class="lineno"> 1110</span> <span class="stringliteral"></span><span class="comment"></span></div> |
| <div class="line"><a name="l01111"></a><span class="lineno"> 1111</span> <span class="comment">/**</span></div> |
| <div class="line"><a name="l01112"></a><span class="lineno"> 1112</span> <span class="comment"> * @brief Noncentral chi-squared cumulative distribution function</span></div> |
| <div class="line"><a name="l01113"></a><span class="lineno"> 1113</span> <span class="comment"> *</span></div> |
| <div class="line"><a name="l01114"></a><span class="lineno"> 1114</span> <span class="comment"> * @param x Random variate \f$ x \f$</span></div> |
| <div class="line"><a name="l01115"></a><span class="lineno"> 1115</span> <span class="comment"> * @param df Degrees of freedom \f$ \nu > 0 \f$</span></div> |
| <div class="line"><a name="l01116"></a><span class="lineno"> 1116</span> <span class="comment"> * @param ncp The noncentrality parameter \f$ \lambda \geq 0 \f$</span></div> |
| <div class="line"><a name="l01117"></a><span class="lineno"> 1117</span> <span class="comment"> * @return \f$ \Pr[X \leq x] \f$ where \f$ X \f$ is a noncentral-chi-squared</span></div> |
| <div class="line"><a name="l01118"></a><span class="lineno"> 1118</span> <span class="comment"> * distributed random variable with \f$ \nu \f$ degrees of freedom and</span></div> |
| <div class="line"><a name="l01119"></a><span class="lineno"> 1119</span> <span class="comment"> * noncentrality parameter \f$ \lambda \f$</span></div> |
| <div class="line"><a name="l01120"></a><span class="lineno"> 1120</span> <span class="comment"> */</span></div> |
| <div class="line"><a name="l01121"></a><span class="lineno"> 1121</span> CREATE FUNCTION MADLIB_SCHEMA.non_central_chi_squared_cdf(</div> |
| <div class="line"><a name="l01122"></a><span class="lineno"><a class="code" href="prob_8sql__in.html#a3073b409eaee3faa6d43df014662c279"> 1122</a></span>  x DOUBLE PRECISION,</div> |
| <div class="line"><a name="l01123"></a><span class="lineno"> 1123</span>  df DOUBLE PRECISION,</div> |
| <div class="line"><a name="l01124"></a><span class="lineno"> 1124</span>  ncp DOUBLE PRECISION</div> |
| <div class="line"><a name="l01125"></a><span class="lineno"> 1125</span> ) RETURNS DOUBLE PRECISION</div> |
| <div class="line"><a name="l01126"></a><span class="lineno"> 1126</span> AS 'MODULE_PATHNAME<span class="stringliteral">'</span></div> |
| <div class="line"><a name="l01127"></a><span class="lineno"> 1127</span> <span class="stringliteral">LANGUAGE C</span></div> |
| <div class="line"><a name="l01128"></a><span class="lineno"> 1128</span> <span class="stringliteral">IMMUTABLE STRICT;</span></div> |
| <div class="line"><a name="l01129"></a><span class="lineno"> 1129</span> <span class="stringliteral"></span><span class="comment"></span></div> |
| <div class="line"><a name="l01130"></a><span class="lineno"> 1130</span> <span class="comment">/**</span></div> |
| <div class="line"><a name="l01131"></a><span class="lineno"> 1131</span> <span class="comment"> * @brief Noncentral chi-squared distribution probability density function</span></div> |
| <div class="line"><a name="l01132"></a><span class="lineno"> 1132</span> <span class="comment"> *</span></div> |
| <div class="line"><a name="l01133"></a><span class="lineno"> 1133</span> <span class="comment"> * @param x Random variate \f$ x \f$</span></div> |
| <div class="line"><a name="l01134"></a><span class="lineno"> 1134</span> <span class="comment"> * @param df Degrees of freedom \f$ \nu > 0 \f$</span></div> |
| <div class="line"><a name="l01135"></a><span class="lineno"> 1135</span> <span class="comment"> * @param ncp The noncentrality parameter \f$ \lambda \geq 0 \f$</span></div> |
| <div class="line"><a name="l01136"></a><span class="lineno"> 1136</span> <span class="comment"> * @return \f$ f(x) \f$ where \f$ f \f$ is the probability density function of</span></div> |
| <div class="line"><a name="l01137"></a><span class="lineno"> 1137</span> <span class="comment"> * a noncentral-chi-squared distributed random variable with \f$ \nu \f$</span></div> |
| <div class="line"><a name="l01138"></a><span class="lineno"> 1138</span> <span class="comment"> * degrees of freedom and noncentrality parameter \f$ \lambda \f$</span></div> |
| <div class="line"><a name="l01139"></a><span class="lineno"> 1139</span> <span class="comment"> */</span></div> |
| <div class="line"><a name="l01140"></a><span class="lineno"> 1140</span> CREATE FUNCTION MADLIB_SCHEMA.non_central_chi_squared_pdf(</div> |
| <div class="line"><a name="l01141"></a><span class="lineno"> 1141</span>  x DOUBLE PRECISION,</div> |
| <div class="line"><a name="l01142"></a><span class="lineno"> 1142</span>  df DOUBLE PRECISION,</div> |
| <div class="line"><a name="l01143"></a><span class="lineno"><a class="code" href="prob_8sql__in.html#ab4b7d2cf10bb031328dcc34c6ff494ad"> 1143</a></span>  ncp DOUBLE PRECISION</div> |
| <div class="line"><a name="l01144"></a><span class="lineno"> 1144</span> ) RETURNS DOUBLE PRECISION</div> |
| <div class="line"><a name="l01145"></a><span class="lineno"> 1145</span> AS 'MODULE_PATHNAME<span class="stringliteral">'</span></div> |
| <div class="line"><a name="l01146"></a><span class="lineno"> 1146</span> <span class="stringliteral">LANGUAGE C</span></div> |
| <div class="line"><a name="l01147"></a><span class="lineno"> 1147</span> <span class="stringliteral">IMMUTABLE STRICT;</span></div> |
| <div class="line"><a name="l01148"></a><span class="lineno"> 1148</span> <span class="stringliteral"></span><span class="comment"></span></div> |
| <div class="line"><a name="l01149"></a><span class="lineno"> 1149</span> <span class="comment">/**</span></div> |
| <div class="line"><a name="l01150"></a><span class="lineno"> 1150</span> <span class="comment"> * @brief Noncentral chi-squared distribution quantile function</span></div> |
| <div class="line"><a name="l01151"></a><span class="lineno"> 1151</span> <span class="comment"> *</span></div> |
| <div class="line"><a name="l01152"></a><span class="lineno"> 1152</span> <span class="comment"> * @param p Probability \f$ p \in [0,1] \f$</span></div> |
| <div class="line"><a name="l01153"></a><span class="lineno"> 1153</span> <span class="comment"> * @param df Degrees of freedom \f$ \nu > 0 \f$</span></div> |
| <div class="line"><a name="l01154"></a><span class="lineno"> 1154</span> <span class="comment"> * @param ncp The noncentrality parameter \f$ \lambda \geq 0 \f$</span></div> |
| <div class="line"><a name="l01155"></a><span class="lineno"> 1155</span> <span class="comment"> * @return \f$ x \f$ such that \f$ p = \Pr[X \leq x] \f$ where \f$ X \f$ is a</span></div> |
| <div class="line"><a name="l01156"></a><span class="lineno"> 1156</span> <span class="comment"> * noncentral-chi-squared distributed random variable with \f$ \nu \f$</span></div> |
| <div class="line"><a name="l01157"></a><span class="lineno"> 1157</span> <span class="comment"> * degrees of freedom and noncentrality parameter \f$ \lambda \f$</span></div> |
| <div class="line"><a name="l01158"></a><span class="lineno"> 1158</span> <span class="comment"> */</span></div> |
| <div class="line"><a name="l01159"></a><span class="lineno"> 1159</span> CREATE FUNCTION MADLIB_SCHEMA.non_central_chi_squared_quantile(</div> |
| <div class="line"><a name="l01160"></a><span class="lineno"> 1160</span>  p DOUBLE PRECISION,</div> |
| <div class="line"><a name="l01161"></a><span class="lineno"> 1161</span>  df DOUBLE PRECISION,</div> |
| <div class="line"><a name="l01162"></a><span class="lineno"><a class="code" href="prob_8sql__in.html#aa7a563183224593d1e0d623a3c5489d8"> 1162</a></span>  ncp DOUBLE PRECISION</div> |
| <div class="line"><a name="l01163"></a><span class="lineno"> 1163</span> ) RETURNS DOUBLE PRECISION</div> |
| <div class="line"><a name="l01164"></a><span class="lineno"> 1164</span> AS 'MODULE_PATHNAME<span class="stringliteral">'</span></div> |
| <div class="line"><a name="l01165"></a><span class="lineno"> 1165</span> <span class="stringliteral">LANGUAGE C</span></div> |
| <div class="line"><a name="l01166"></a><span class="lineno"> 1166</span> <span class="stringliteral">IMMUTABLE STRICT;</span></div> |
| <div class="line"><a name="l01167"></a><span class="lineno"> 1167</span> <span class="stringliteral"></span></div> |
| <div class="line"><a name="l01168"></a><span class="lineno"> 1168</span> <span class="stringliteral"></span><span class="comment"></span></div> |
| <div class="line"><a name="l01169"></a><span class="lineno"> 1169</span> <span class="comment">/**</span></div> |
| <div class="line"><a name="l01170"></a><span class="lineno"> 1170</span> <span class="comment"> * @brief Noncentral Fisher F cumulative distribution function</span></div> |
| <div class="line"><a name="l01171"></a><span class="lineno"> 1171</span> <span class="comment"> *</span></div> |
| <div class="line"><a name="l01172"></a><span class="lineno"> 1172</span> <span class="comment"> * @param x Random variate \f$ x \f$</span></div> |
| <div class="line"><a name="l01173"></a><span class="lineno"> 1173</span> <span class="comment"> * @param df1 Degrees of freedom in numerator \f$ \nu_1 > 0 \f$</span></div> |
| <div class="line"><a name="l01174"></a><span class="lineno"> 1174</span> <span class="comment"> * @param df2 Degrees of freedom in denominator \f$ \nu_1 > 0 \f$</span></div> |
| <div class="line"><a name="l01175"></a><span class="lineno"> 1175</span> <span class="comment"> * @param ncp The noncentrality parameter \f$ \lambda \geq 0 \f$</span></div> |
| <div class="line"><a name="l01176"></a><span class="lineno"> 1176</span> <span class="comment"> * @return \f$ \Pr[X \leq x] \f$ where \f$ X \f$ is a</span></div> |
| <div class="line"><a name="l01177"></a><span class="lineno"> 1177</span> <span class="comment"> * noncentral Fisher F-distributed random variable with parameters</span></div> |
| <div class="line"><a name="l01178"></a><span class="lineno"> 1178</span> <span class="comment"> * \f$ \nu_1, \nu_2, \lambda \f$</span></div> |
| <div class="line"><a name="l01179"></a><span class="lineno"> 1179</span> <span class="comment"> */</span></div> |
| <div class="line"><a name="l01180"></a><span class="lineno"> 1180</span> CREATE FUNCTION MADLIB_SCHEMA.non_central_f_cdf(</div> |
| <div class="line"><a name="l01181"></a><span class="lineno"><a class="code" href="prob_8sql__in.html#ad694e29187b629ae683ef1235d2b9270"> 1181</a></span>  x DOUBLE PRECISION,</div> |
| <div class="line"><a name="l01182"></a><span class="lineno"> 1182</span>  df1 DOUBLE PRECISION,</div> |
| <div class="line"><a name="l01183"></a><span class="lineno"> 1183</span>  df2 DOUBLE PRECISION,</div> |
| <div class="line"><a name="l01184"></a><span class="lineno"> 1184</span>  ncp DOUBLE PRECISION</div> |
| <div class="line"><a name="l01185"></a><span class="lineno"> 1185</span> ) RETURNS DOUBLE PRECISION</div> |
| <div class="line"><a name="l01186"></a><span class="lineno"> 1186</span> AS 'MODULE_PATHNAME<span class="stringliteral">'</span></div> |
| <div class="line"><a name="l01187"></a><span class="lineno"> 1187</span> <span class="stringliteral">LANGUAGE C</span></div> |
| <div class="line"><a name="l01188"></a><span class="lineno"> 1188</span> <span class="stringliteral">IMMUTABLE STRICT;</span></div> |
| <div class="line"><a name="l01189"></a><span class="lineno"> 1189</span> <span class="stringliteral"></span><span class="comment"></span></div> |
| <div class="line"><a name="l01190"></a><span class="lineno"> 1190</span> <span class="comment">/**</span></div> |
| <div class="line"><a name="l01191"></a><span class="lineno"> 1191</span> <span class="comment"> * @brief Noncentral Fisher F probability density function</span></div> |
| <div class="line"><a name="l01192"></a><span class="lineno"> 1192</span> <span class="comment"> *</span></div> |
| <div class="line"><a name="l01193"></a><span class="lineno"> 1193</span> <span class="comment"> * @param x Random variate \f$ x \f$</span></div> |
| <div class="line"><a name="l01194"></a><span class="lineno"> 1194</span> <span class="comment"> * @param df1 Degrees of freedom in numerator \f$ \nu_1 > 0 \f$</span></div> |
| <div class="line"><a name="l01195"></a><span class="lineno"> 1195</span> <span class="comment"> * @param df2 Degrees of freedom in denominator \f$ \nu_1 > 0 \f$</span></div> |
| <div class="line"><a name="l01196"></a><span class="lineno"> 1196</span> <span class="comment"> * @param ncp The noncentrality parameter \f$ \lambda \geq 0 \f$</span></div> |
| <div class="line"><a name="l01197"></a><span class="lineno"> 1197</span> <span class="comment"> * @return \f$ f(x) \f$ where \f$ f \f$ is the probability density function of a</span></div> |
| <div class="line"><a name="l01198"></a><span class="lineno"> 1198</span> <span class="comment"> * noncentral Fisher F-distributed random variable with parameters</span></div> |
| <div class="line"><a name="l01199"></a><span class="lineno"> 1199</span> <span class="comment"> * \f$ \nu_1, \nu_2, \lambda \f$</span></div> |
| <div class="line"><a name="l01200"></a><span class="lineno"> 1200</span> <span class="comment"> */</span></div> |
| <div class="line"><a name="l01201"></a><span class="lineno"> 1201</span> CREATE FUNCTION MADLIB_SCHEMA.non_central_f_pdf(</div> |
| <div class="line"><a name="l01202"></a><span class="lineno"><a class="code" href="prob_8sql__in.html#a00051df630007b530ce86b4ab44a0434"> 1202</a></span>  x DOUBLE PRECISION,</div> |
| <div class="line"><a name="l01203"></a><span class="lineno"> 1203</span>  df1 DOUBLE PRECISION,</div> |
| <div class="line"><a name="l01204"></a><span class="lineno"> 1204</span>  df2 DOUBLE PRECISION,</div> |
| <div class="line"><a name="l01205"></a><span class="lineno"> 1205</span>  ncp DOUBLE PRECISION</div> |
| <div class="line"><a name="l01206"></a><span class="lineno"> 1206</span> ) RETURNS DOUBLE PRECISION</div> |
| <div class="line"><a name="l01207"></a><span class="lineno"> 1207</span> AS 'MODULE_PATHNAME<span class="stringliteral">'</span></div> |
| <div class="line"><a name="l01208"></a><span class="lineno"> 1208</span> <span class="stringliteral">LANGUAGE C</span></div> |
| <div class="line"><a name="l01209"></a><span class="lineno"> 1209</span> <span class="stringliteral">IMMUTABLE STRICT;</span></div> |
| <div class="line"><a name="l01210"></a><span class="lineno"> 1210</span> <span class="stringliteral"></span><span class="comment"></span></div> |
| <div class="line"><a name="l01211"></a><span class="lineno"> 1211</span> <span class="comment">/**</span></div> |
| <div class="line"><a name="l01212"></a><span class="lineno"> 1212</span> <span class="comment"> * @brief Noncentral Fisher F quantile function</span></div> |
| <div class="line"><a name="l01213"></a><span class="lineno"> 1213</span> <span class="comment"> *</span></div> |
| <div class="line"><a name="l01214"></a><span class="lineno"> 1214</span> <span class="comment"> * @param p Probability \f$ p \in [0,1] \f$</span></div> |
| <div class="line"><a name="l01215"></a><span class="lineno"> 1215</span> <span class="comment"> * @param df1 Degrees of freedom in numerator \f$ \nu_1 > 0 \f$</span></div> |
| <div class="line"><a name="l01216"></a><span class="lineno"> 1216</span> <span class="comment"> * @param df2 Degrees of freedom in denominator \f$ \nu_1 > 0 \f$</span></div> |
| <div class="line"><a name="l01217"></a><span class="lineno"> 1217</span> <span class="comment"> * @param ncp The noncentrality parameter \f$ \lambda \geq 0 \f$</span></div> |
| <div class="line"><a name="l01218"></a><span class="lineno"> 1218</span> <span class="comment"> * @return \f$ x \f$ such that \f$ p = \Pr[X \leq x] \f$ where \f$ X \f$ is a</span></div> |
| <div class="line"><a name="l01219"></a><span class="lineno"> 1219</span> <span class="comment"> * noncentral Fisher F-distributed random variable with parameters</span></div> |
| <div class="line"><a name="l01220"></a><span class="lineno"> 1220</span> <span class="comment"> * \f$ \nu_1, \nu_2, \lambda \f$</span></div> |
| <div class="line"><a name="l01221"></a><span class="lineno"> 1221</span> <span class="comment"> */</span></div> |
| <div class="line"><a name="l01222"></a><span class="lineno"> 1222</span> CREATE FUNCTION MADLIB_SCHEMA.non_central_f_quantile(</div> |
| <div class="line"><a name="l01223"></a><span class="lineno"><a class="code" href="prob_8sql__in.html#a3d94edcf90fca1fa52671293a9ea9c2f"> 1223</a></span>  p DOUBLE PRECISION,</div> |
| <div class="line"><a name="l01224"></a><span class="lineno"> 1224</span>  df1 DOUBLE PRECISION,</div> |
| <div class="line"><a name="l01225"></a><span class="lineno"> 1225</span>  df2 DOUBLE PRECISION,</div> |
| <div class="line"><a name="l01226"></a><span class="lineno"> 1226</span>  ncp DOUBLE PRECISION</div> |
| <div class="line"><a name="l01227"></a><span class="lineno"> 1227</span> ) RETURNS DOUBLE PRECISION</div> |
| <div class="line"><a name="l01228"></a><span class="lineno"> 1228</span> AS 'MODULE_PATHNAME<span class="stringliteral">'</span></div> |
| <div class="line"><a name="l01229"></a><span class="lineno"> 1229</span> <span class="stringliteral">LANGUAGE C</span></div> |
| <div class="line"><a name="l01230"></a><span class="lineno"> 1230</span> <span class="stringliteral">IMMUTABLE STRICT;</span></div> |
| <div class="line"><a name="l01231"></a><span class="lineno"> 1231</span> <span class="stringliteral"></span></div> |
| <div class="line"><a name="l01232"></a><span class="lineno"> 1232</span> <span class="stringliteral"></span><span class="comment"></span></div> |
| <div class="line"><a name="l01233"></a><span class="lineno"> 1233</span> <span class="comment">/**</span></div> |
| <div class="line"><a name="l01234"></a><span class="lineno"> 1234</span> <span class="comment"> * @brief Noncentral Student-t cumulative distribution function</span></div> |
| <div class="line"><a name="l01235"></a><span class="lineno"> 1235</span> <span class="comment"> *</span></div> |
| <div class="line"><a name="l01236"></a><span class="lineno"> 1236</span> <span class="comment"> * @param x Random variate \f$ x \f$</span></div> |
| <div class="line"><a name="l01237"></a><span class="lineno"> 1237</span> <span class="comment"> * @param df Degrees of freedom \f$ \nu > 0 \f$</span></div> |
| <div class="line"><a name="l01238"></a><span class="lineno"> 1238</span> <span class="comment"> * @param ncp Noncentrality parameter \f$ \delta \f$</span></div> |
| <div class="line"><a name="l01239"></a><span class="lineno"> 1239</span> <span class="comment"> * @return \f$ \Pr[X \leq x] \f$ where \f$ X \f$ is a noncentral Student's</span></div> |
| <div class="line"><a name="l01240"></a><span class="lineno"> 1240</span> <span class="comment"> * t-distributed random variable with \f$ \nu \f$ degrees of freedom and</span></div> |
| <div class="line"><a name="l01241"></a><span class="lineno"> 1241</span> <span class="comment"> * noncentrality parameter \f$ \delta \f$</span></div> |
| <div class="line"><a name="l01242"></a><span class="lineno"> 1242</span> <span class="comment"> */</span></div> |
| <div class="line"><a name="l01243"></a><span class="lineno"> 1243</span> CREATE FUNCTION MADLIB_SCHEMA.non_central_t_cdf(</div> |
| <div class="line"><a name="l01244"></a><span class="lineno"><a class="code" href="prob_8sql__in.html#a92b2a978db480a6c78cfb708107ecb92"> 1244</a></span>  x DOUBLE PRECISION,</div> |
| <div class="line"><a name="l01245"></a><span class="lineno"> 1245</span>  df DOUBLE PRECISION,</div> |
| <div class="line"><a name="l01246"></a><span class="lineno"> 1246</span>  ncp DOUBLE PRECISION</div> |
| <div class="line"><a name="l01247"></a><span class="lineno"> 1247</span> ) RETURNS DOUBLE PRECISION</div> |
| <div class="line"><a name="l01248"></a><span class="lineno"> 1248</span> AS 'MODULE_PATHNAME<span class="stringliteral">'</span></div> |
| <div class="line"><a name="l01249"></a><span class="lineno"> 1249</span> <span class="stringliteral">LANGUAGE C</span></div> |
| <div class="line"><a name="l01250"></a><span class="lineno"> 1250</span> <span class="stringliteral">IMMUTABLE STRICT;</span></div> |
| <div class="line"><a name="l01251"></a><span class="lineno"> 1251</span> <span class="stringliteral"></span><span class="comment"></span></div> |
| <div class="line"><a name="l01252"></a><span class="lineno"> 1252</span> <span class="comment">/**</span></div> |
| <div class="line"><a name="l01253"></a><span class="lineno"> 1253</span> <span class="comment"> * @brief Noncentral Student-t probability density function</span></div> |
| <div class="line"><a name="l01254"></a><span class="lineno"> 1254</span> <span class="comment"> *</span></div> |
| <div class="line"><a name="l01255"></a><span class="lineno"> 1255</span> <span class="comment"> * @param x Random variate \f$ x \f$</span></div> |
| <div class="line"><a name="l01256"></a><span class="lineno"> 1256</span> <span class="comment"> * @param df Degrees of freedom \f$ \nu > 0 \f$</span></div> |
| <div class="line"><a name="l01257"></a><span class="lineno"> 1257</span> <span class="comment"> * @param ncp Noncentrality parameter \f$ \delta \f$</span></div> |
| <div class="line"><a name="l01258"></a><span class="lineno"> 1258</span> <span class="comment"> * @return \f$ x \f$ such that \f$ p = \Pr[X \leq x] \f$ where \f$ X \f$ is a</span></div> |
| <div class="line"><a name="l01259"></a><span class="lineno"> 1259</span> <span class="comment"> * noncentral Student's t-distributed random variable with \f$ \nu \f$</span></div> |
| <div class="line"><a name="l01260"></a><span class="lineno"> 1260</span> <span class="comment"> * degrees of freedom and noncentrality parameter \f$ \delta \f$</span></div> |
| <div class="line"><a name="l01261"></a><span class="lineno"> 1261</span> <span class="comment"> */</span></div> |
| <div class="line"><a name="l01262"></a><span class="lineno"> 1262</span> CREATE FUNCTION MADLIB_SCHEMA.non_central_t_pdf(</div> |
| <div class="line"><a name="l01263"></a><span class="lineno"> 1263</span>  x DOUBLE PRECISION,</div> |
| <div class="line"><a name="l01264"></a><span class="lineno"> 1264</span>  df DOUBLE PRECISION,</div> |
| <div class="line"><a name="l01265"></a><span class="lineno"><a class="code" href="prob_8sql__in.html#afaf4374d2720b230a54713e21ecb1955"> 1265</a></span>  ncp DOUBLE PRECISION</div> |
| <div class="line"><a name="l01266"></a><span class="lineno"> 1266</span> ) RETURNS DOUBLE PRECISION</div> |
| <div class="line"><a name="l01267"></a><span class="lineno"> 1267</span> AS 'MODULE_PATHNAME<span class="stringliteral">'</span></div> |
| <div class="line"><a name="l01268"></a><span class="lineno"> 1268</span> <span class="stringliteral">LANGUAGE C</span></div> |
| <div class="line"><a name="l01269"></a><span class="lineno"> 1269</span> <span class="stringliteral">IMMUTABLE STRICT;</span></div> |
| <div class="line"><a name="l01270"></a><span class="lineno"> 1270</span> <span class="stringliteral"></span><span class="comment"></span></div> |
| <div class="line"><a name="l01271"></a><span class="lineno"> 1271</span> <span class="comment">/**</span></div> |
| <div class="line"><a name="l01272"></a><span class="lineno"> 1272</span> <span class="comment"> * @brief Noncentral Student-t quantile function</span></div> |
| <div class="line"><a name="l01273"></a><span class="lineno"> 1273</span> <span class="comment"> *</span></div> |
| <div class="line"><a name="l01274"></a><span class="lineno"> 1274</span> <span class="comment"> * @param p Probability \f$ p \in [0,1] \f$</span></div> |
| <div class="line"><a name="l01275"></a><span class="lineno"> 1275</span> <span class="comment"> * @param df Degrees of freedom \f$ \nu > 0 \f$</span></div> |
| <div class="line"><a name="l01276"></a><span class="lineno"> 1276</span> <span class="comment"> * @param ncp Noncentrality parameter \f$ \delta \f$</span></div> |
| <div class="line"><a name="l01277"></a><span class="lineno"> 1277</span> <span class="comment"> * @return \f$ x \f$ such that \f$ p = \Pr[X \leq x] \f$ where \f$ X \f$ is a</span></div> |
| <div class="line"><a name="l01278"></a><span class="lineno"> 1278</span> <span class="comment"> * noncentral Student's t-distributed random variable with \f$ \nu \f$</span></div> |
| <div class="line"><a name="l01279"></a><span class="lineno"> 1279</span> <span class="comment"> * degrees of freedom and noncentrality parameter \f$ \delta \f$</span></div> |
| <div class="line"><a name="l01280"></a><span class="lineno"> 1280</span> <span class="comment"> */</span></div> |
| <div class="line"><a name="l01281"></a><span class="lineno"> 1281</span> CREATE FUNCTION MADLIB_SCHEMA.non_central_t_quantile(</div> |
| <div class="line"><a name="l01282"></a><span class="lineno"> 1282</span>  p DOUBLE PRECISION,</div> |
| <div class="line"><a name="l01283"></a><span class="lineno"> 1283</span>  df DOUBLE PRECISION,</div> |
| <div class="line"><a name="l01284"></a><span class="lineno"><a class="code" href="prob_8sql__in.html#a4799e3bb68a496d9bc1ef1ea85265409"> 1284</a></span>  ncp DOUBLE PRECISION</div> |
| <div class="line"><a name="l01285"></a><span class="lineno"> 1285</span> ) RETURNS DOUBLE PRECISION</div> |
| <div class="line"><a name="l01286"></a><span class="lineno"> 1286</span> AS 'MODULE_PATHNAME<span class="stringliteral">'</span></div> |
| <div class="line"><a name="l01287"></a><span class="lineno"> 1287</span> <span class="stringliteral">LANGUAGE C</span></div> |
| <div class="line"><a name="l01288"></a><span class="lineno"> 1288</span> <span class="stringliteral">IMMUTABLE STRICT;</span></div> |
| <div class="line"><a name="l01289"></a><span class="lineno"> 1289</span> <span class="stringliteral"></span></div> |
| <div class="line"><a name="l01290"></a><span class="lineno"> 1290</span> <span class="stringliteral"></span><span class="comment"></span></div> |
| <div class="line"><a name="l01291"></a><span class="lineno"> 1291</span> <span class="comment">/**</span></div> |
| <div class="line"><a name="l01292"></a><span class="lineno"> 1292</span> <span class="comment"> * @brief Normal cumulative distribution function</span></div> |
| <div class="line"><a name="l01293"></a><span class="lineno"> 1293</span> <span class="comment"> *</span></div> |
| <div class="line"><a name="l01294"></a><span class="lineno"> 1294</span> <span class="comment"> * @param x Random variate \f$ x \f$</span></div> |
| <div class="line"><a name="l01295"></a><span class="lineno"> 1295</span> <span class="comment"> * @param mean Mean \f$ \mu \f$</span></div> |
| <div class="line"><a name="l01296"></a><span class="lineno"> 1296</span> <span class="comment"> * @param sd Standard deviation \f$ \sigma > 0 \f$</span></div> |
| <div class="line"><a name="l01297"></a><span class="lineno"> 1297</span> <span class="comment"> * @return \f$ \Pr[X \leq x] \f$ where \f$ T \f$ is a normally distributed</span></div> |
| <div class="line"><a name="l01298"></a><span class="lineno"> 1298</span> <span class="comment"> * random variable with mean \f$ \mu \f$ and variance \f$ \sigma^2 \f$</span></div> |
| <div class="line"><a name="l01299"></a><span class="lineno"> 1299</span> <span class="comment"> */</span></div> |
| <div class="line"><a name="l01300"></a><span class="lineno"> 1300</span> CREATE FUNCTION MADLIB_SCHEMA.normal_cdf(</div> |
| <div class="line"><a name="l01301"></a><span class="lineno"> 1301</span>  x DOUBLE PRECISION,</div> |
| <div class="line"><a name="l01302"></a><span class="lineno"> 1302</span>  mean DOUBLE PRECISION /*+ DEFAULT 0 */,</div> |
| <div class="line"><a name="l01303"></a><span class="lineno"><a class="code" href="prob_8sql__in.html#af50865aba2ece2e23b2af461a02f7d12"> 1303</a></span>  sd DOUBLE PRECISION /*+ DEFAULT 1 */</div> |
| <div class="line"><a name="l01304"></a><span class="lineno"> 1304</span> ) RETURNS DOUBLE PRECISION</div> |
| <div class="line"><a name="l01305"></a><span class="lineno"> 1305</span> AS 'MODULE_PATHNAME<span class="stringliteral">'</span></div> |
| <div class="line"><a name="l01306"></a><span class="lineno"> 1306</span> <span class="stringliteral">LANGUAGE C</span></div> |
| <div class="line"><a name="l01307"></a><span class="lineno"> 1307</span> <span class="stringliteral">IMMUTABLE STRICT;</span></div> |
| <div class="line"><a name="l01308"></a><span class="lineno"> 1308</span> <span class="stringliteral"></span></div> |
| <div class="line"><a name="l01309"></a><span class="lineno"> 1309</span> <span class="stringliteral">CREATE FUNCTION MADLIB_SCHEMA.normal_cdf(</span></div> |
| <div class="line"><a name="l01310"></a><span class="lineno"> 1310</span> <span class="stringliteral"> x DOUBLE PRECISION,</span></div> |
| <div class="line"><a name="l01311"></a><span class="lineno"> 1311</span> <span class="stringliteral"> mean DOUBLE PRECISION</span></div> |
| <div class="line"><a name="l01312"></a><span class="lineno"> 1312</span> <span class="stringliteral">) RETURNS DOUBLE PRECISION</span></div> |
| <div class="line"><a name="l01313"></a><span class="lineno"> 1313</span> <span class="stringliteral">IMMUTABLE</span></div> |
| <div class="line"><a name="l01314"></a><span class="lineno"> 1314</span> <span class="stringliteral">STRICT</span></div> |
| <div class="line"><a name="l01315"></a><span class="lineno"> 1315</span> <span class="stringliteral">LANGUAGE sql AS $$</span></div> |
| <div class="line"><a name="l01316"></a><span class="lineno"> 1316</span> <span class="stringliteral"> SELECT MADLIB_SCHEMA.normal_cdf($1, $2, 1)</span></div> |
| <div class="line"><a name="l01317"></a><span class="lineno"> 1317</span> <span class="stringliteral">$$;</span></div> |
| <div class="line"><a name="l01318"></a><span class="lineno"> 1318</span> <span class="stringliteral"></span></div> |
| <div class="line"><a name="l01319"></a><span class="lineno"> 1319</span> <span class="stringliteral">CREATE FUNCTION MADLIB_SCHEMA.normal_cdf(</span></div> |
| <div class="line"><a name="l01320"></a><span class="lineno"> 1320</span> <span class="stringliteral"> x DOUBLE PRECISION</span></div> |
| <div class="line"><a name="l01321"></a><span class="lineno"> 1321</span> <span class="stringliteral">) RETURNS DOUBLE PRECISION</span></div> |
| <div class="line"><a name="l01322"></a><span class="lineno"><a class="code" href="prob_8sql__in.html#aebcd34ad7b1ca4b31d9699112c9a3b90"> 1322</a></span> <span class="stringliteral">IMMUTABLE</span></div> |
| <div class="line"><a name="l01323"></a><span class="lineno"> 1323</span> <span class="stringliteral">STRICT</span></div> |
| <div class="line"><a name="l01324"></a><span class="lineno"> 1324</span> <span class="stringliteral">LANGUAGE sql AS $$</span></div> |
| <div class="line"><a name="l01325"></a><span class="lineno"> 1325</span> <span class="stringliteral"> SELECT MADLIB_SCHEMA.normal_cdf($1, 0, 1)</span></div> |
| <div class="line"><a name="l01326"></a><span class="lineno"> 1326</span> <span class="stringliteral">$$;</span></div> |
| <div class="line"><a name="l01327"></a><span class="lineno"> 1327</span> <span class="stringliteral"></span><span class="comment"></span></div> |
| <div class="line"><a name="l01328"></a><span class="lineno"> 1328</span> <span class="comment">/**</span></div> |
| <div class="line"><a name="l01329"></a><span class="lineno"> 1329</span> <span class="comment"> * @brief Normal probability density function</span></div> |
| <div class="line"><a name="l01330"></a><span class="lineno"> 1330</span> <span class="comment"> *</span></div> |
| <div class="line"><a name="l01331"></a><span class="lineno"> 1331</span> <span class="comment"> * @param x Random variate \f$ x \f$</span></div> |
| <div class="line"><a name="l01332"></a><span class="lineno"> 1332</span> <span class="comment"> * @param mean Mean \f$ \mu \f$</span></div> |
| <div class="line"><a name="l01333"></a><span class="lineno"> 1333</span> <span class="comment"> * @param sd Standard deviation \f$ \sigma > 0 \f$</span></div> |
| <div class="line"><a name="l01334"></a><span class="lineno"> 1334</span> <span class="comment"> * @return \f$ f(x) \f$ where \f$ f \f$ is the probability density function of</span></div> |
| <div class="line"><a name="l01335"></a><span class="lineno"> 1335</span> <span class="comment"> * a normally distributed random variable with mean \f$ \mu \f$ and</span></div> |
| <div class="line"><a name="l01336"></a><span class="lineno"> 1336</span> <span class="comment"> * variance \f$ \sigma^2 \f$</span></div> |
| <div class="line"><a name="l01337"></a><span class="lineno"> 1337</span> <span class="comment"> */</span></div> |
| <div class="line"><a name="l01338"></a><span class="lineno"> 1338</span> CREATE FUNCTION MADLIB_SCHEMA.normal_pdf(</div> |
| <div class="line"><a name="l01339"></a><span class="lineno"> 1339</span>  x DOUBLE PRECISION,</div> |
| <div class="line"><a name="l01340"></a><span class="lineno"> 1340</span>  mean DOUBLE PRECISION /*+ DEFAULT 0 */,</div> |
| <div class="line"><a name="l01341"></a><span class="lineno"> 1341</span>  sd DOUBLE PRECISION /*+ DEFAULT 1 */</div> |
| <div class="line"><a name="l01342"></a><span class="lineno"> 1342</span> ) RETURNS DOUBLE PRECISION</div> |
| <div class="line"><a name="l01343"></a><span class="lineno"> 1343</span> AS 'MODULE_PATHNAME<span class="stringliteral">'</span></div> |
| <div class="line"><a name="l01344"></a><span class="lineno"> 1344</span> <span class="stringliteral">LANGUAGE C</span></div> |
| <div class="line"><a name="l01345"></a><span class="lineno"> 1345</span> <span class="stringliteral">IMMUTABLE STRICT;</span></div> |
| <div class="line"><a name="l01346"></a><span class="lineno"> 1346</span> <span class="stringliteral"></span></div> |
| <div class="line"><a name="l01347"></a><span class="lineno"> 1347</span> <span class="stringliteral">CREATE FUNCTION MADLIB_SCHEMA.normal_pdf(</span></div> |
| <div class="line"><a name="l01348"></a><span class="lineno"> 1348</span> <span class="stringliteral"> x DOUBLE PRECISION,</span></div> |
| <div class="line"><a name="l01349"></a><span class="lineno"> 1349</span> <span class="stringliteral"> mean DOUBLE PRECISION</span></div> |
| <div class="line"><a name="l01350"></a><span class="lineno"> 1350</span> <span class="stringliteral">) RETURNS DOUBLE PRECISION</span></div> |
| <div class="line"><a name="l01351"></a><span class="lineno"> 1351</span> <span class="stringliteral">IMMUTABLE</span></div> |
| <div class="line"><a name="l01352"></a><span class="lineno"> 1352</span> <span class="stringliteral">STRICT</span></div> |
| <div class="line"><a name="l01353"></a><span class="lineno"> 1353</span> <span class="stringliteral">LANGUAGE sql AS $$</span></div> |
| <div class="line"><a name="l01354"></a><span class="lineno"> 1354</span> <span class="stringliteral"> SELECT MADLIB_SCHEMA.normal_pdf($1, $2, 1)</span></div> |
| <div class="line"><a name="l01355"></a><span class="lineno"> 1355</span> <span class="stringliteral">$$;</span></div> |
| <div class="line"><a name="l01356"></a><span class="lineno"> 1356</span> <span class="stringliteral"></span></div> |
| <div class="line"><a name="l01357"></a><span class="lineno"> 1357</span> <span class="stringliteral">CREATE FUNCTION MADLIB_SCHEMA.normal_pdf(</span></div> |
| <div class="line"><a name="l01358"></a><span class="lineno"> 1358</span> <span class="stringliteral"> x DOUBLE PRECISION</span></div> |
| <div class="line"><a name="l01359"></a><span class="lineno"> 1359</span> <span class="stringliteral">) RETURNS DOUBLE PRECISION</span></div> |
| <div class="line"><a name="l01360"></a><span class="lineno"><a class="code" href="prob_8sql__in.html#a63f555f36385d86e229cdca223e39567"> 1360</a></span> <span class="stringliteral">IMMUTABLE</span></div> |
| <div class="line"><a name="l01361"></a><span class="lineno"> 1361</span> <span class="stringliteral">STRICT</span></div> |
| <div class="line"><a name="l01362"></a><span class="lineno"> 1362</span> <span class="stringliteral">LANGUAGE sql AS $$</span></div> |
| <div class="line"><a name="l01363"></a><span class="lineno"> 1363</span> <span class="stringliteral"> SELECT MADLIB_SCHEMA.normal_pdf($1, 0, 1)</span></div> |
| <div class="line"><a name="l01364"></a><span class="lineno"> 1364</span> <span class="stringliteral">$$;</span></div> |
| <div class="line"><a name="l01365"></a><span class="lineno"> 1365</span> <span class="stringliteral"></span><span class="comment"></span></div> |
| <div class="line"><a name="l01366"></a><span class="lineno"> 1366</span> <span class="comment">/**</span></div> |
| <div class="line"><a name="l01367"></a><span class="lineno"> 1367</span> <span class="comment"> * @brief Normal quantile function</span></div> |
| <div class="line"><a name="l01368"></a><span class="lineno"> 1368</span> <span class="comment"> *</span></div> |
| <div class="line"><a name="l01369"></a><span class="lineno"> 1369</span> <span class="comment"> * @param p Probability \f$ p \in [0,1] \f$</span></div> |
| <div class="line"><a name="l01370"></a><span class="lineno"> 1370</span> <span class="comment"> * @param mean Mean \f$ \mu \f$</span></div> |
| <div class="line"><a name="l01371"></a><span class="lineno"> 1371</span> <span class="comment"> * @param sd Standard deviation \f$ \sigma > 0 \f$</span></div> |
| <div class="line"><a name="l01372"></a><span class="lineno"> 1372</span> <span class="comment"> * @return \f$ x \f$ such that \f$ p = \Pr[X \leq x] \f$ where \f$ X \f$ is a</span></div> |
| <div class="line"><a name="l01373"></a><span class="lineno"> 1373</span> <span class="comment"> * normally distributed random variable with mean \f$ \mu \f$ and</span></div> |
| <div class="line"><a name="l01374"></a><span class="lineno"> 1374</span> <span class="comment"> * variance \f$ \sigma^2 \f$</span></div> |
| <div class="line"><a name="l01375"></a><span class="lineno"> 1375</span> <span class="comment"> */</span></div> |
| <div class="line"><a name="l01376"></a><span class="lineno"> 1376</span> CREATE FUNCTION MADLIB_SCHEMA.normal_quantile(</div> |
| <div class="line"><a name="l01377"></a><span class="lineno"> 1377</span>  p DOUBLE PRECISION,</div> |
| <div class="line"><a name="l01378"></a><span class="lineno"> 1378</span>  mean DOUBLE PRECISION /*+ DEFAULT 0 */,</div> |
| <div class="line"><a name="l01379"></a><span class="lineno"> 1379</span>  sd DOUBLE PRECISION /*+ DEFAULT 1 */</div> |
| <div class="line"><a name="l01380"></a><span class="lineno"> 1380</span> ) RETURNS DOUBLE PRECISION</div> |
| <div class="line"><a name="l01381"></a><span class="lineno"> 1381</span> AS 'MODULE_PATHNAME<span class="stringliteral">'</span></div> |
| <div class="line"><a name="l01382"></a><span class="lineno"> 1382</span> <span class="stringliteral">LANGUAGE C</span></div> |
| <div class="line"><a name="l01383"></a><span class="lineno"> 1383</span> <span class="stringliteral">IMMUTABLE STRICT;</span></div> |
| <div class="line"><a name="l01384"></a><span class="lineno"> 1384</span> <span class="stringliteral"></span></div> |
| <div class="line"><a name="l01385"></a><span class="lineno"> 1385</span> <span class="stringliteral">CREATE FUNCTION MADLIB_SCHEMA.normal_quantile(</span></div> |
| <div class="line"><a name="l01386"></a><span class="lineno"> 1386</span> <span class="stringliteral"> p DOUBLE PRECISION,</span></div> |
| <div class="line"><a name="l01387"></a><span class="lineno"> 1387</span> <span class="stringliteral"> mean DOUBLE PRECISION</span></div> |
| <div class="line"><a name="l01388"></a><span class="lineno"> 1388</span> <span class="stringliteral">) RETURNS DOUBLE PRECISION</span></div> |
| <div class="line"><a name="l01389"></a><span class="lineno"> 1389</span> <span class="stringliteral">IMMUTABLE</span></div> |
| <div class="line"><a name="l01390"></a><span class="lineno"> 1390</span> <span class="stringliteral">STRICT</span></div> |
| <div class="line"><a name="l01391"></a><span class="lineno"> 1391</span> <span class="stringliteral">LANGUAGE sql AS $$</span></div> |
| <div class="line"><a name="l01392"></a><span class="lineno"> 1392</span> <span class="stringliteral"> SELECT MADLIB_SCHEMA.normal_quantile($1, $2, 1)</span></div> |
| <div class="line"><a name="l01393"></a><span class="lineno"> 1393</span> <span class="stringliteral">$$;</span></div> |
| <div class="line"><a name="l01394"></a><span class="lineno"> 1394</span> <span class="stringliteral"></span></div> |
| <div class="line"><a name="l01395"></a><span class="lineno"> 1395</span> <span class="stringliteral">CREATE FUNCTION MADLIB_SCHEMA.normal_quantile(</span></div> |
| <div class="line"><a name="l01396"></a><span class="lineno"> 1396</span> <span class="stringliteral"> p DOUBLE PRECISION</span></div> |
| <div class="line"><a name="l01397"></a><span class="lineno"> 1397</span> <span class="stringliteral">) RETURNS DOUBLE PRECISION</span></div> |
| <div class="line"><a name="l01398"></a><span class="lineno"><a class="code" href="prob_8sql__in.html#a53d56b672fe4cd1277cb5eac5de5118f"> 1398</a></span> <span class="stringliteral">IMMUTABLE</span></div> |
| <div class="line"><a name="l01399"></a><span class="lineno"> 1399</span> <span class="stringliteral">STRICT</span></div> |
| <div class="line"><a name="l01400"></a><span class="lineno"> 1400</span> <span class="stringliteral">LANGUAGE sql AS $$</span></div> |
| <div class="line"><a name="l01401"></a><span class="lineno"> 1401</span> <span class="stringliteral"> SELECT MADLIB_SCHEMA.normal_quantile($1, 0, 1)</span></div> |
| <div class="line"><a name="l01402"></a><span class="lineno"> 1402</span> <span class="stringliteral">$$;</span></div> |
| <div class="line"><a name="l01403"></a><span class="lineno"> 1403</span> <span class="stringliteral"></span></div> |
| <div class="line"><a name="l01404"></a><span class="lineno"> 1404</span> <span class="stringliteral"></span><span class="comment"></span></div> |
| <div class="line"><a name="l01405"></a><span class="lineno"> 1405</span> <span class="comment">/**</span></div> |
| <div class="line"><a name="l01406"></a><span class="lineno"> 1406</span> <span class="comment"> * @brief Pareto cumulative distribution function</span></div> |
| <div class="line"><a name="l01407"></a><span class="lineno"> 1407</span> <span class="comment"> *</span></div> |
| <div class="line"><a name="l01408"></a><span class="lineno"> 1408</span> <span class="comment"> * @param x Random variate \f$ x \f$</span></div> |
| <div class="line"><a name="l01409"></a><span class="lineno"> 1409</span> <span class="comment"> * @param scale Scale \f$ \beta > 0 \f$</span></div> |
| <div class="line"><a name="l01410"></a><span class="lineno"> 1410</span> <span class="comment"> * @param shape Shape \f$ \alpha > 0 \f$</span></div> |
| <div class="line"><a name="l01411"></a><span class="lineno"> 1411</span> <span class="comment"> * @return \f$ \Pr[X \leq x] \f$ where \f$ X \f$ is a Pareto-distributed random</span></div> |
| <div class="line"><a name="l01412"></a><span class="lineno"> 1412</span> <span class="comment"> * variable with shape and scale parameters \f$ \alpha \f$ and</span></div> |
| <div class="line"><a name="l01413"></a><span class="lineno"> 1413</span> <span class="comment"> * \f$ \beta \f$, respectively</span></div> |
| <div class="line"><a name="l01414"></a><span class="lineno"> 1414</span> <span class="comment"> */</span></div> |
| <div class="line"><a name="l01415"></a><span class="lineno"> 1415</span> CREATE FUNCTION MADLIB_SCHEMA.pareto_cdf(</div> |
| <div class="line"><a name="l01416"></a><span class="lineno"> 1416</span>  x DOUBLE PRECISION,</div> |
| <div class="line"><a name="l01417"></a><span class="lineno"> 1417</span>  scale DOUBLE PRECISION,</div> |
| <div class="line"><a name="l01418"></a><span class="lineno"> 1418</span>  shape DOUBLE PRECISION</div> |
| <div class="line"><a name="l01419"></a><span class="lineno"> 1419</span> ) RETURNS DOUBLE PRECISION</div> |
| <div class="line"><a name="l01420"></a><span class="lineno"> 1420</span> AS 'MODULE_PATHNAME<span class="stringliteral">'</span></div> |
| <div class="line"><a name="l01421"></a><span class="lineno"> 1421</span> <span class="stringliteral">LANGUAGE C</span></div> |
| <div class="line"><a name="l01422"></a><span class="lineno"> 1422</span> <span class="stringliteral">IMMUTABLE STRICT;</span></div> |
| <div class="line"><a name="l01423"></a><span class="lineno"> 1423</span> <span class="stringliteral"></span><span class="comment"></span></div> |
| <div class="line"><a name="l01424"></a><span class="lineno"> 1424</span> <span class="comment">/**</span></div> |
| <div class="line"><a name="l01425"></a><span class="lineno"> 1425</span> <span class="comment"> * @brief Pareto probability density function</span></div> |
| <div class="line"><a name="l01426"></a><span class="lineno"> 1426</span> <span class="comment"> *</span></div> |
| <div class="line"><a name="l01427"></a><span class="lineno"> 1427</span> <span class="comment"> * @param x Random variate \f$ x \f$</span></div> |
| <div class="line"><a name="l01428"></a><span class="lineno"> 1428</span> <span class="comment"> * @param scale Scale \f$ \beta > 0 \f$</span></div> |
| <div class="line"><a name="l01429"></a><span class="lineno"> 1429</span> <span class="comment"> * @param shape Shape \f$ \alpha > 0 \f$</span></div> |
| <div class="line"><a name="l01430"></a><span class="lineno"> 1430</span> <span class="comment"> * @return \f$ f(x) \f$ where \f$ f \f$ is the probability density function of</span></div> |
| <div class="line"><a name="l01431"></a><span class="lineno"> 1431</span> <span class="comment"> * a Pareto-distributed random variable with shape and scale parameters</span></div> |
| <div class="line"><a name="l01432"></a><span class="lineno"> 1432</span> <span class="comment"> * \f$ \alpha \f$ and \f$ \beta \f$, respectively</span></div> |
| <div class="line"><a name="l01433"></a><span class="lineno"> 1433</span> <span class="comment"> */</span></div> |
| <div class="line"><a name="l01434"></a><span class="lineno"> 1434</span> CREATE FUNCTION MADLIB_SCHEMA.pareto_pdf(</div> |
| <div class="line"><a name="l01435"></a><span class="lineno"> 1435</span>  x DOUBLE PRECISION,</div> |
| <div class="line"><a name="l01436"></a><span class="lineno"> 1436</span>  scale DOUBLE PRECISION,</div> |
| <div class="line"><a name="l01437"></a><span class="lineno"><a class="code" href="prob_8sql__in.html#aa1a42ebd68f20f65bc1784b427721b5d"> 1437</a></span>  shape DOUBLE PRECISION</div> |
| <div class="line"><a name="l01438"></a><span class="lineno"> 1438</span> ) RETURNS DOUBLE PRECISION</div> |
| <div class="line"><a name="l01439"></a><span class="lineno"> 1439</span> AS 'MODULE_PATHNAME<span class="stringliteral">'</span></div> |
| <div class="line"><a name="l01440"></a><span class="lineno"> 1440</span> <span class="stringliteral">LANGUAGE C</span></div> |
| <div class="line"><a name="l01441"></a><span class="lineno"> 1441</span> <span class="stringliteral">IMMUTABLE STRICT;</span></div> |
| <div class="line"><a name="l01442"></a><span class="lineno"> 1442</span> <span class="stringliteral"></span><span class="comment"></span></div> |
| <div class="line"><a name="l01443"></a><span class="lineno"> 1443</span> <span class="comment">/**</span></div> |
| <div class="line"><a name="l01444"></a><span class="lineno"> 1444</span> <span class="comment"> * @brief Pareto quantile function</span></div> |
| <div class="line"><a name="l01445"></a><span class="lineno"> 1445</span> <span class="comment"> *</span></div> |
| <div class="line"><a name="l01446"></a><span class="lineno"> 1446</span> <span class="comment"> * @param p Probability \f$ p \in [0,1] \f$</span></div> |
| <div class="line"><a name="l01447"></a><span class="lineno"> 1447</span> <span class="comment"> * @param scale Scale \f$ \beta > 0 \f$</span></div> |
| <div class="line"><a name="l01448"></a><span class="lineno"> 1448</span> <span class="comment"> * @param shape Shape \f$ \alpha > 0 \f$</span></div> |
| <div class="line"><a name="l01449"></a><span class="lineno"> 1449</span> <span class="comment"> * @return \f$ x \f$ such that \f$ p = \Pr[X \leq x] \f$ where \f$ X \f$ is a</span></div> |
| <div class="line"><a name="l01450"></a><span class="lineno"> 1450</span> <span class="comment"> * Pareto-distributed random variable with shape and scale parameters</span></div> |
| <div class="line"><a name="l01451"></a><span class="lineno"> 1451</span> <span class="comment"> * \f$ \alpha \f$ and \f$ \beta \f$, respectively</span></div> |
| <div class="line"><a name="l01452"></a><span class="lineno"> 1452</span> <span class="comment"> */</span></div> |
| <div class="line"><a name="l01453"></a><span class="lineno"> 1453</span> CREATE FUNCTION MADLIB_SCHEMA.pareto_quantile(</div> |
| <div class="line"><a name="l01454"></a><span class="lineno"> 1454</span>  p DOUBLE PRECISION,</div> |
| <div class="line"><a name="l01455"></a><span class="lineno"> 1455</span>  scale DOUBLE PRECISION,</div> |
| <div class="line"><a name="l01456"></a><span class="lineno"><a class="code" href="prob_8sql__in.html#a22c56a6e48bc442435b13afac2a1eb37"> 1456</a></span>  shape DOUBLE PRECISION</div> |
| <div class="line"><a name="l01457"></a><span class="lineno"> 1457</span> ) RETURNS DOUBLE PRECISION</div> |
| <div class="line"><a name="l01458"></a><span class="lineno"> 1458</span> AS 'MODULE_PATHNAME<span class="stringliteral">'</span></div> |
| <div class="line"><a name="l01459"></a><span class="lineno"> 1459</span> <span class="stringliteral">LANGUAGE C</span></div> |
| <div class="line"><a name="l01460"></a><span class="lineno"> 1460</span> <span class="stringliteral">IMMUTABLE STRICT;</span></div> |
| <div class="line"><a name="l01461"></a><span class="lineno"> 1461</span> <span class="stringliteral"></span></div> |
| <div class="line"><a name="l01462"></a><span class="lineno"> 1462</span> <span class="stringliteral"></span><span class="comment"></span></div> |
| <div class="line"><a name="l01463"></a><span class="lineno"> 1463</span> <span class="comment">/**</span></div> |
| <div class="line"><a name="l01464"></a><span class="lineno"> 1464</span> <span class="comment"> * @brief Poisson cumulative distribution function</span></div> |
| <div class="line"><a name="l01465"></a><span class="lineno"> 1465</span> <span class="comment"> *</span></div> |
| <div class="line"><a name="l01466"></a><span class="lineno"> 1466</span> <span class="comment"> * @param x Random variate \f$ x \f$</span></div> |
| <div class="line"><a name="l01467"></a><span class="lineno"> 1467</span> <span class="comment"> * @param mean Average occurrence rate \f$ \lambda > 0 \f$</span></div> |
| <div class="line"><a name="l01468"></a><span class="lineno"> 1468</span> <span class="comment"> * @return \f$ \Pr[X \leq x] \f$ where \f$ X \f$ is a Poisson distributed random</span></div> |
| <div class="line"><a name="l01469"></a><span class="lineno"> 1469</span> <span class="comment"> * variable with mean \f$ \lambda \f$</span></div> |
| <div class="line"><a name="l01470"></a><span class="lineno"> 1470</span> <span class="comment"> */</span></div> |
| <div class="line"><a name="l01471"></a><span class="lineno"> 1471</span> CREATE FUNCTION MADLIB_SCHEMA.poisson_cdf(</div> |
| <div class="line"><a name="l01472"></a><span class="lineno"> 1472</span>  x DOUBLE PRECISION,</div> |
| <div class="line"><a name="l01473"></a><span class="lineno"> 1473</span>  mean DOUBLE PRECISION</div> |
| <div class="line"><a name="l01474"></a><span class="lineno"> 1474</span> ) RETURNS DOUBLE PRECISION</div> |
| <div class="line"><a name="l01475"></a><span class="lineno"><a class="code" href="prob_8sql__in.html#a77779e2b5fa951189ccba6806c503c4d"> 1475</a></span> AS 'MODULE_PATHNAME<span class="stringliteral">'</span></div> |
| <div class="line"><a name="l01476"></a><span class="lineno"> 1476</span> <span class="stringliteral">LANGUAGE C</span></div> |
| <div class="line"><a name="l01477"></a><span class="lineno"> 1477</span> <span class="stringliteral">IMMUTABLE STRICT;</span></div> |
| <div class="line"><a name="l01478"></a><span class="lineno"> 1478</span> <span class="stringliteral"></span><span class="comment"></span></div> |
| <div class="line"><a name="l01479"></a><span class="lineno"> 1479</span> <span class="comment">/**</span></div> |
| <div class="line"><a name="l01480"></a><span class="lineno"> 1480</span> <span class="comment"> * @brief Poisson probability mass function</span></div> |
| <div class="line"><a name="l01481"></a><span class="lineno"> 1481</span> <span class="comment"> *</span></div> |
| <div class="line"><a name="l01482"></a><span class="lineno"> 1482</span> <span class="comment"> * @param x Random variate \f$ x \f$</span></div> |
| <div class="line"><a name="l01483"></a><span class="lineno"> 1483</span> <span class="comment"> * @param mean Average occurrence rate \f$ \lambda > 0 \f$</span></div> |
| <div class="line"><a name="l01484"></a><span class="lineno"> 1484</span> <span class="comment"> * @return \f$ f(x) \f$ where \f$ f \f$ is the probability mass function of a</span></div> |
| <div class="line"><a name="l01485"></a><span class="lineno"> 1485</span> <span class="comment"> * Poisson distributed random variable with mean \f$ \lambda \f$</span></div> |
| <div class="line"><a name="l01486"></a><span class="lineno"> 1486</span> <span class="comment"> */</span></div> |
| <div class="line"><a name="l01487"></a><span class="lineno"> 1487</span> CREATE FUNCTION MADLIB_SCHEMA.poisson_pmf(</div> |
| <div class="line"><a name="l01488"></a><span class="lineno"> 1488</span>  x INT4,</div> |
| <div class="line"><a name="l01489"></a><span class="lineno"> 1489</span>  mean DOUBLE PRECISION</div> |
| <div class="line"><a name="l01490"></a><span class="lineno"> 1490</span> ) RETURNS DOUBLE PRECISION</div> |
| <div class="line"><a name="l01491"></a><span class="lineno"> 1491</span> AS 'MODULE_PATHNAME<span class="stringliteral">'</span></div> |
| <div class="line"><a name="l01492"></a><span class="lineno"> 1492</span> <span class="stringliteral">LANGUAGE C</span></div> |
| <div class="line"><a name="l01493"></a><span class="lineno"><a class="code" href="prob_8sql__in.html#ae0b4313d9fe730d6efb3f7c44206f345"> 1493</a></span> <span class="stringliteral">IMMUTABLE STRICT;</span></div> |
| <div class="line"><a name="l01494"></a><span class="lineno"> 1494</span> <span class="stringliteral"></span><span class="comment"></span></div> |
| <div class="line"><a name="l01495"></a><span class="lineno"> 1495</span> <span class="comment">/**</span></div> |
| <div class="line"><a name="l01496"></a><span class="lineno"> 1496</span> <span class="comment"> * @brief Poisson quantile function</span></div> |
| <div class="line"><a name="l01497"></a><span class="lineno"> 1497</span> <span class="comment"> *</span></div> |
| <div class="line"><a name="l01498"></a><span class="lineno"> 1498</span> <span class="comment"> * @param p Probability \f$ p \in [0,1] \f$</span></div> |
| <div class="line"><a name="l01499"></a><span class="lineno"> 1499</span> <span class="comment"> * @param mean Average occurrence rate \f$ \lambda > 0 \f$</span></div> |
| <div class="line"><a name="l01500"></a><span class="lineno"> 1500</span> <span class="comment"> * @return If \f$ p < 0.5 \f$ the maximum \f$ x \f$ such that</span></div> |
| <div class="line"><a name="l01501"></a><span class="lineno"> 1501</span> <span class="comment"> * \f$ p \geq \Pr[X \leq x] \f$. If \f$ p \geq 0.5 \f$ the minimum \f$ x \f$</span></div> |
| <div class="line"><a name="l01502"></a><span class="lineno"> 1502</span> <span class="comment"> * such that \f$ p \leq \Pr[X \leq x] \f$. Here, \f$ X \f$ is a</span></div> |
| <div class="line"><a name="l01503"></a><span class="lineno"> 1503</span> <span class="comment"> * Poisson distributed random variable with mean \f$ \lambda \f$</span></div> |
| <div class="line"><a name="l01504"></a><span class="lineno"> 1504</span> <span class="comment"> */</span></div> |
| <div class="line"><a name="l01505"></a><span class="lineno"> 1505</span> CREATE FUNCTION MADLIB_SCHEMA.poisson_quantile(</div> |
| <div class="line"><a name="l01506"></a><span class="lineno"> 1506</span>  p DOUBLE PRECISION,</div> |
| <div class="line"><a name="l01507"></a><span class="lineno"> 1507</span>  mean DOUBLE PRECISION</div> |
| <div class="line"><a name="l01508"></a><span class="lineno"> 1508</span> ) RETURNS DOUBLE PRECISION</div> |
| <div class="line"><a name="l01509"></a><span class="lineno"><a class="code" href="prob_8sql__in.html#a82f1edc27261021c73cd080ff2677a9f"> 1509</a></span> AS 'MODULE_PATHNAME<span class="stringliteral">'</span></div> |
| <div class="line"><a name="l01510"></a><span class="lineno"> 1510</span> <span class="stringliteral">LANGUAGE C</span></div> |
| <div class="line"><a name="l01511"></a><span class="lineno"> 1511</span> <span class="stringliteral">IMMUTABLE STRICT;</span></div> |
| <div class="line"><a name="l01512"></a><span class="lineno"> 1512</span> <span class="stringliteral"></span></div> |
| <div class="line"><a name="l01513"></a><span class="lineno"> 1513</span> <span class="stringliteral"></span><span class="comment"></span></div> |
| <div class="line"><a name="l01514"></a><span class="lineno"> 1514</span> <span class="comment">/**</span></div> |
| <div class="line"><a name="l01515"></a><span class="lineno"> 1515</span> <span class="comment"> * @brief Rayleigh cumulative distribution function</span></div> |
| <div class="line"><a name="l01516"></a><span class="lineno"> 1516</span> <span class="comment"> *</span></div> |
| <div class="line"><a name="l01517"></a><span class="lineno"> 1517</span> <span class="comment"> * @param x Random variate \f$ x \f$</span></div> |
| <div class="line"><a name="l01518"></a><span class="lineno"> 1518</span> <span class="comment"> * @param scale Scale \f$ \sigma > 0 \f$</span></div> |
| <div class="line"><a name="l01519"></a><span class="lineno"> 1519</span> <span class="comment"> * @return \f$ \Pr[X \leq x] \f$ where \f$ X \f$ is a Rayleigh-distributed</span></div> |
| <div class="line"><a name="l01520"></a><span class="lineno"> 1520</span> <span class="comment"> * random variable with parameter \f$ \sigma \f$</span></div> |
| <div class="line"><a name="l01521"></a><span class="lineno"> 1521</span> <span class="comment"> */</span></div> |
| <div class="line"><a name="l01522"></a><span class="lineno"> 1522</span> CREATE FUNCTION MADLIB_SCHEMA.rayleigh_cdf(</div> |
| <div class="line"><a name="l01523"></a><span class="lineno"> 1523</span>  x DOUBLE PRECISION,</div> |
| <div class="line"><a name="l01524"></a><span class="lineno"> 1524</span>  scale DOUBLE PRECISION</div> |
| <div class="line"><a name="l01525"></a><span class="lineno"> 1525</span> ) RETURNS DOUBLE PRECISION</div> |
| <div class="line"><a name="l01526"></a><span class="lineno"> 1526</span> AS 'MODULE_PATHNAME<span class="stringliteral">'</span></div> |
| <div class="line"><a name="l01527"></a><span class="lineno"><a class="code" href="prob_8sql__in.html#a032d26db18b2ee1034085f5521939c61"> 1527</a></span> <span class="stringliteral">LANGUAGE C</span></div> |
| <div class="line"><a name="l01528"></a><span class="lineno"> 1528</span> <span class="stringliteral">IMMUTABLE STRICT;</span></div> |
| <div class="line"><a name="l01529"></a><span class="lineno"> 1529</span> <span class="stringliteral"></span><span class="comment"></span></div> |
| <div class="line"><a name="l01530"></a><span class="lineno"> 1530</span> <span class="comment">/**</span></div> |
| <div class="line"><a name="l01531"></a><span class="lineno"> 1531</span> <span class="comment"> * @brief Rayleigh probability density function</span></div> |
| <div class="line"><a name="l01532"></a><span class="lineno"> 1532</span> <span class="comment"> *</span></div> |
| <div class="line"><a name="l01533"></a><span class="lineno"> 1533</span> <span class="comment"> * @param x Random variate \f$ x \f$</span></div> |
| <div class="line"><a name="l01534"></a><span class="lineno"> 1534</span> <span class="comment"> * @param scale Scale \f$ \sigma > 0 \f$</span></div> |
| <div class="line"><a name="l01535"></a><span class="lineno"> 1535</span> <span class="comment"> * @return \f$ f(x) \f$ where \f$ f \f$ is the probability density function of</span></div> |
| <div class="line"><a name="l01536"></a><span class="lineno"> 1536</span> <span class="comment"> * a Rayleigh-distributed random variable with parameter \f$ \sigma \f$</span></div> |
| <div class="line"><a name="l01537"></a><span class="lineno"> 1537</span> <span class="comment"> */</span></div> |
| <div class="line"><a name="l01538"></a><span class="lineno"> 1538</span> CREATE FUNCTION MADLIB_SCHEMA.rayleigh_pdf(</div> |
| <div class="line"><a name="l01539"></a><span class="lineno"> 1539</span>  x DOUBLE PRECISION,</div> |
| <div class="line"><a name="l01540"></a><span class="lineno"> 1540</span>  scale DOUBLE PRECISION</div> |
| <div class="line"><a name="l01541"></a><span class="lineno"> 1541</span> ) RETURNS DOUBLE PRECISION</div> |
| <div class="line"><a name="l01542"></a><span class="lineno"> 1542</span> AS 'MODULE_PATHNAME<span class="stringliteral">'</span></div> |
| <div class="line"><a name="l01543"></a><span class="lineno"> 1543</span> <span class="stringliteral">LANGUAGE C</span></div> |
| <div class="line"><a name="l01544"></a><span class="lineno"><a class="code" href="prob_8sql__in.html#aab0ddb8a5348cfa387d777043a3cb6d0"> 1544</a></span> <span class="stringliteral">IMMUTABLE STRICT;</span></div> |
| <div class="line"><a name="l01545"></a><span class="lineno"> 1545</span> <span class="stringliteral"></span><span class="comment"></span></div> |
| <div class="line"><a name="l01546"></a><span class="lineno"> 1546</span> <span class="comment">/**</span></div> |
| <div class="line"><a name="l01547"></a><span class="lineno"> 1547</span> <span class="comment"> * @brief Rayleigh quantile function</span></div> |
| <div class="line"><a name="l01548"></a><span class="lineno"> 1548</span> <span class="comment"> *</span></div> |
| <div class="line"><a name="l01549"></a><span class="lineno"> 1549</span> <span class="comment"> * @param p Probability \f$ p \in [0,1] \f$</span></div> |
| <div class="line"><a name="l01550"></a><span class="lineno"> 1550</span> <span class="comment"> * @param scale Scale \f$ \sigma > 0 \f$</span></div> |
| <div class="line"><a name="l01551"></a><span class="lineno"> 1551</span> <span class="comment"> * @return \f$ x \f$ such that \f$ p = \Pr[X \leq x] \f$ where \f$ X \f$ is a</span></div> |
| <div class="line"><a name="l01552"></a><span class="lineno"> 1552</span> <span class="comment"> * Rayleigh-distributed random variable with parameter \f$ \sigma \f$</span></div> |
| <div class="line"><a name="l01553"></a><span class="lineno"> 1553</span> <span class="comment"> */</span></div> |
| <div class="line"><a name="l01554"></a><span class="lineno"> 1554</span> CREATE FUNCTION MADLIB_SCHEMA.rayleigh_quantile(</div> |
| <div class="line"><a name="l01555"></a><span class="lineno"> 1555</span>  p DOUBLE PRECISION,</div> |
| <div class="line"><a name="l01556"></a><span class="lineno"> 1556</span>  scale DOUBLE PRECISION</div> |
| <div class="line"><a name="l01557"></a><span class="lineno"> 1557</span> ) RETURNS DOUBLE PRECISION</div> |
| <div class="line"><a name="l01558"></a><span class="lineno"> 1558</span> AS 'MODULE_PATHNAME<span class="stringliteral">'</span></div> |
| <div class="line"><a name="l01559"></a><span class="lineno"> 1559</span> <span class="stringliteral">LANGUAGE C</span></div> |
| <div class="line"><a name="l01560"></a><span class="lineno"><a class="code" href="prob_8sql__in.html#a798541736d9255bdd5c0bd94924d47bc"> 1560</a></span> <span class="stringliteral">IMMUTABLE STRICT;</span></div> |
| <div class="line"><a name="l01561"></a><span class="lineno"> 1561</span> <span class="stringliteral"></span></div> |
| <div class="line"><a name="l01562"></a><span class="lineno"> 1562</span> <span class="stringliteral"></span><span class="comment"></span></div> |
| <div class="line"><a name="l01563"></a><span class="lineno"> 1563</span> <span class="comment">/**</span></div> |
| <div class="line"><a name="l01564"></a><span class="lineno"> 1564</span> <span class="comment"> * @brief Student's t cumulative distribution function</span></div> |
| <div class="line"><a name="l01565"></a><span class="lineno"> 1565</span> <span class="comment"> *</span></div> |
| <div class="line"><a name="l01566"></a><span class="lineno"> 1566</span> <span class="comment"> * @param x Random variate \f$ x \f$</span></div> |
| <div class="line"><a name="l01567"></a><span class="lineno"> 1567</span> <span class="comment"> * @param df Degrees of freedom \f$ \nu > 0 \f$</span></div> |
| <div class="line"><a name="l01568"></a><span class="lineno"> 1568</span> <span class="comment"> * @return \f$ \Pr[X \leq x] \f$ where \f$ X \f$ is a Student's t-distributed</span></div> |
| <div class="line"><a name="l01569"></a><span class="lineno"> 1569</span> <span class="comment"> * random variable with \f$ \nu \f$ degrees of freedom</span></div> |
| <div class="line"><a name="l01570"></a><span class="lineno"> 1570</span> <span class="comment"> */</span></div> |
| <div class="line"><a name="l01571"></a><span class="lineno"> 1571</span> CREATE FUNCTION MADLIB_SCHEMA.students_t_cdf(</div> |
| <div class="line"><a name="l01572"></a><span class="lineno"> 1572</span>  x DOUBLE PRECISION,</div> |
| <div class="line"><a name="l01573"></a><span class="lineno"> 1573</span>  df DOUBLE PRECISION</div> |
| <div class="line"><a name="l01574"></a><span class="lineno"> 1574</span> ) RETURNS DOUBLE PRECISION</div> |
| <div class="line"><a name="l01575"></a><span class="lineno"> 1575</span> AS 'MODULE_PATHNAME<span class="stringliteral">'</span></div> |
| <div class="line"><a name="l01576"></a><span class="lineno"><a class="code" href="prob_8sql__in.html#acd6757acab1683c735e2b57901494336"> 1576</a></span> <span class="stringliteral">LANGUAGE C</span></div> |
| <div class="line"><a name="l01577"></a><span class="lineno"> 1577</span> <span class="stringliteral">IMMUTABLE STRICT;</span></div> |
| <div class="line"><a name="l01578"></a><span class="lineno"> 1578</span> <span class="stringliteral"></span><span class="comment"></span></div> |
| <div class="line"><a name="l01579"></a><span class="lineno"> 1579</span> <span class="comment">/**</span></div> |
| <div class="line"><a name="l01580"></a><span class="lineno"> 1580</span> <span class="comment"> * @brief Student's t probability density function</span></div> |
| <div class="line"><a name="l01581"></a><span class="lineno"> 1581</span> <span class="comment"> *</span></div> |
| <div class="line"><a name="l01582"></a><span class="lineno"> 1582</span> <span class="comment"> * @param x Random variate \f$ x \f$</span></div> |
| <div class="line"><a name="l01583"></a><span class="lineno"> 1583</span> <span class="comment"> * @param df Degrees of freedom \f$ \nu > 0 \f$</span></div> |
| <div class="line"><a name="l01584"></a><span class="lineno"> 1584</span> <span class="comment"> * @return \f$ f(x) \f$ where \f$ f \f$ is the probability density function of</span></div> |
| <div class="line"><a name="l01585"></a><span class="lineno"> 1585</span> <span class="comment"> * a Stundent's t-distributed random variable with \f$ \nu \f$ degrees of</span></div> |
| <div class="line"><a name="l01586"></a><span class="lineno"> 1586</span> <span class="comment"> * freedom</span></div> |
| <div class="line"><a name="l01587"></a><span class="lineno"> 1587</span> <span class="comment"> */</span></div> |
| <div class="line"><a name="l01588"></a><span class="lineno"> 1588</span> CREATE FUNCTION MADLIB_SCHEMA.students_t_pdf(</div> |
| <div class="line"><a name="l01589"></a><span class="lineno"> 1589</span>  x DOUBLE PRECISION,</div> |
| <div class="line"><a name="l01590"></a><span class="lineno"> 1590</span>  df DOUBLE PRECISION</div> |
| <div class="line"><a name="l01591"></a><span class="lineno"> 1591</span> ) RETURNS DOUBLE PRECISION</div> |
| <div class="line"><a name="l01592"></a><span class="lineno"> 1592</span> AS 'MODULE_PATHNAME<span class="stringliteral">'</span></div> |
| <div class="line"><a name="l01593"></a><span class="lineno"><a class="code" href="prob_8sql__in.html#a5322531131074c23a2dbf067ee504ef7"> 1593</a></span> <span class="stringliteral">LANGUAGE C</span></div> |
| <div class="line"><a name="l01594"></a><span class="lineno"> 1594</span> <span class="stringliteral">IMMUTABLE STRICT;</span></div> |
| <div class="line"><a name="l01595"></a><span class="lineno"> 1595</span> <span class="stringliteral"></span><span class="comment"></span></div> |
| <div class="line"><a name="l01596"></a><span class="lineno"> 1596</span> <span class="comment">/**</span></div> |
| <div class="line"><a name="l01597"></a><span class="lineno"> 1597</span> <span class="comment"> * @brief Student's t quantile function</span></div> |
| <div class="line"><a name="l01598"></a><span class="lineno"> 1598</span> <span class="comment"> *</span></div> |
| <div class="line"><a name="l01599"></a><span class="lineno"> 1599</span> <span class="comment"> * @param p Probability \f$ p \in [0,1] \f$</span></div> |
| <div class="line"><a name="l01600"></a><span class="lineno"> 1600</span> <span class="comment"> * @param df Degrees of freedom \f$ \nu > 0 \f$</span></div> |
| <div class="line"><a name="l01601"></a><span class="lineno"> 1601</span> <span class="comment"> * @return \f$ x \f$ such that \f$ p = \Pr[X \leq x] \f$ where \f$ X \f$ is a</span></div> |
| <div class="line"><a name="l01602"></a><span class="lineno"> 1602</span> <span class="comment"> * Student's t-distributed random variable with \f$ \nu \f$ degrees of</span></div> |
| <div class="line"><a name="l01603"></a><span class="lineno"> 1603</span> <span class="comment"> * freedom</span></div> |
| <div class="line"><a name="l01604"></a><span class="lineno"> 1604</span> <span class="comment"> */</span></div> |
| <div class="line"><a name="l01605"></a><span class="lineno"> 1605</span> CREATE FUNCTION MADLIB_SCHEMA.students_t_quantile(</div> |
| <div class="line"><a name="l01606"></a><span class="lineno"> 1606</span>  p DOUBLE PRECISION,</div> |
| <div class="line"><a name="l01607"></a><span class="lineno"> 1607</span>  df DOUBLE PRECISION</div> |
| <div class="line"><a name="l01608"></a><span class="lineno"> 1608</span> ) RETURNS DOUBLE PRECISION</div> |
| <div class="line"><a name="l01609"></a><span class="lineno"> 1609</span> AS 'MODULE_PATHNAME<span class="stringliteral">'</span></div> |
| <div class="line"><a name="l01610"></a><span class="lineno"><a class="code" href="prob_8sql__in.html#a8815c21670fff9d31946553a84b845b1"> 1610</a></span> <span class="stringliteral">LANGUAGE C</span></div> |
| <div class="line"><a name="l01611"></a><span class="lineno"> 1611</span> <span class="stringliteral">IMMUTABLE STRICT;</span></div> |
| <div class="line"><a name="l01612"></a><span class="lineno"> 1612</span> <span class="stringliteral"></span></div> |
| <div class="line"><a name="l01613"></a><span class="lineno"> 1613</span> <span class="stringliteral"></span><span class="comment"></span></div> |
| <div class="line"><a name="l01614"></a><span class="lineno"> 1614</span> <span class="comment">/**</span></div> |
| <div class="line"><a name="l01615"></a><span class="lineno"> 1615</span> <span class="comment"> * @brief Triangular cumulative distribution function</span></div> |
| <div class="line"><a name="l01616"></a><span class="lineno"> 1616</span> <span class="comment"> *</span></div> |
| <div class="line"><a name="l01617"></a><span class="lineno"> 1617</span> <span class="comment"> * @param x Random variate \f$ x \f$</span></div> |
| <div class="line"><a name="l01618"></a><span class="lineno"> 1618</span> <span class="comment"> * @param lower Lower bound \f$ a \f$</span></div> |
| <div class="line"><a name="l01619"></a><span class="lineno"> 1619</span> <span class="comment"> * @param mode Mode \f$ c \geq a \f$</span></div> |
| <div class="line"><a name="l01620"></a><span class="lineno"> 1620</span> <span class="comment"> * @param upper Upper bound \f$ b \geq c \f$, where \f$ b > a \f$</span></div> |
| <div class="line"><a name="l01621"></a><span class="lineno"> 1621</span> <span class="comment"> * @return \f$ \Pr[X \leq x] \f$ where \f$ X \f$ is a triangular distributed</span></div> |
| <div class="line"><a name="l01622"></a><span class="lineno"> 1622</span> <span class="comment"> * random variable with parameters \f$ a, b, c \f$</span></div> |
| <div class="line"><a name="l01623"></a><span class="lineno"> 1623</span> <span class="comment"> */</span></div> |
| <div class="line"><a name="l01624"></a><span class="lineno"> 1624</span> CREATE FUNCTION MADLIB_SCHEMA.triangular_cdf(</div> |
| <div class="line"><a name="l01625"></a><span class="lineno"> 1625</span>  x DOUBLE PRECISION,</div> |
| <div class="line"><a name="l01626"></a><span class="lineno"> 1626</span>  lower DOUBLE PRECISION,</div> |
| <div class="line"><a name="l01627"></a><span class="lineno"><a class="code" href="prob_8sql__in.html#a7d64add02af21a95d73502b2dd466a75"> 1627</a></span>  mode DOUBLE PRECISION,</div> |
| <div class="line"><a name="l01628"></a><span class="lineno"> 1628</span>  upper DOUBLE PRECISION</div> |
| <div class="line"><a name="l01629"></a><span class="lineno"> 1629</span> ) RETURNS DOUBLE PRECISION</div> |
| <div class="line"><a name="l01630"></a><span class="lineno"> 1630</span> AS 'MODULE_PATHNAME<span class="stringliteral">'</span></div> |
| <div class="line"><a name="l01631"></a><span class="lineno"> 1631</span> <span class="stringliteral">LANGUAGE C</span></div> |
| <div class="line"><a name="l01632"></a><span class="lineno"> 1632</span> <span class="stringliteral">IMMUTABLE STRICT;</span></div> |
| <div class="line"><a name="l01633"></a><span class="lineno"> 1633</span> <span class="stringliteral"></span><span class="comment"></span></div> |
| <div class="line"><a name="l01634"></a><span class="lineno"> 1634</span> <span class="comment">/**</span></div> |
| <div class="line"><a name="l01635"></a><span class="lineno"> 1635</span> <span class="comment"> * @brief Triangular probability density function</span></div> |
| <div class="line"><a name="l01636"></a><span class="lineno"> 1636</span> <span class="comment"> *</span></div> |
| <div class="line"><a name="l01637"></a><span class="lineno"> 1637</span> <span class="comment"> * @param x Random variate \f$ x \f$</span></div> |
| <div class="line"><a name="l01638"></a><span class="lineno"> 1638</span> <span class="comment"> * @param lower Lower bound \f$ a \f$</span></div> |
| <div class="line"><a name="l01639"></a><span class="lineno"> 1639</span> <span class="comment"> * @param mode Mode \f$ c \geq a \f$</span></div> |
| <div class="line"><a name="l01640"></a><span class="lineno"> 1640</span> <span class="comment"> * @param upper Upper bound \f$ b \geq c \f$, where \f$ b > a \f$</span></div> |
| <div class="line"><a name="l01641"></a><span class="lineno"> 1641</span> <span class="comment"> * @return \f$ f(x) \f$ where \f$ f \f$ is the probability density function of</span></div> |
| <div class="line"><a name="l01642"></a><span class="lineno"> 1642</span> <span class="comment"> * a triangular distributed random variable with parameters \f$ a, b, c \f$</span></div> |
| <div class="line"><a name="l01643"></a><span class="lineno"> 1643</span> <span class="comment"> */</span></div> |
| <div class="line"><a name="l01644"></a><span class="lineno"> 1644</span> CREATE FUNCTION MADLIB_SCHEMA.triangular_pdf(</div> |
| <div class="line"><a name="l01645"></a><span class="lineno"> 1645</span>  x DOUBLE PRECISION,</div> |
| <div class="line"><a name="l01646"></a><span class="lineno"><a class="code" href="prob_8sql__in.html#abf9c7d870bcfe68cacaa421749bbdf35"> 1646</a></span>  lower DOUBLE PRECISION,</div> |
| <div class="line"><a name="l01647"></a><span class="lineno"> 1647</span>  mode DOUBLE PRECISION,</div> |
| <div class="line"><a name="l01648"></a><span class="lineno"> 1648</span>  upper DOUBLE PRECISION</div> |
| <div class="line"><a name="l01649"></a><span class="lineno"> 1649</span> ) RETURNS DOUBLE PRECISION</div> |
| <div class="line"><a name="l01650"></a><span class="lineno"> 1650</span> AS 'MODULE_PATHNAME<span class="stringliteral">'</span></div> |
| <div class="line"><a name="l01651"></a><span class="lineno"> 1651</span> <span class="stringliteral">LANGUAGE C</span></div> |
| <div class="line"><a name="l01652"></a><span class="lineno"> 1652</span> <span class="stringliteral">IMMUTABLE STRICT;</span></div> |
| <div class="line"><a name="l01653"></a><span class="lineno"> 1653</span> <span class="stringliteral"></span><span class="comment"></span></div> |
| <div class="line"><a name="l01654"></a><span class="lineno"> 1654</span> <span class="comment">/**</span></div> |
| <div class="line"><a name="l01655"></a><span class="lineno"> 1655</span> <span class="comment"> * @brief Triangular quantile function</span></div> |
| <div class="line"><a name="l01656"></a><span class="lineno"> 1656</span> <span class="comment"> *</span></div> |
| <div class="line"><a name="l01657"></a><span class="lineno"> 1657</span> <span class="comment"> * @param p Probability \f$ p \in [0,1] \f$</span></div> |
| <div class="line"><a name="l01658"></a><span class="lineno"> 1658</span> <span class="comment"> * @param lower Lower bound \f$ a \f$</span></div> |
| <div class="line"><a name="l01659"></a><span class="lineno"> 1659</span> <span class="comment"> * @param mode Mode \f$ c \geq a \f$</span></div> |
| <div class="line"><a name="l01660"></a><span class="lineno"> 1660</span> <span class="comment"> * @param upper Upper bound \f$ b \geq c \f$, where \f$ b > a \f$</span></div> |
| <div class="line"><a name="l01661"></a><span class="lineno"> 1661</span> <span class="comment"> * @return \f$ x \f$ such that \f$ p = \Pr[X \leq x] \f$ where \f$ X \f$ is a</span></div> |
| <div class="line"><a name="l01662"></a><span class="lineno"> 1662</span> <span class="comment"> * trianbular distributed random variable with parameters \f$ a, b, c \f$</span></div> |
| <div class="line"><a name="l01663"></a><span class="lineno"> 1663</span> <span class="comment"> */</span></div> |
| <div class="line"><a name="l01664"></a><span class="lineno"> 1664</span> CREATE FUNCTION MADLIB_SCHEMA.triangular_quantile(</div> |
| <div class="line"><a name="l01665"></a><span class="lineno"> 1665</span>  p DOUBLE PRECISION,</div> |
| <div class="line"><a name="l01666"></a><span class="lineno"><a class="code" href="prob_8sql__in.html#a0c511b9748b2f7a21fe56aaf5f66d188"> 1666</a></span>  lower DOUBLE PRECISION,</div> |
| <div class="line"><a name="l01667"></a><span class="lineno"> 1667</span>  mode DOUBLE PRECISION,</div> |
| <div class="line"><a name="l01668"></a><span class="lineno"> 1668</span>  upper DOUBLE PRECISION</div> |
| <div class="line"><a name="l01669"></a><span class="lineno"> 1669</span> ) RETURNS DOUBLE PRECISION</div> |
| <div class="line"><a name="l01670"></a><span class="lineno"> 1670</span> AS 'MODULE_PATHNAME<span class="stringliteral">'</span></div> |
| <div class="line"><a name="l01671"></a><span class="lineno"> 1671</span> <span class="stringliteral">LANGUAGE C</span></div> |
| <div class="line"><a name="l01672"></a><span class="lineno"> 1672</span> <span class="stringliteral">IMMUTABLE STRICT;</span></div> |
| <div class="line"><a name="l01673"></a><span class="lineno"> 1673</span> <span class="stringliteral"></span></div> |
| <div class="line"><a name="l01674"></a><span class="lineno"> 1674</span> <span class="stringliteral"></span><span class="comment"></span></div> |
| <div class="line"><a name="l01675"></a><span class="lineno"> 1675</span> <span class="comment">/**</span></div> |
| <div class="line"><a name="l01676"></a><span class="lineno"> 1676</span> <span class="comment"> * @brief Uniform cumulative distribution function</span></div> |
| <div class="line"><a name="l01677"></a><span class="lineno"> 1677</span> <span class="comment"> *</span></div> |
| <div class="line"><a name="l01678"></a><span class="lineno"> 1678</span> <span class="comment"> * @param x Random variate \f$ x \f$</span></div> |
| <div class="line"><a name="l01679"></a><span class="lineno"> 1679</span> <span class="comment"> * @param lower Lower bound \f$ a \f$</span></div> |
| <div class="line"><a name="l01680"></a><span class="lineno"> 1680</span> <span class="comment"> * @param upper Upper bound \f$ b \f$</span></div> |
| <div class="line"><a name="l01681"></a><span class="lineno"> 1681</span> <span class="comment"> * @return \f$ \Pr[X \leq x] \f$ where \f$ X \f$ is a uniform distributed random</span></div> |
| <div class="line"><a name="l01682"></a><span class="lineno"> 1682</span> <span class="comment"> * variable with support \f$ [a, b] \f$</span></div> |
| <div class="line"><a name="l01683"></a><span class="lineno"> 1683</span> <span class="comment"> */</span></div> |
| <div class="line"><a name="l01684"></a><span class="lineno"> 1684</span> CREATE FUNCTION MADLIB_SCHEMA.uniform_cdf(</div> |
| <div class="line"><a name="l01685"></a><span class="lineno"> 1685</span>  x DOUBLE PRECISION,</div> |
| <div class="line"><a name="l01686"></a><span class="lineno"><a class="code" href="prob_8sql__in.html#a4777540ab1b003ff92d484c4bc26af27"> 1686</a></span>  lower DOUBLE PRECISION,</div> |
| <div class="line"><a name="l01687"></a><span class="lineno"> 1687</span>  upper DOUBLE PRECISION</div> |
| <div class="line"><a name="l01688"></a><span class="lineno"> 1688</span> ) RETURNS DOUBLE PRECISION</div> |
| <div class="line"><a name="l01689"></a><span class="lineno"> 1689</span> AS 'MODULE_PATHNAME<span class="stringliteral">'</span></div> |
| <div class="line"><a name="l01690"></a><span class="lineno"> 1690</span> <span class="stringliteral">LANGUAGE C</span></div> |
| <div class="line"><a name="l01691"></a><span class="lineno"> 1691</span> <span class="stringliteral">IMMUTABLE STRICT;</span></div> |
| <div class="line"><a name="l01692"></a><span class="lineno"> 1692</span> <span class="stringliteral"></span><span class="comment"></span></div> |
| <div class="line"><a name="l01693"></a><span class="lineno"> 1693</span> <span class="comment">/**</span></div> |
| <div class="line"><a name="l01694"></a><span class="lineno"> 1694</span> <span class="comment"> * @brief Uniform probability density function</span></div> |
| <div class="line"><a name="l01695"></a><span class="lineno"> 1695</span> <span class="comment"> *</span></div> |
| <div class="line"><a name="l01696"></a><span class="lineno"> 1696</span> <span class="comment"> * @param x Random variate \f$ x \f$</span></div> |
| <div class="line"><a name="l01697"></a><span class="lineno"> 1697</span> <span class="comment"> * @param lower Lower bound \f$ a \f$</span></div> |
| <div class="line"><a name="l01698"></a><span class="lineno"> 1698</span> <span class="comment"> * @param upper Upper bound \f$ b \f$</span></div> |
| <div class="line"><a name="l01699"></a><span class="lineno"> 1699</span> <span class="comment"> * @return \f$ f(x) \f$ where \f$ f \f$ is the probability density function of</span></div> |
| <div class="line"><a name="l01700"></a><span class="lineno"> 1700</span> <span class="comment"> * a uniform distributed random variable with support \f$ [a, b] \f$</span></div> |
| <div class="line"><a name="l01701"></a><span class="lineno"> 1701</span> <span class="comment"> */</span></div> |
| <div class="line"><a name="l01702"></a><span class="lineno"> 1702</span> CREATE FUNCTION MADLIB_SCHEMA.uniform_pdf(</div> |
| <div class="line"><a name="l01703"></a><span class="lineno"> 1703</span>  x DOUBLE PRECISION,</div> |
| <div class="line"><a name="l01704"></a><span class="lineno"> 1704</span>  lower DOUBLE PRECISION,</div> |
| <div class="line"><a name="l01705"></a><span class="lineno"> 1705</span>  upper DOUBLE PRECISION</div> |
| <div class="line"><a name="l01706"></a><span class="lineno"><a class="code" href="prob_8sql__in.html#aa3a05f4f2e0ef9eb65e828261ecfbed9"> 1706</a></span> ) RETURNS DOUBLE PRECISION</div> |
| <div class="line"><a name="l01707"></a><span class="lineno"> 1707</span> AS 'MODULE_PATHNAME<span class="stringliteral">'</span></div> |
| <div class="line"><a name="l01708"></a><span class="lineno"> 1708</span> <span class="stringliteral">LANGUAGE C</span></div> |
| <div class="line"><a name="l01709"></a><span class="lineno"> 1709</span> <span class="stringliteral">IMMUTABLE STRICT;</span></div> |
| <div class="line"><a name="l01710"></a><span class="lineno"> 1710</span> <span class="stringliteral"></span><span class="comment"></span></div> |
| <div class="line"><a name="l01711"></a><span class="lineno"> 1711</span> <span class="comment">/**</span></div> |
| <div class="line"><a name="l01712"></a><span class="lineno"> 1712</span> <span class="comment"> * @brief Uniform quantile function</span></div> |
| <div class="line"><a name="l01713"></a><span class="lineno"> 1713</span> <span class="comment"> *</span></div> |
| <div class="line"><a name="l01714"></a><span class="lineno"> 1714</span> <span class="comment"> * @param p Probability \f$ p \in [0,1] \f$</span></div> |
| <div class="line"><a name="l01715"></a><span class="lineno"> 1715</span> <span class="comment"> * @param lower Lower bound \f$ a \f$</span></div> |
| <div class="line"><a name="l01716"></a><span class="lineno"> 1716</span> <span class="comment"> * @param upper Upper bound \f$ b \f$</span></div> |
| <div class="line"><a name="l01717"></a><span class="lineno"> 1717</span> <span class="comment"> * @return \f$ x \f$ such that \f$ p = \Pr[X \leq x] \f$ where \f$ X \f$ is a</span></div> |
| <div class="line"><a name="l01718"></a><span class="lineno"> 1718</span> <span class="comment"> * uniform distributed random variable with support \f$ [a, b] \f$</span></div> |
| <div class="line"><a name="l01719"></a><span class="lineno"> 1719</span> <span class="comment"> */</span></div> |
| <div class="line"><a name="l01720"></a><span class="lineno"> 1720</span> CREATE FUNCTION MADLIB_SCHEMA.uniform_quantile(</div> |
| <div class="line"><a name="l01721"></a><span class="lineno"> 1721</span>  p DOUBLE PRECISION,</div> |
| <div class="line"><a name="l01722"></a><span class="lineno"> 1722</span>  lower DOUBLE PRECISION,</div> |
| <div class="line"><a name="l01723"></a><span class="lineno"> 1723</span>  upper DOUBLE PRECISION</div> |
| <div class="line"><a name="l01724"></a><span class="lineno"><a class="code" href="prob_8sql__in.html#ab90fa34d90a9c75747a34c3f210df239"> 1724</a></span> ) RETURNS DOUBLE PRECISION</div> |
| <div class="line"><a name="l01725"></a><span class="lineno"> 1725</span> AS 'MODULE_PATHNAME<span class="stringliteral">'</span></div> |
| <div class="line"><a name="l01726"></a><span class="lineno"> 1726</span> <span class="stringliteral">LANGUAGE C</span></div> |
| <div class="line"><a name="l01727"></a><span class="lineno"> 1727</span> <span class="stringliteral">IMMUTABLE STRICT;</span></div> |
| <div class="line"><a name="l01728"></a><span class="lineno"> 1728</span> <span class="stringliteral"></span></div> |
| <div class="line"><a name="l01729"></a><span class="lineno"> 1729</span> <span class="stringliteral"></span><span class="comment"></span></div> |
| <div class="line"><a name="l01730"></a><span class="lineno"> 1730</span> <span class="comment">/**</span></div> |
| <div class="line"><a name="l01731"></a><span class="lineno"> 1731</span> <span class="comment"> * @brief Weibull cumulative distribution function</span></div> |
| <div class="line"><a name="l01732"></a><span class="lineno"> 1732</span> <span class="comment"> *</span></div> |
| <div class="line"><a name="l01733"></a><span class="lineno"> 1733</span> <span class="comment"> * @param x Random variate \f$ x \f$</span></div> |
| <div class="line"><a name="l01734"></a><span class="lineno"> 1734</span> <span class="comment"> * @param shape Shape \f$ \alpha > 0 \f$</span></div> |
| <div class="line"><a name="l01735"></a><span class="lineno"> 1735</span> <span class="comment"> * @param scale Scale \f$ \beta > 0 \f$</span></div> |
| <div class="line"><a name="l01736"></a><span class="lineno"> 1736</span> <span class="comment"> * @return \f$ \Pr[X \leq x] \f$ where \f$ X \f$ is a weibull distributed random</span></div> |
| <div class="line"><a name="l01737"></a><span class="lineno"> 1737</span> <span class="comment"> * variable with shape and scale parameters \f$ \alpha \f$ and</span></div> |
| <div class="line"><a name="l01738"></a><span class="lineno"> 1738</span> <span class="comment"> * \f$ \beta \f$, respectively</span></div> |
| <div class="line"><a name="l01739"></a><span class="lineno"> 1739</span> <span class="comment"> */</span></div> |
| <div class="line"><a name="l01740"></a><span class="lineno"> 1740</span> CREATE FUNCTION MADLIB_SCHEMA.weibull_cdf(</div> |
| <div class="line"><a name="l01741"></a><span class="lineno"> 1741</span>  x DOUBLE PRECISION,</div> |
| <div class="line"><a name="l01742"></a><span class="lineno"><a class="code" href="prob_8sql__in.html#a629587a0fdefb588d28b15517ae5cc04"> 1742</a></span>  shape DOUBLE PRECISION,</div> |
| <div class="line"><a name="l01743"></a><span class="lineno"> 1743</span>  scale DOUBLE PRECISION</div> |
| <div class="line"><a name="l01744"></a><span class="lineno"> 1744</span> ) RETURNS DOUBLE PRECISION</div> |
| <div class="line"><a name="l01745"></a><span class="lineno"> 1745</span> AS 'MODULE_PATHNAME<span class="stringliteral">'</span></div> |
| <div class="line"><a name="l01746"></a><span class="lineno"> 1746</span> <span class="stringliteral">LANGUAGE C</span></div> |
| <div class="line"><a name="l01747"></a><span class="lineno"> 1747</span> <span class="stringliteral">IMMUTABLE STRICT;</span></div> |
| <div class="line"><a name="l01748"></a><span class="lineno"> 1748</span> <span class="stringliteral"></span><span class="comment"></span></div> |
| <div class="line"><a name="l01749"></a><span class="lineno"> 1749</span> <span class="comment">/**</span></div> |
| <div class="line"><a name="l01750"></a><span class="lineno"> 1750</span> <span class="comment"> * @brief Weibull probability density function</span></div> |
| <div class="line"><a name="l01751"></a><span class="lineno"> 1751</span> <span class="comment"> *</span></div> |
| <div class="line"><a name="l01752"></a><span class="lineno"> 1752</span> <span class="comment"> * @param x Random variate \f$ x \f$</span></div> |
| <div class="line"><a name="l01753"></a><span class="lineno"> 1753</span> <span class="comment"> * @param shape Shape \f$ \alpha > 0 \f$</span></div> |
| <div class="line"><a name="l01754"></a><span class="lineno"> 1754</span> <span class="comment"> * @param scale Scale \f$ \beta > 0 \f$</span></div> |
| <div class="line"><a name="l01755"></a><span class="lineno"> 1755</span> <span class="comment"> * @return \f$ f(x) \f$ where \f$ f \f$ is the probability density function of</span></div> |
| <div class="line"><a name="l01756"></a><span class="lineno"> 1756</span> <span class="comment"> * a weibull distributed random variable with shape and scale parameters</span></div> |
| <div class="line"><a name="l01757"></a><span class="lineno"> 1757</span> <span class="comment"> * \f$ \alpha \f$ and \f$ \beta \f$, respectively</span></div> |
| <div class="line"><a name="l01758"></a><span class="lineno"> 1758</span> <span class="comment"> */</span></div> |
| <div class="line"><a name="l01759"></a><span class="lineno"> 1759</span> CREATE FUNCTION MADLIB_SCHEMA.weibull_pdf(</div> |
| <div class="line"><a name="l01760"></a><span class="lineno"> 1760</span>  x DOUBLE PRECISION,</div> |
| <div class="line"><a name="l01761"></a><span class="lineno"> 1761</span>  shape DOUBLE PRECISION,</div> |
| <div class="line"><a name="l01762"></a><span class="lineno"><a class="code" href="prob_8sql__in.html#a50e4a1883588cd7a4c1ff1017399e4af"> 1762</a></span>  scale DOUBLE PRECISION</div> |
| <div class="line"><a name="l01763"></a><span class="lineno"> 1763</span> ) RETURNS DOUBLE PRECISION</div> |
| <div class="line"><a name="l01764"></a><span class="lineno"> 1764</span> AS 'MODULE_PATHNAME<span class="stringliteral">'</span></div> |
| <div class="line"><a name="l01765"></a><span class="lineno"> 1765</span> <span class="stringliteral">LANGUAGE C</span></div> |
| <div class="line"><a name="l01766"></a><span class="lineno"> 1766</span> <span class="stringliteral">IMMUTABLE STRICT;</span></div> |
| <div class="line"><a name="l01767"></a><span class="lineno"> 1767</span> <span class="stringliteral"></span><span class="comment"></span></div> |
| <div class="line"><a name="l01768"></a><span class="lineno"> 1768</span> <span class="comment">/**</span></div> |
| <div class="line"><a name="l01769"></a><span class="lineno"> 1769</span> <span class="comment"> * @brief Weibull quantile function</span></div> |
| <div class="line"><a name="l01770"></a><span class="lineno"> 1770</span> <span class="comment"> *</span></div> |
| <div class="line"><a name="l01771"></a><span class="lineno"> 1771</span> <span class="comment"> * @param p Probability \f$ p \in [0,1] \f$</span></div> |
| <div class="line"><a name="l01772"></a><span class="lineno"> 1772</span> <span class="comment"> * @param shape Shape \f$ \alpha > 0 \f$</span></div> |
| <div class="line"><a name="l01773"></a><span class="lineno"> 1773</span> <span class="comment"> * @param scale Scale \f$ \beta > 0 \f$</span></div> |
| <div class="line"><a name="l01774"></a><span class="lineno"> 1774</span> <span class="comment"> * @return \f$ x \f$ such that \f$ p = \Pr[X \leq x] \f$ where \f$ X \f$ is a</span></div> |
| <div class="line"><a name="l01775"></a><span class="lineno"> 1775</span> <span class="comment"> * weibull distributed random variable with shape and scale parameters</span></div> |
| <div class="line"><a name="l01776"></a><span class="lineno"> 1776</span> <span class="comment"> * \f$ \alpha \f$ and \f$ \beta \f$, respectively</span></div> |
| <div class="line"><a name="l01777"></a><span class="lineno"> 1777</span> <span class="comment"> */</span></div> |
| <div class="line"><a name="l01778"></a><span class="lineno"> 1778</span> CREATE FUNCTION MADLIB_SCHEMA.weibull_quantile(</div> |
| <div class="line"><a name="l01779"></a><span class="lineno"> 1779</span>  p DOUBLE PRECISION,</div> |
| <div class="line"><a name="l01780"></a><span class="lineno"> 1780</span>  shape DOUBLE PRECISION,</div> |
| <div class="line"><a name="l01781"></a><span class="lineno"><a class="code" href="prob_8sql__in.html#a81a876ae2b8598f060dadb179b9324d2"> 1781</a></span>  scale DOUBLE PRECISION</div> |
| <div class="line"><a name="l01782"></a><span class="lineno"> 1782</span> ) RETURNS DOUBLE PRECISION</div> |
| <div class="line"><a name="l01783"></a><span class="lineno"> 1783</span> AS 'MODULE_PATHNAME<span class="stringliteral">'</span></div> |
| <div class="line"><a name="l01784"></a><span class="lineno"> 1784</span> <span class="stringliteral">LANGUAGE C</span></div> |
| <div class="line"><a name="l01785"></a><span class="lineno"> 1785</span> <span class="stringliteral">IMMUTABLE STRICT;</span></div> |
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