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| <a href="prob_8sql__in.html">Go to the documentation of this file.</a><div class="fragment"><pre class="fragment"><a name="l00001"></a>00001 <span class="comment">/* ----------------------------------------------------------------------- */</span><span class="comment">/**</span> |
| <a name="l00002"></a>00002 <span class="comment"> *</span> |
| <a name="l00003"></a>00003 <span class="comment"> * @file prob.sql_in</span> |
| <a name="l00004"></a>00004 <span class="comment"> *</span> |
| <a name="l00005"></a>00005 <span class="comment"> * @brief SQL functions for evaluating probability functions</span> |
| <a name="l00006"></a>00006 <span class="comment"> *</span> |
| <a name="l00007"></a>00007 <span class="comment"> * @sa For an overview of probability functions, see the module</span> |
| <a name="l00008"></a>00008 <span class="comment"> * description \ref grp_prob.</span> |
| <a name="l00009"></a>00009 <span class="comment"> *</span> |
| <a name="l00010"></a>00010 <span class="comment"> */</span><span class="comment">/* ----------------------------------------------------------------------- */</span> |
| <a name="l00011"></a>00011 |
| <a name="l00012"></a>00012 m4_include(`SQLCommon.m4<span class="stringliteral">')</span> |
| <a name="l00013"></a>00013 <span class="stringliteral"></span><span class="comment"></span> |
| <a name="l00014"></a>00014 <span class="comment">/**</span> |
| <a name="l00015"></a>00015 <span class="comment">@addtogroup grp_prob</span> |
| <a name="l00016"></a>00016 <span class="comment"></span> |
| <a name="l00017"></a>00017 <span class="comment">@about</span> |
| <a name="l00018"></a>00018 <span class="comment"></span> |
| <a name="l00019"></a>00019 <span class="comment">The Probability Functions module provides cumulative distribution, density/mass,</span> |
| <a name="l00020"></a>00020 <span class="comment">and quantile functions for a wide range of probability distributions.</span> |
| <a name="l00021"></a>00021 <span class="comment"></span> |
| <a name="l00022"></a>00022 <span class="comment">Unless otherwise documented, all of these functions are wrappers around</span> |
| <a name="l00023"></a>00023 <span class="comment">functionality provided by the boost C++ library [1, “<a href=</span> |
| <a name="l00024"></a>00024 <span class="comment">"http://www.boost.org/doc/libs/1_49_0/libs/math/doc/sf_and_dist/html/math_toolkit/dist.html"</span> |
| <a name="l00025"></a>00025 <span class="comment">>Statistical Distributions and Functions</a>”].</span> |
| <a name="l00026"></a>00026 <span class="comment"></span> |
| <a name="l00027"></a>00027 <span class="comment">For convenience, all cumulative distribution and density/mass functions (CDFs</span> |
| <a name="l00028"></a>00028 <span class="comment">and PDF/PMFs in short) are defined over the range of all floating-point numbers</span> |
| <a name="l00029"></a>00029 <span class="comment">including infinity. Inputs that are \c NULL or \c NaN (not a number) will always</span> |
| <a name="l00030"></a>00030 <span class="comment">produce a \c NULL or \c NaN result, respectively. Inputs that are plus or minus</span> |
| <a name="l00031"></a>00031 <span class="comment">infinity will return the respective limits.</span> |
| <a name="l00032"></a>00032 <span class="comment"></span> |
| <a name="l00033"></a>00033 <span class="comment">A quantile function for a probability distrution with CDF \f$ F \f$ takes a</span> |
| <a name="l00034"></a>00034 <span class="comment">probability argument \f$ p \in [0,1] \f$ and returns the value \f$ x \f$ so that</span> |
| <a name="l00035"></a>00035 <span class="comment">\f$ F(x) = p \f$, provided such an \f$ x \f$ exists and it is unique. If it does</span> |
| <a name="l00036"></a>00036 <span class="comment">not, the result will be</span> |
| <a name="l00037"></a>00037 <span class="comment">\f$</span> |
| <a name="l00038"></a>00038 <span class="comment"> \sup \{ x \in D \mid F(x) \leq p \}</span> |
| <a name="l00039"></a>00039 <span class="comment">\f$</span> |
| <a name="l00040"></a>00040 <span class="comment">(interpreted as 0 if the supremum is over an empty set) if \f$ p < 0.5 \f$, and</span> |
| <a name="l00041"></a>00041 <span class="comment">\f$</span> |
| <a name="l00042"></a>00042 <span class="comment"> \inf \{ x \in D \mid F(x) \geq p \}</span> |
| <a name="l00043"></a>00043 <span class="comment">\f$</span> |
| <a name="l00044"></a>00044 <span class="comment">if \f$ p \geq 0.5 \f$. Here \f$ D \f$ denotes the domain of the distribution,</span> |
| <a name="l00045"></a>00045 <span class="comment">which is the set of reals \f$ \mathbb R \f$ for continuous and the set of</span> |
| <a name="l00046"></a>00046 <span class="comment">nonnegative integers \f$ \mathbb N_0 \f$ for discrete distributions.</span> |
| <a name="l00047"></a>00047 <span class="comment"></span> |
| <a name="l00048"></a>00048 <span class="comment">Intuitively, the formulas in the previous paragraph deal with the following</span> |
| <a name="l00049"></a>00049 <span class="comment">special cases. The 0-quantile will always be the “left end” of the support,</span> |
| <a name="l00050"></a>00050 <span class="comment">and the 1-quantile will be the “right end” of the support of the distribution.</span> |
| <a name="l00051"></a>00051 <span class="comment">For discrete distributions, most values of \f$ p \in [0,1] \f$ do not admit an</span> |
| <a name="l00052"></a>00052 <span class="comment">\f$ x \f$ with \f$ F(x) = p \f$. Instead, there is an \f$ x \in \mathbb N_0 \f$</span> |
| <a name="l00053"></a>00053 <span class="comment">so that \f$ F(x) < p < F(x + 1) \f$. The above formulas mean that the</span> |
| <a name="l00054"></a>00054 <span class="comment">value returned as \f$ p \f$-quantile is \f$ x \f$ if \f$ p < 0.5 \f$, and it</span> |
| <a name="l00055"></a>00055 <span class="comment">is \f$ x + 1 \f$ if \f$ p \geq 0.5 \f$. (As a special case, in order to ensure</span> |
| <a name="l00056"></a>00056 <span class="comment">that quantiles are always within the support, the \f$ p \f$-quantile will be 0</span> |
| <a name="l00057"></a>00057 <span class="comment">if \f$ p < F(0) \f$).</span> |
| <a name="l00058"></a>00058 <span class="comment"></span> |
| <a name="l00059"></a>00059 <span class="comment">The rationale for choosing this behavior is that \f$p\f$-quantiles for</span> |
| <a name="l00060"></a>00060 <span class="comment">\f$ p < 0.5 \f$ are typically requested when interested in the value</span> |
| <a name="l00061"></a>00061 <span class="comment">\f$ x \f$ such that with confidence level <strong>at least</strong></span> |
| <a name="l00062"></a>00062 <span class="comment">\f$ 1 - p \f$ a random variable will be \f$ > x \f$ (or equivalently, with</span> |
| <a name="l00063"></a>00063 <span class="comment">probability <strong>at most</strong> \f$ p \f$, it will be \f$ \leq x \f$).</span> |
| <a name="l00064"></a>00064 <span class="comment">Likewise, \f$p\f$-quantiles for \f$ p \geq 0.5 \f$ are typically requested when</span> |
| <a name="l00065"></a>00065 <span class="comment">interested in the value \f$ x \f$ such that with confidence level <strong>at</span> |
| <a name="l00066"></a>00066 <span class="comment">least</strong> \f$ p \f$ a random variable will be \f$ \leq x \f$. See also</span> |
| <a name="l00067"></a>00067 <span class="comment">[1, “<a href=</span> |
| <a name="l00068"></a>00068 <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> |
| <a name="l00069"></a>00069 <span class="comment">>Understanding Quantiles of Discrete Distributions</a>”].</span> |
| <a name="l00070"></a>00070 <span class="comment"></span> |
| <a name="l00071"></a>00071 <span class="comment">@usage</span> |
| <a name="l00072"></a>00072 <span class="comment"></span> |
| <a name="l00073"></a>00073 <span class="comment">- Cumulative distribution functions:</span> |
| <a name="l00074"></a>00074 <span class="comment"> <pre>SELECT <em>distribution</em>_cdf(<em>random variate</em>[, <em>parameter1</em> [, <em>parameter2</em> [, <em>parameter3</em>] ] ])</pre></span> |
| <a name="l00075"></a>00075 <span class="comment">- Probability density/mass functions:</span> |
| <a name="l00076"></a>00076 <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> |
| <a name="l00077"></a>00077 <span class="comment">- Quantile functions:</span> |
| <a name="l00078"></a>00078 <span class="comment"> <pre>SELECT <em>distribution</em>_quantile(<em>probability</em>[, <em>parameter1</em> [, <em>parameter2</em> [, <em>parameter3</em>] ] ])</pre></span> |
| <a name="l00079"></a>00079 <span class="comment"></span> |
| <a name="l00080"></a>00080 <span class="comment">For concrete function signatures, see \ref prob.sql_in.</span> |
| <a name="l00081"></a>00081 <span class="comment"></span> |
| <a name="l00082"></a>00082 <span class="comment">@examp</span> |
| <a name="l00083"></a>00083 <span class="comment"></span> |
| <a name="l00084"></a>00084 <span class="comment">@verbatim</span> |
| <a name="l00085"></a>00085 <span class="comment">sql> SELECT normal_cdf(0);</span> |
| <a name="l00086"></a>00086 <span class="comment"> normal_cdf</span> |
| <a name="l00087"></a>00087 <span class="comment">------------</span> |
| <a name="l00088"></a>00088 <span class="comment"> 0.5</span> |
| <a name="l00089"></a>00089 <span class="comment"></span> |
| <a name="l00090"></a>00090 <span class="comment">sql> SELECT normal_quantile(0.5, 0, 1);</span> |
| <a name="l00091"></a>00091 <span class="comment"> normal_quantile</span> |
| <a name="l00092"></a>00092 <span class="comment">-----------------</span> |
| <a name="l00093"></a>00093 <span class="comment"> 0</span> |
| <a name="l00094"></a>00094 <span class="comment">(1 row)</span> |
| <a name="l00095"></a>00095 <span class="comment">@endverbatim</span> |
| <a name="l00096"></a>00096 <span class="comment"></span> |
| <a name="l00097"></a>00097 <span class="comment">@literature</span> |
| <a name="l00098"></a>00098 <span class="comment"></span> |
| <a name="l00099"></a>00099 <span class="comment">[1] John Maddock, Paul A. Bristow, Hubert Holin, Xiaogang Zhang, Bruno Lalande,</span> |
| <a name="l00100"></a>00100 <span class="comment"> Johan Råde, Gautam Sewani and Thijs van den Berg:</span> |
| <a name="l00101"></a>00101 <span class="comment"> <em>Boost Math Toolkit</em>, Version 1.49, available at:</span> |
| <a name="l00102"></a>00102 <span class="comment"> http://www.boost.org/doc/libs/1_49_0/libs/math/doc/sf_and_dist/html/index.html</span> |
| <a name="l00103"></a>00103 <span class="comment"></span> |
| <a name="l00104"></a>00104 <span class="comment">@sa File prob.sql_in documenting the SQL functions.</span> |
| <a name="l00105"></a>00105 <span class="comment">*/</span> |
| <a name="l00106"></a>00106 |
| <a name="l00107"></a>00107 <span class="comment"></span> |
| <a name="l00108"></a>00108 <span class="comment">/**</span> |
| <a name="l00109"></a>00109 <span class="comment"> * @brief Bernoulli cumulative distribution function</span> |
| <a name="l00110"></a>00110 <span class="comment"> *</span> |
| <a name="l00111"></a>00111 <span class="comment"> * @param x Random variate \f$ x \f$</span> |
| <a name="l00112"></a>00112 <span class="comment"> * @param sp Success probability \f$ p \in [0,1] \f$</span> |
| <a name="l00113"></a>00113 <span class="comment"> * @return \f$ \Pr[X \leq x] \f$ where \f$ X \f$ is a Bernoulli-distributed</span> |
| <a name="l00114"></a>00114 <span class="comment"> * random variable with success probability \f$ \mathit{sp} \f$</span> |
| <a name="l00115"></a>00115 <span class="comment"> */</span> |
| <a name="l00116"></a>00116 CREATE FUNCTION MADLIB_SCHEMA.bernoulli_cdf( |
| <a name="l00117"></a>00117 x DOUBLE PRECISION, |
| <a name="l00118"></a>00118 sp DOUBLE PRECISION |
| <a name="l00119"></a>00119 ) RETURNS DOUBLE PRECISION |
| <a name="l00120"></a>00120 AS 'MODULE_PATHNAME<span class="stringliteral">'</span> |
| <a name="l00121"></a>00121 <span class="stringliteral">LANGUAGE C</span> |
| <a name="l00122"></a>00122 <span class="stringliteral">IMMUTABLE STRICT;</span> |
| <a name="l00123"></a>00123 <span class="stringliteral"></span><span class="comment"></span> |
| <a name="l00124"></a>00124 <span class="comment">/**</span> |
| <a name="l00125"></a>00125 <span class="comment"> * @brief Bernoulli probability mass function</span> |
| <a name="l00126"></a>00126 <span class="comment"> *</span> |
| <a name="l00127"></a>00127 <span class="comment"> * @param x Random variate \f$ x \f$</span> |
| <a name="l00128"></a>00128 <span class="comment"> * @param sp Success probability \f$ \mathit{sp} \in [0,1] \f$</span> |
| <a name="l00129"></a>00129 <span class="comment"> * @return \f$ f(x) \f$ where \f$ f \f$ is the probability mass function of</span> |
| <a name="l00130"></a>00130 <span class="comment"> * a Bernoulli-distributed random variable with success probability</span> |
| <a name="l00131"></a>00131 <span class="comment"> * \f$ \mathit{sp} \f$</span> |
| <a name="l00132"></a>00132 <span class="comment"> */</span> |
| <a name="l00133"></a>00133 CREATE FUNCTION MADLIB_SCHEMA.bernoulli_pmf( |
| <a name="l00134"></a>00134 x INT4, |
| <a name="l00135"></a>00135 sp DOUBLE PRECISION |
| <a name="l00136"></a>00136 ) RETURNS DOUBLE PRECISION |
| <a name="l00137"></a>00137 AS 'MODULE_PATHNAME<span class="stringliteral">'</span> |
| <a name="l00138"></a><a class="code" href="prob_8sql__in.html#aea21a931dc5578a570e3370af3d8d43a">00138</a> <span class="stringliteral">LANGUAGE C</span> |
| <a name="l00139"></a>00139 <span class="stringliteral">IMMUTABLE STRICT;</span> |
| <a name="l00140"></a>00140 <span class="stringliteral"></span><span class="comment"></span> |
| <a name="l00141"></a>00141 <span class="comment">/**</span> |
| <a name="l00142"></a>00142 <span class="comment"> * @brief Bernoulli quantile function</span> |
| <a name="l00143"></a>00143 <span class="comment"> *</span> |
| <a name="l00144"></a>00144 <span class="comment"> * @param p Probability \f$ p \in [0,1] \f$</span> |
| <a name="l00145"></a>00145 <span class="comment"> * @param sp Success probability \f$ \mathit{sp} \in [0,1] \f$</span> |
| <a name="l00146"></a>00146 <span class="comment"> * @return 0 if \f$ p \leq 1 - \mathit{sp} \f$ and 1 otherwise</span> |
| <a name="l00147"></a>00147 <span class="comment"> */</span> |
| <a name="l00148"></a>00148 CREATE FUNCTION MADLIB_SCHEMA.bernoulli_quantile( |
| <a name="l00149"></a>00149 p DOUBLE PRECISION, |
| <a name="l00150"></a>00150 sp DOUBLE PRECISION |
| <a name="l00151"></a>00151 ) RETURNS DOUBLE PRECISION |
| <a name="l00152"></a>00152 AS 'MODULE_PATHNAME<span class="stringliteral">'</span> |
| <a name="l00153"></a>00153 <span class="stringliteral">LANGUAGE C</span> |
| <a name="l00154"></a>00154 <span class="stringliteral">IMMUTABLE STRICT;</span> |
| <a name="l00155"></a><a class="code" href="prob_8sql__in.html#a434b3ad1f3964835834dc2a942b820ef">00155</a> <span class="stringliteral"></span> |
| <a name="l00156"></a>00156 <span class="stringliteral"></span><span class="comment"></span> |
| <a name="l00157"></a>00157 <span class="comment">/**</span> |
| <a name="l00158"></a>00158 <span class="comment"> * @brief Beta cumulative distribution function</span> |
| <a name="l00159"></a>00159 <span class="comment"> *</span> |
| <a name="l00160"></a>00160 <span class="comment"> * @param x Random variate \f$ x \f$</span> |
| <a name="l00161"></a>00161 <span class="comment"> * @param alpha Shape \f$ \alpha > 0 \f$</span> |
| <a name="l00162"></a>00162 <span class="comment"> * @param beta Shape \f$ \beta > 0 \f$</span> |
| <a name="l00163"></a>00163 <span class="comment"> * @return \f$ \Pr[X \leq x] \f$ where \f$ X \f$ is a beta distributed random</span> |
| <a name="l00164"></a>00164 <span class="comment"> * variable with shape parameters \f$ \alpha \f$ and \f$ \beta \f$</span> |
| <a name="l00165"></a>00165 <span class="comment"> */</span> |
| <a name="l00166"></a>00166 CREATE FUNCTION MADLIB_SCHEMA.beta_cdf( |
| <a name="l00167"></a>00167 x DOUBLE PRECISION, |
| <a name="l00168"></a>00168 alpha DOUBLE PRECISION, |
| <a name="l00169"></a>00169 beta DOUBLE PRECISION |
| <a name="l00170"></a><a class="code" href="prob_8sql__in.html#a7133c2e86fd2f6384416ee0e4fd3a60b">00170</a> ) RETURNS DOUBLE PRECISION |
| <a name="l00171"></a>00171 AS 'MODULE_PATHNAME<span class="stringliteral">'</span> |
| <a name="l00172"></a>00172 <span class="stringliteral">LANGUAGE C</span> |
| <a name="l00173"></a>00173 <span class="stringliteral">IMMUTABLE STRICT;</span> |
| <a name="l00174"></a>00174 <span class="stringliteral"></span><span class="comment"></span> |
| <a name="l00175"></a>00175 <span class="comment">/**</span> |
| <a name="l00176"></a>00176 <span class="comment"> * @brief Beta probability density function</span> |
| <a name="l00177"></a>00177 <span class="comment"> *</span> |
| <a name="l00178"></a>00178 <span class="comment"> * @param x Random variate \f$ x \f$</span> |
| <a name="l00179"></a>00179 <span class="comment"> * @param alpha Shape \f$ \alpha > 0 \f$</span> |
| <a name="l00180"></a>00180 <span class="comment"> * @param beta Shape \f$ \beta > 0 \f$</span> |
| <a name="l00181"></a>00181 <span class="comment"> * @return \f$ f(x) \f$ where \f$ f \f$ is the probability density function of</span> |
| <a name="l00182"></a>00182 <span class="comment"> * a beta random variable with shape parameters \f$ \alpha \f$ and</span> |
| <a name="l00183"></a>00183 <span class="comment"> * \f$ \beta \f$</span> |
| <a name="l00184"></a>00184 <span class="comment"> */</span> |
| <a name="l00185"></a>00185 CREATE FUNCTION MADLIB_SCHEMA.beta_pdf( |
| <a name="l00186"></a>00186 x DOUBLE PRECISION, |
| <a name="l00187"></a>00187 alpha DOUBLE PRECISION, |
| <a name="l00188"></a><a class="code" href="prob_8sql__in.html#a72e1cca872da35592075dbcfb18aed3f">00188</a> beta DOUBLE PRECISION |
| <a name="l00189"></a>00189 ) RETURNS DOUBLE PRECISION |
| <a name="l00190"></a>00190 AS 'MODULE_PATHNAME<span class="stringliteral">'</span> |
| <a name="l00191"></a>00191 <span class="stringliteral">LANGUAGE C</span> |
| <a name="l00192"></a>00192 <span class="stringliteral">IMMUTABLE STRICT;</span> |
| <a name="l00193"></a>00193 <span class="stringliteral"></span><span class="comment"></span> |
| <a name="l00194"></a>00194 <span class="comment">/**</span> |
| <a name="l00195"></a>00195 <span class="comment"> * @brief Beta quantile function</span> |
| <a name="l00196"></a>00196 <span class="comment"> *</span> |
| <a name="l00197"></a>00197 <span class="comment"> * @param p Probability \f$ p \in [0,1] \f$</span> |
| <a name="l00198"></a>00198 <span class="comment"> * @param alpha Shape \f$ \alpha > 0 \f$</span> |
| <a name="l00199"></a>00199 <span class="comment"> * @param beta Shape \f$ \beta > 0 \f$</span> |
| <a name="l00200"></a>00200 <span class="comment"> * @return \f$ x \f$ such that \f$ p = \Pr[X \leq x] \f$ where \f$ X \f$ is</span> |
| <a name="l00201"></a>00201 <span class="comment"> * beta distribution random variable with shape parameters \f$ \alpha \f$</span> |
| <a name="l00202"></a>00202 <span class="comment"> * and \f$ \beta \f$</span> |
| <a name="l00203"></a>00203 <span class="comment"> */</span> |
| <a name="l00204"></a>00204 CREATE FUNCTION MADLIB_SCHEMA.beta_quantile( |
| <a name="l00205"></a>00205 p DOUBLE PRECISION, |
| <a name="l00206"></a>00206 alpha DOUBLE PRECISION, |
| <a name="l00207"></a><a class="code" href="prob_8sql__in.html#aa105049e6e3bb9b3891b0ed1b343e28e">00207</a> beta DOUBLE PRECISION |
| <a name="l00208"></a>00208 ) RETURNS DOUBLE PRECISION |
| <a name="l00209"></a>00209 AS 'MODULE_PATHNAME<span class="stringliteral">'</span> |
| <a name="l00210"></a>00210 <span class="stringliteral">LANGUAGE C</span> |
| <a name="l00211"></a>00211 <span class="stringliteral">IMMUTABLE STRICT;</span> |
| <a name="l00212"></a>00212 <span class="stringliteral"></span> |
| <a name="l00213"></a>00213 <span class="stringliteral"></span><span class="comment"></span> |
| <a name="l00214"></a>00214 <span class="comment">/**</span> |
| <a name="l00215"></a>00215 <span class="comment"> * @brief Binomial cumulative distribution function</span> |
| <a name="l00216"></a>00216 <span class="comment"> *</span> |
| <a name="l00217"></a>00217 <span class="comment"> * @param x Random variate \f$ x \f$</span> |
| <a name="l00218"></a>00218 <span class="comment"> * @param n The number of trials \f$ n \in \mathbb N_0 \f$</span> |
| <a name="l00219"></a>00219 <span class="comment"> * @param sp Success probability \f$ \mathit{sp} \in [0,1] \f$</span> |
| <a name="l00220"></a>00220 <span class="comment"> * @return \f$ \Pr[X \leq x] \f$ where \f$ X \f$ is a binomially distributed</span> |
| <a name="l00221"></a>00221 <span class="comment"> * random variable with \f$ n \f$ trials and success probability</span> |
| <a name="l00222"></a>00222 <span class="comment"> * \f$ \mathit{sp} \f$</span> |
| <a name="l00223"></a>00223 <span class="comment"> */</span> |
| <a name="l00224"></a>00224 CREATE FUNCTION MADLIB_SCHEMA.binomial_cdf( |
| <a name="l00225"></a>00225 x DOUBLE PRECISION, |
| <a name="l00226"></a><a class="code" href="prob_8sql__in.html#a32433aa742c0504d33e98e28a3e2f190">00226</a> n INT4, |
| <a name="l00227"></a>00227 sp DOUBLE PRECISION |
| <a name="l00228"></a>00228 ) RETURNS DOUBLE PRECISION |
| <a name="l00229"></a>00229 AS 'MODULE_PATHNAME<span class="stringliteral">'</span> |
| <a name="l00230"></a>00230 <span class="stringliteral">LANGUAGE C</span> |
| <a name="l00231"></a>00231 <span class="stringliteral">IMMUTABLE STRICT;</span> |
| <a name="l00232"></a>00232 <span class="stringliteral"></span><span class="comment"></span> |
| <a name="l00233"></a>00233 <span class="comment">/**</span> |
| <a name="l00234"></a>00234 <span class="comment"> * @brief Binomial probability mass function</span> |
| <a name="l00235"></a>00235 <span class="comment"> *</span> |
| <a name="l00236"></a>00236 <span class="comment"> * @param x Random variate \f$ x \f$</span> |
| <a name="l00237"></a>00237 <span class="comment"> * @param n The number of trials \f$ n \in \mathbb N_0 \f$</span> |
| <a name="l00238"></a>00238 <span class="comment"> * @param sp Success probability \f$ \mathit{sp} \in [0,1] \f$</span> |
| <a name="l00239"></a>00239 <span class="comment"> * @return \f$ f(x) \f$ where \f$ f \f$ is the probability mass function of</span> |
| <a name="l00240"></a>00240 <span class="comment"> * a binomially distributed random variable with \f$ n \f$ trials and</span> |
| <a name="l00241"></a>00241 <span class="comment"> * success probability \f$ \mathit{sp} \f$</span> |
| <a name="l00242"></a>00242 <span class="comment"> */</span> |
| <a name="l00243"></a>00243 CREATE FUNCTION MADLIB_SCHEMA.binomial_pmf( |
| <a name="l00244"></a>00244 x INT4, |
| <a name="l00245"></a>00245 n INT4, |
| <a name="l00246"></a><a class="code" href="prob_8sql__in.html#aa5000bad6e2e4af1c8cbfec7ea884476">00246</a> sp DOUBLE PRECISION |
| <a name="l00247"></a>00247 ) RETURNS DOUBLE PRECISION |
| <a name="l00248"></a>00248 AS 'MODULE_PATHNAME<span class="stringliteral">'</span> |
| <a name="l00249"></a>00249 <span class="stringliteral">LANGUAGE C</span> |
| <a name="l00250"></a>00250 <span class="stringliteral">IMMUTABLE STRICT;</span> |
| <a name="l00251"></a>00251 <span class="stringliteral"></span><span class="comment"></span> |
| <a name="l00252"></a>00252 <span class="comment">/**</span> |
| <a name="l00253"></a>00253 <span class="comment"> * @brief Binomial quantile function</span> |
| <a name="l00254"></a>00254 <span class="comment"> *</span> |
| <a name="l00255"></a>00255 <span class="comment"> * @param p Probability \f$ p \in [0,1] \f$</span> |
| <a name="l00256"></a>00256 <span class="comment"> * @param n The number of trials \f$ n \in \mathbb N_0 \f$</span> |
| <a name="l00257"></a>00257 <span class="comment"> * @param sp Success probability \f$ \mathit{sp} \in [0,1] \f$</span> |
| <a name="l00258"></a>00258 <span class="comment"> * @return If \f$ p < 0.5 \f$ the maximum \f$ x \f$ such that</span> |
| <a name="l00259"></a>00259 <span class="comment"> * \f$ p \geq \Pr[X \leq x] \f$. If \f$ p \geq 0.5 \f$ the minimum \f$ x \f$</span> |
| <a name="l00260"></a>00260 <span class="comment"> * such that \f$ p \leq \Pr[X \leq x] \f$. Here, \f$ X \f$ is a</span> |
| <a name="l00261"></a>00261 <span class="comment"> * binomially distributed random variable with \f$ n \f$ trials and</span> |
| <a name="l00262"></a>00262 <span class="comment"> * success probability \f$ \mathit{sp} \f$.</span> |
| <a name="l00263"></a>00263 <span class="comment"> */</span> |
| <a name="l00264"></a>00264 CREATE FUNCTION MADLIB_SCHEMA.binomial_quantile( |
| <a name="l00265"></a><a class="code" href="prob_8sql__in.html#aa0614475b8685bf8e37533d2ac5bb116">00265</a> p DOUBLE PRECISION, |
| <a name="l00266"></a>00266 n INT4, |
| <a name="l00267"></a>00267 sp DOUBLE PRECISION |
| <a name="l00268"></a>00268 ) RETURNS DOUBLE PRECISION |
| <a name="l00269"></a>00269 AS 'MODULE_PATHNAME<span class="stringliteral">'</span> |
| <a name="l00270"></a>00270 <span class="stringliteral">LANGUAGE C</span> |
| <a name="l00271"></a>00271 <span class="stringliteral">IMMUTABLE STRICT;</span> |
| <a name="l00272"></a>00272 <span class="stringliteral"></span> |
| <a name="l00273"></a>00273 <span class="stringliteral"></span><span class="comment"></span> |
| <a name="l00274"></a>00274 <span class="comment">/**</span> |
| <a name="l00275"></a>00275 <span class="comment"> * @brief Cauchy cumulative distribution function</span> |
| <a name="l00276"></a>00276 <span class="comment"> *</span> |
| <a name="l00277"></a>00277 <span class="comment"> * @param x Random variate \f$ x \f$</span> |
| <a name="l00278"></a>00278 <span class="comment"> * @param location Location \f$ x_0 \f$</span> |
| <a name="l00279"></a>00279 <span class="comment"> * @param scale Scale \f$ \gamma > 0 \f$</span> |
| <a name="l00280"></a>00280 <span class="comment"> * @return \f$ \Pr[X \leq x] \f$ where \f$ X \f$ is a Cauchy-distributed random</span> |
| <a name="l00281"></a>00281 <span class="comment"> * variable with location and scale parameters \f$ x_0 \f$ and</span> |
| <a name="l00282"></a>00282 <span class="comment"> * \f$ \gamma \f$, respectively</span> |
| <a name="l00283"></a>00283 <span class="comment"> */</span> |
| <a name="l00284"></a>00284 CREATE FUNCTION MADLIB_SCHEMA.cauchy_cdf( |
| <a name="l00285"></a>00285 x DOUBLE PRECISION, |
| <a name="l00286"></a><a class="code" href="prob_8sql__in.html#a49f421c58d2e1abd63b83d71af9edf21">00286</a> location DOUBLE PRECISION, |
| <a name="l00287"></a>00287 scale DOUBLE PRECISION |
| <a name="l00288"></a>00288 ) RETURNS DOUBLE PRECISION |
| <a name="l00289"></a>00289 AS 'MODULE_PATHNAME<span class="stringliteral">'</span> |
| <a name="l00290"></a>00290 <span class="stringliteral">LANGUAGE C</span> |
| <a name="l00291"></a>00291 <span class="stringliteral">IMMUTABLE STRICT;</span> |
| <a name="l00292"></a>00292 <span class="stringliteral"></span><span class="comment"></span> |
| <a name="l00293"></a>00293 <span class="comment">/**</span> |
| <a name="l00294"></a>00294 <span class="comment"> * @brief Cauchy probability density function</span> |
| <a name="l00295"></a>00295 <span class="comment"> *</span> |
| <a name="l00296"></a>00296 <span class="comment"> * @param x Random variate \f$ x \f$</span> |
| <a name="l00297"></a>00297 <span class="comment"> * @param location Location \f$ x_0 \f$</span> |
| <a name="l00298"></a>00298 <span class="comment"> * @param scale Scale \f$ \gamma > 0 \f$</span> |
| <a name="l00299"></a>00299 <span class="comment"> * @return \f$ f(x) \f$ where \f$ f \f$ is the probability density function of</span> |
| <a name="l00300"></a>00300 <span class="comment"> * a Cauchy-distributed random variable with location and scale parameters</span> |
| <a name="l00301"></a>00301 <span class="comment"> * \f$ x_0 \f$ and \f$ \gamma \f$, respectively</span> |
| <a name="l00302"></a>00302 <span class="comment"> */</span> |
| <a name="l00303"></a>00303 CREATE FUNCTION MADLIB_SCHEMA.cauchy_pdf( |
| <a name="l00304"></a>00304 x DOUBLE PRECISION, |
| <a name="l00305"></a>00305 location DOUBLE PRECISION, |
| <a name="l00306"></a><a class="code" href="prob_8sql__in.html#a2d8874c2a5679403a473bfedb14467a4">00306</a> scale DOUBLE PRECISION |
| <a name="l00307"></a>00307 ) RETURNS DOUBLE PRECISION |
| <a name="l00308"></a>00308 AS 'MODULE_PATHNAME<span class="stringliteral">'</span> |
| <a name="l00309"></a>00309 <span class="stringliteral">LANGUAGE C</span> |
| <a name="l00310"></a>00310 <span class="stringliteral">IMMUTABLE STRICT;</span> |
| <a name="l00311"></a>00311 <span class="stringliteral"></span><span class="comment"></span> |
| <a name="l00312"></a>00312 <span class="comment">/**</span> |
| <a name="l00313"></a>00313 <span class="comment"> * @brief Cauchy quantile function</span> |
| <a name="l00314"></a>00314 <span class="comment"> *</span> |
| <a name="l00315"></a>00315 <span class="comment"> * @param p Probability \f$ p \in [0,1] \f$</span> |
| <a name="l00316"></a>00316 <span class="comment"> * @param location Location \f$ x_0 \f$</span> |
| <a name="l00317"></a>00317 <span class="comment"> * @param scale Scale \f$ \gamma > 0 \f$</span> |
| <a name="l00318"></a>00318 <span class="comment"> * @return \f$ x \f$ such that \f$ p = \Pr[X \leq x] \f$ where \f$ X \f$ is a</span> |
| <a name="l00319"></a>00319 <span class="comment"> * Cauchy-distributed random variable with location and scale parameters</span> |
| <a name="l00320"></a>00320 <span class="comment"> * \f$ x_0 \f$ and \f$ \gamma \f$, respectively</span> |
| <a name="l00321"></a>00321 <span class="comment"> */</span> |
| <a name="l00322"></a>00322 CREATE FUNCTION MADLIB_SCHEMA.cauchy_quantile( |
| <a name="l00323"></a>00323 p DOUBLE PRECISION, |
| <a name="l00324"></a>00324 location DOUBLE PRECISION, |
| <a name="l00325"></a><a class="code" href="prob_8sql__in.html#aebfad9365a7fc7a553c3b5c7931f2450">00325</a> scale DOUBLE PRECISION |
| <a name="l00326"></a>00326 ) RETURNS DOUBLE PRECISION |
| <a name="l00327"></a>00327 AS 'MODULE_PATHNAME<span class="stringliteral">'</span> |
| <a name="l00328"></a>00328 <span class="stringliteral">LANGUAGE C</span> |
| <a name="l00329"></a>00329 <span class="stringliteral">IMMUTABLE STRICT;</span> |
| <a name="l00330"></a>00330 <span class="stringliteral"></span> |
| <a name="l00331"></a>00331 <span class="stringliteral"></span><span class="comment"></span> |
| <a name="l00332"></a>00332 <span class="comment">/**</span> |
| <a name="l00333"></a>00333 <span class="comment"> * @brief Chi-squared cumulative distribution function</span> |
| <a name="l00334"></a>00334 <span class="comment"> *</span> |
| <a name="l00335"></a>00335 <span class="comment"> * @param x Random variate \f$ x \f$</span> |
| <a name="l00336"></a>00336 <span class="comment"> * @param df Degrees of freedom \f$ \nu > 0 \f$</span> |
| <a name="l00337"></a>00337 <span class="comment"> * @return \f$ \Pr[X \leq x] \f$ where \f$ X \f$ is a chi-squared distributed</span> |
| <a name="l00338"></a>00338 <span class="comment"> * random variable with \f$ \nu \f$ degrees of freedom</span> |
| <a name="l00339"></a>00339 <span class="comment"> */</span> |
| <a name="l00340"></a>00340 CREATE FUNCTION MADLIB_SCHEMA.chi_squared_cdf( |
| <a name="l00341"></a>00341 x DOUBLE PRECISION, |
| <a name="l00342"></a>00342 df DOUBLE PRECISION |
| <a name="l00343"></a>00343 ) RETURNS DOUBLE PRECISION |
| <a name="l00344"></a><a class="code" href="prob_8sql__in.html#ae8aa9b741e89c8d9236a682d218006e0">00344</a> AS 'MODULE_PATHNAME<span class="stringliteral">'</span> |
| <a name="l00345"></a>00345 <span class="stringliteral">LANGUAGE C</span> |
| <a name="l00346"></a>00346 <span class="stringliteral">IMMUTABLE STRICT;</span> |
| <a name="l00347"></a>00347 <span class="stringliteral"></span><span class="comment"></span> |
| <a name="l00348"></a>00348 <span class="comment">/**</span> |
| <a name="l00349"></a>00349 <span class="comment"> * @brief Chi-squared distribution probability density function</span> |
| <a name="l00350"></a>00350 <span class="comment"> *</span> |
| <a name="l00351"></a>00351 <span class="comment"> * @param x Random variate \f$ x \f$</span> |
| <a name="l00352"></a>00352 <span class="comment"> * @param df Degrees of freedom \f$ \nu > 0 \f$</span> |
| <a name="l00353"></a>00353 <span class="comment"> * @return \f$ f(x) \f$ where \f$ f \f$ is the probability density function of</span> |
| <a name="l00354"></a>00354 <span class="comment"> * a chi-squared distributed random variable with \f$ \nu \f$ degrees of</span> |
| <a name="l00355"></a>00355 <span class="comment"> * freedom</span> |
| <a name="l00356"></a>00356 <span class="comment"> */</span> |
| <a name="l00357"></a>00357 CREATE FUNCTION MADLIB_SCHEMA.chi_squared_pdf( |
| <a name="l00358"></a>00358 x DOUBLE PRECISION, |
| <a name="l00359"></a>00359 df DOUBLE PRECISION |
| <a name="l00360"></a>00360 ) RETURNS DOUBLE PRECISION |
| <a name="l00361"></a>00361 AS 'MODULE_PATHNAME<span class="stringliteral">'</span> |
| <a name="l00362"></a><a class="code" href="prob_8sql__in.html#a230513b6b549d5b445cbacbdbab42c15">00362</a> <span class="stringliteral">LANGUAGE C</span> |
| <a name="l00363"></a>00363 <span class="stringliteral">IMMUTABLE STRICT;</span> |
| <a name="l00364"></a>00364 <span class="stringliteral"></span><span class="comment"></span> |
| <a name="l00365"></a>00365 <span class="comment">/**</span> |
| <a name="l00366"></a>00366 <span class="comment"> * @brief Chi-squared distribution quantile function</span> |
| <a name="l00367"></a>00367 <span class="comment"> *</span> |
| <a name="l00368"></a>00368 <span class="comment"> * @param p Probability \f$ p \in [0,1] \f$</span> |
| <a name="l00369"></a>00369 <span class="comment"> * @param df Degrees of freedom \f$ \mu > 0 \f$</span> |
| <a name="l00370"></a>00370 <span class="comment"> * @return \f$ x \f$ such that \f$ p = \Pr[X \leq x] \f$ where \f$ X \f$ is a</span> |
| <a name="l00371"></a>00371 <span class="comment"> * chi-squared distributed random variable with \f$ \nu \f$ degrees of</span> |
| <a name="l00372"></a>00372 <span class="comment"> * freedom</span> |
| <a name="l00373"></a>00373 <span class="comment"> */</span> |
| <a name="l00374"></a>00374 CREATE FUNCTION MADLIB_SCHEMA.chi_squared_quantile( |
| <a name="l00375"></a>00375 p DOUBLE PRECISION, |
| <a name="l00376"></a>00376 df DOUBLE PRECISION |
| <a name="l00377"></a>00377 ) RETURNS DOUBLE PRECISION |
| <a name="l00378"></a>00378 AS 'MODULE_PATHNAME<span class="stringliteral">'</span> |
| <a name="l00379"></a><a class="code" href="prob_8sql__in.html#a90bccc717d7052e83bafd7f160a783b1">00379</a> <span class="stringliteral">LANGUAGE C</span> |
| <a name="l00380"></a>00380 <span class="stringliteral">IMMUTABLE STRICT;</span> |
| <a name="l00381"></a>00381 <span class="stringliteral"></span> |
| <a name="l00382"></a>00382 <span class="stringliteral"></span><span class="comment"></span> |
| <a name="l00383"></a>00383 <span class="comment">/**</span> |
| <a name="l00384"></a>00384 <span class="comment"> * @brief Exponential cumulative distribution function</span> |
| <a name="l00385"></a>00385 <span class="comment"> *</span> |
| <a name="l00386"></a>00386 <span class="comment"> * @param x Random variate \f$ x \f$</span> |
| <a name="l00387"></a>00387 <span class="comment"> * @param lambda Rate parameter \f$ \lambda > 0 \f$</span> |
| <a name="l00388"></a>00388 <span class="comment"> * @return \f$ \Pr[X \leq x] \f$ where \f$ X \f$ is an exponentially distributed</span> |
| <a name="l00389"></a>00389 <span class="comment"> * random variable with rate parameter \f$ \lambda \f$</span> |
| <a name="l00390"></a>00390 <span class="comment"> */</span> |
| <a name="l00391"></a>00391 CREATE FUNCTION MADLIB_SCHEMA.exponential_cdf( |
| <a name="l00392"></a>00392 x DOUBLE PRECISION, |
| <a name="l00393"></a>00393 lambda DOUBLE PRECISION |
| <a name="l00394"></a>00394 ) RETURNS DOUBLE PRECISION |
| <a name="l00395"></a>00395 AS 'MODULE_PATHNAME<span class="stringliteral">'</span> |
| <a name="l00396"></a><a class="code" href="prob_8sql__in.html#ad125307fe65a33b60f6dd524037d4548">00396</a> <span class="stringliteral">LANGUAGE C</span> |
| <a name="l00397"></a>00397 <span class="stringliteral">IMMUTABLE STRICT;</span> |
| <a name="l00398"></a>00398 <span class="stringliteral"></span><span class="comment"></span> |
| <a name="l00399"></a>00399 <span class="comment">/**</span> |
| <a name="l00400"></a>00400 <span class="comment"> * @brief Exponential probability density function</span> |
| <a name="l00401"></a>00401 <span class="comment"> *</span> |
| <a name="l00402"></a>00402 <span class="comment"> * @param x Random variate \f$ x \f$</span> |
| <a name="l00403"></a>00403 <span class="comment"> * @param lambda Rate parameter \f$ \lambda > 0 \f$</span> |
| <a name="l00404"></a>00404 <span class="comment"> * @return \f$ f(x) \f$ where \f$ f \f$ is the probability density function of</span> |
| <a name="l00405"></a>00405 <span class="comment"> * exponentially distributed random variable with rate parameter</span> |
| <a name="l00406"></a>00406 <span class="comment"> * \f$ \lambda \f$</span> |
| <a name="l00407"></a>00407 <span class="comment"> */</span> |
| <a name="l00408"></a>00408 CREATE FUNCTION MADLIB_SCHEMA.exponential_pdf( |
| <a name="l00409"></a>00409 x DOUBLE PRECISION, |
| <a name="l00410"></a>00410 lambda DOUBLE PRECISION |
| <a name="l00411"></a>00411 ) RETURNS DOUBLE PRECISION |
| <a name="l00412"></a>00412 AS 'MODULE_PATHNAME<span class="stringliteral">'</span> |
| <a name="l00413"></a><a class="code" href="prob_8sql__in.html#a6d1bf6816f56b8e5ba6bf6ca94752f46">00413</a> <span class="stringliteral">LANGUAGE C</span> |
| <a name="l00414"></a>00414 <span class="stringliteral">IMMUTABLE STRICT;</span> |
| <a name="l00415"></a>00415 <span class="stringliteral"></span><span class="comment"></span> |
| <a name="l00416"></a>00416 <span class="comment">/**</span> |
| <a name="l00417"></a>00417 <span class="comment"> * @brief Exponential quantile function</span> |
| <a name="l00418"></a>00418 <span class="comment"> *</span> |
| <a name="l00419"></a>00419 <span class="comment"> * @param p Probability \f$ p \in [0,1] \f$</span> |
| <a name="l00420"></a>00420 <span class="comment"> * @param lambda Rate parameter \f$ \lambda > 0 \f$</span> |
| <a name="l00421"></a>00421 <span class="comment"> * @return \f$ x \f$ such that \f$ p = \Pr[X \leq x] \f$ where \f$ X \f$ is a</span> |
| <a name="l00422"></a>00422 <span class="comment"> * exponentially distributed random variable with rate parameter</span> |
| <a name="l00423"></a>00423 <span class="comment"> * \f$ \lambda \f$</span> |
| <a name="l00424"></a>00424 <span class="comment"> */</span> |
| <a name="l00425"></a>00425 CREATE FUNCTION MADLIB_SCHEMA.exponential_quantile( |
| <a name="l00426"></a>00426 p DOUBLE PRECISION, |
| <a name="l00427"></a>00427 lambda DOUBLE PRECISION |
| <a name="l00428"></a>00428 ) RETURNS DOUBLE PRECISION |
| <a name="l00429"></a>00429 AS 'MODULE_PATHNAME<span class="stringliteral">'</span> |
| <a name="l00430"></a><a class="code" href="prob_8sql__in.html#a18a5458c4bc85f0c4ea321317f90bdbb">00430</a> <span class="stringliteral">LANGUAGE C</span> |
| <a name="l00431"></a>00431 <span class="stringliteral">IMMUTABLE STRICT;</span> |
| <a name="l00432"></a>00432 <span class="stringliteral"></span> |
| <a name="l00433"></a>00433 <span class="stringliteral"></span><span class="comment"></span> |
| <a name="l00434"></a>00434 <span class="comment">/**</span> |
| <a name="l00435"></a>00435 <span class="comment"> * @brief Extreme Value cumulative distribution function</span> |
| <a name="l00436"></a>00436 <span class="comment"> *</span> |
| <a name="l00437"></a>00437 <span class="comment"> * @param x Random variate \f$ x \f$</span> |
| <a name="l00438"></a>00438 <span class="comment"> * @param location Location \f$ \alpha \f$</span> |
| <a name="l00439"></a>00439 <span class="comment"> * @param scale Scale \f$ \beta > 0 \f$</span> |
| <a name="l00440"></a>00440 <span class="comment"> * @return \f$ \Pr[X \leq x] \f$ where \f$ X \f$ is an extreme-value distributed</span> |
| <a name="l00441"></a>00441 <span class="comment"> * random variable with location and scale parameters \f$ \alpha \f$ and</span> |
| <a name="l00442"></a>00442 <span class="comment"> * \f$ \beta \f$, respectively</span> |
| <a name="l00443"></a>00443 <span class="comment"> */</span> |
| <a name="l00444"></a>00444 CREATE FUNCTION MADLIB_SCHEMA.extreme_value_cdf( |
| <a name="l00445"></a>00445 x DOUBLE PRECISION, |
| <a name="l00446"></a>00446 location DOUBLE PRECISION, |
| <a name="l00447"></a><a class="code" href="prob_8sql__in.html#ae3687b8e69a402154b829a6531b1b279">00447</a> scale DOUBLE PRECISION |
| <a name="l00448"></a>00448 ) RETURNS DOUBLE PRECISION |
| <a name="l00449"></a>00449 AS 'MODULE_PATHNAME<span class="stringliteral">'</span> |
| <a name="l00450"></a>00450 <span class="stringliteral">LANGUAGE C</span> |
| <a name="l00451"></a>00451 <span class="stringliteral">IMMUTABLE STRICT;</span> |
| <a name="l00452"></a>00452 <span class="stringliteral"></span><span class="comment"></span> |
| <a name="l00453"></a>00453 <span class="comment">/**</span> |
| <a name="l00454"></a>00454 <span class="comment"> * @brief Extreme Value probability density function</span> |
| <a name="l00455"></a>00455 <span class="comment"> *</span> |
| <a name="l00456"></a>00456 <span class="comment"> * @param x Random variate \f$ x \f$</span> |
| <a name="l00457"></a>00457 <span class="comment"> * @param location Location \f$ \alpha \f$</span> |
| <a name="l00458"></a>00458 <span class="comment"> * @param scale Scale \f$ \beta > 0 \f$</span> |
| <a name="l00459"></a>00459 <span class="comment"> * @return \f$ f(x) \f$ where \f$ f \f$ is the probability density function of</span> |
| <a name="l00460"></a>00460 <span class="comment"> * an extreme-value distributed random variable with location and scale</span> |
| <a name="l00461"></a>00461 <span class="comment"> * parameters \f$ \alpha \f$ and \f$ \beta \f$, respectively</span> |
| <a name="l00462"></a>00462 <span class="comment"> */</span> |
| <a name="l00463"></a>00463 CREATE FUNCTION MADLIB_SCHEMA.extreme_value_pdf( |
| <a name="l00464"></a>00464 x DOUBLE PRECISION, |
| <a name="l00465"></a>00465 location DOUBLE PRECISION, |
| <a name="l00466"></a><a class="code" href="prob_8sql__in.html#acffffe04c15eccd2e88cdac250bccc68">00466</a> scale DOUBLE PRECISION |
| <a name="l00467"></a>00467 ) RETURNS DOUBLE PRECISION |
| <a name="l00468"></a>00468 AS 'MODULE_PATHNAME<span class="stringliteral">'</span> |
| <a name="l00469"></a>00469 <span class="stringliteral">LANGUAGE C</span> |
| <a name="l00470"></a>00470 <span class="stringliteral">IMMUTABLE STRICT;</span> |
| <a name="l00471"></a>00471 <span class="stringliteral"></span><span class="comment"></span> |
| <a name="l00472"></a>00472 <span class="comment">/**</span> |
| <a name="l00473"></a>00473 <span class="comment"> * @brief Extreme Value quantile function</span> |
| <a name="l00474"></a>00474 <span class="comment"> *</span> |
| <a name="l00475"></a>00475 <span class="comment"> * @param p Probability \f$ p \in [0,1] \f$</span> |
| <a name="l00476"></a>00476 <span class="comment"> * @param location Location \f$ \alpha \f$</span> |
| <a name="l00477"></a>00477 <span class="comment"> * @param scale Scale \f$ \beta > 0 \f$</span> |
| <a name="l00478"></a>00478 <span class="comment"> * @return \f$ x \f$ such that \f$ p = \Pr[X \leq x] \f$ where \f$ X \f$ is</span> |
| <a name="l00479"></a>00479 <span class="comment"> * an extreme-value distributed random variable with location and scale</span> |
| <a name="l00480"></a>00480 <span class="comment"> * parameters \f$ \alpha \f$ and \f$ \beta \f$, respectively</span> |
| <a name="l00481"></a>00481 <span class="comment"> */</span> |
| <a name="l00482"></a>00482 CREATE FUNCTION MADLIB_SCHEMA.extreme_value_quantile( |
| <a name="l00483"></a>00483 p DOUBLE PRECISION, |
| <a name="l00484"></a>00484 location DOUBLE PRECISION, |
| <a name="l00485"></a><a class="code" href="prob_8sql__in.html#a03a3494462f4cb8c9fb6212e72b0b2e9">00485</a> scale DOUBLE PRECISION |
| <a name="l00486"></a>00486 ) RETURNS DOUBLE PRECISION |
| <a name="l00487"></a>00487 AS 'MODULE_PATHNAME<span class="stringliteral">'</span> |
| <a name="l00488"></a>00488 <span class="stringliteral">LANGUAGE C</span> |
| <a name="l00489"></a>00489 <span class="stringliteral">IMMUTABLE STRICT;</span> |
| <a name="l00490"></a>00490 <span class="stringliteral"></span> |
| <a name="l00491"></a>00491 <span class="stringliteral"></span><span class="comment"></span> |
| <a name="l00492"></a>00492 <span class="comment">/**</span> |
| <a name="l00493"></a>00493 <span class="comment"> * @brief Fisher F cumulative distribution function</span> |
| <a name="l00494"></a>00494 <span class="comment"> *</span> |
| <a name="l00495"></a>00495 <span class="comment"> * @param x Random variate \f$ x \f$</span> |
| <a name="l00496"></a>00496 <span class="comment"> * @param df1 Degrees of freedom in numerator \f$ \nu_1 > 0 \f$</span> |
| <a name="l00497"></a>00497 <span class="comment"> * @param df2 Degrees of freedom in denominator \f$ \nu_1 > 0 \f$</span> |
| <a name="l00498"></a>00498 <span class="comment"> * @return \f$ \Pr[X \leq x] \f$ where \f$ X \f$ is a Fisher F-distributed</span> |
| <a name="l00499"></a>00499 <span class="comment"> * random variable with parameters \f$ \nu_1 \f$ and \f$ \nu_2 \f$</span> |
| <a name="l00500"></a>00500 <span class="comment"> */</span> |
| <a name="l00501"></a>00501 CREATE FUNCTION MADLIB_SCHEMA.fisher_f_cdf( |
| <a name="l00502"></a>00502 x DOUBLE PRECISION, |
| <a name="l00503"></a>00503 df1 DOUBLE PRECISION, |
| <a name="l00504"></a><a class="code" href="prob_8sql__in.html#aeb5a7d295b83a891774a4fb0ef27c458">00504</a> df2 DOUBLE PRECISION |
| <a name="l00505"></a>00505 ) RETURNS DOUBLE PRECISION |
| <a name="l00506"></a>00506 AS 'MODULE_PATHNAME<span class="stringliteral">'</span> |
| <a name="l00507"></a>00507 <span class="stringliteral">LANGUAGE C</span> |
| <a name="l00508"></a>00508 <span class="stringliteral">IMMUTABLE STRICT;</span> |
| <a name="l00509"></a>00509 <span class="stringliteral"></span><span class="comment"></span> |
| <a name="l00510"></a>00510 <span class="comment">/**</span> |
| <a name="l00511"></a>00511 <span class="comment"> * @brief Fisher F probability density function</span> |
| <a name="l00512"></a>00512 <span class="comment"> *</span> |
| <a name="l00513"></a>00513 <span class="comment"> * @param x Random variate \f$ x \f$</span> |
| <a name="l00514"></a>00514 <span class="comment"> * @param df1 Degrees of freedom in numerator \f$ \nu_1 > 0 \f$</span> |
| <a name="l00515"></a>00515 <span class="comment"> * @param df2 Degrees of freedom in denominator \f$ \nu_1 > 0 \f$</span> |
| <a name="l00516"></a>00516 <span class="comment"> * @return \f$ f(x) \f$ where \f$ f \f$ is the probability density function of</span> |
| <a name="l00517"></a>00517 <span class="comment"> * a Fisher F-distributed random variable with parameters \f$ \nu_1 \f$ and</span> |
| <a name="l00518"></a>00518 <span class="comment"> * \f$ \nu_2 \f$</span> |
| <a name="l00519"></a>00519 <span class="comment"> */</span> |
| <a name="l00520"></a>00520 CREATE FUNCTION MADLIB_SCHEMA.fisher_f_pdf( |
| <a name="l00521"></a>00521 x DOUBLE PRECISION, |
| <a name="l00522"></a>00522 df1 DOUBLE PRECISION, |
| <a name="l00523"></a><a class="code" href="prob_8sql__in.html#a6c5b3e35531e44098f9d0cbef14cb8a6">00523</a> df2 DOUBLE PRECISION |
| <a name="l00524"></a>00524 ) RETURNS DOUBLE PRECISION |
| <a name="l00525"></a>00525 AS 'MODULE_PATHNAME<span class="stringliteral">'</span> |
| <a name="l00526"></a>00526 <span class="stringliteral">LANGUAGE C</span> |
| <a name="l00527"></a>00527 <span class="stringliteral">IMMUTABLE STRICT;</span> |
| <a name="l00528"></a>00528 <span class="stringliteral"></span><span class="comment"></span> |
| <a name="l00529"></a>00529 <span class="comment">/**</span> |
| <a name="l00530"></a>00530 <span class="comment"> * @brief Fisher F quantile function</span> |
| <a name="l00531"></a>00531 <span class="comment"> *</span> |
| <a name="l00532"></a>00532 <span class="comment"> * @param p Probability \f$ p \in [0,1] \f$</span> |
| <a name="l00533"></a>00533 <span class="comment"> * @param df1 Degrees of freedom in numerator \f$ \nu_1 > 0 \f$</span> |
| <a name="l00534"></a>00534 <span class="comment"> * @param df2 Degrees of freedom in denominator \f$ \nu_1 > 0 \f$</span> |
| <a name="l00535"></a>00535 <span class="comment"> * @return \f$ x \f$ such that \f$ p = \Pr[X \leq x] \f$ where \f$ X \f$ is a</span> |
| <a name="l00536"></a>00536 <span class="comment"> * Fisher F-distributed random variable with parameters \f$ \nu_1 \f$ and</span> |
| <a name="l00537"></a>00537 <span class="comment"> * \f$ \nu_2 \f$</span> |
| <a name="l00538"></a>00538 <span class="comment"> */</span> |
| <a name="l00539"></a>00539 CREATE FUNCTION MADLIB_SCHEMA.fisher_f_quantile( |
| <a name="l00540"></a>00540 p DOUBLE PRECISION, |
| <a name="l00541"></a>00541 df1 DOUBLE PRECISION, |
| <a name="l00542"></a><a class="code" href="prob_8sql__in.html#a1c7937426379a8913519a6abc5a38ac2">00542</a> df2 DOUBLE PRECISION |
| <a name="l00543"></a>00543 ) RETURNS DOUBLE PRECISION |
| <a name="l00544"></a>00544 AS 'MODULE_PATHNAME<span class="stringliteral">'</span> |
| <a name="l00545"></a>00545 <span class="stringliteral">LANGUAGE C</span> |
| <a name="l00546"></a>00546 <span class="stringliteral">IMMUTABLE STRICT;</span> |
| <a name="l00547"></a>00547 <span class="stringliteral"></span> |
| <a name="l00548"></a>00548 <span class="stringliteral"></span><span class="comment"></span> |
| <a name="l00549"></a>00549 <span class="comment">/**</span> |
| <a name="l00550"></a>00550 <span class="comment"> * @brief Gamma cumulative distribution function</span> |
| <a name="l00551"></a>00551 <span class="comment"> *</span> |
| <a name="l00552"></a>00552 <span class="comment"> * @param x Random variate \f$ x \f$</span> |
| <a name="l00553"></a>00553 <span class="comment"> * @param shape Shape \f$ k > 0 \f$</span> |
| <a name="l00554"></a>00554 <span class="comment"> * @param scale Scale \f$ \theta > 0 \f$</span> |
| <a name="l00555"></a>00555 <span class="comment"> * @return \f$ \Pr[X \leq x] \f$ where \f$ X \f$ is a gamma distributed random</span> |
| <a name="l00556"></a>00556 <span class="comment"> * variable with shape and scale parameters \f$ k \f$ and</span> |
| <a name="l00557"></a>00557 <span class="comment"> * \f$ \theta \f$, respectively</span> |
| <a name="l00558"></a>00558 <span class="comment"> */</span> |
| <a name="l00559"></a>00559 CREATE FUNCTION MADLIB_SCHEMA.gamma_cdf( |
| <a name="l00560"></a>00560 x DOUBLE PRECISION, |
| <a name="l00561"></a><a class="code" href="prob_8sql__in.html#ab6ed888a5338a0bee9c55edf4d33847f">00561</a> shape DOUBLE PRECISION, |
| <a name="l00562"></a>00562 scale DOUBLE PRECISION |
| <a name="l00563"></a>00563 ) RETURNS DOUBLE PRECISION |
| <a name="l00564"></a>00564 AS 'MODULE_PATHNAME<span class="stringliteral">'</span> |
| <a name="l00565"></a>00565 <span class="stringliteral">LANGUAGE C</span> |
| <a name="l00566"></a>00566 <span class="stringliteral">IMMUTABLE STRICT;</span> |
| <a name="l00567"></a>00567 <span class="stringliteral"></span><span class="comment"></span> |
| <a name="l00568"></a>00568 <span class="comment">/**</span> |
| <a name="l00569"></a>00569 <span class="comment"> * @brief Gamma probability density function</span> |
| <a name="l00570"></a>00570 <span class="comment"> *</span> |
| <a name="l00571"></a>00571 <span class="comment"> * @param x Random variate \f$ x \f$</span> |
| <a name="l00572"></a>00572 <span class="comment"> * @param shape Shape \f$ k > 0 \f$</span> |
| <a name="l00573"></a>00573 <span class="comment"> * @param scale Scale \f$ \theta > 0 \f$</span> |
| <a name="l00574"></a>00574 <span class="comment"> * @return \f$ f(x) \f$ where \f$ f \f$ is the probability density function of</span> |
| <a name="l00575"></a>00575 <span class="comment"> * a gamma distributed random variable with shape and scale parameters</span> |
| <a name="l00576"></a>00576 <span class="comment"> * \f$ k \f$ and \f$ \theta \f$, respectively</span> |
| <a name="l00577"></a>00577 <span class="comment"> */</span> |
| <a name="l00578"></a>00578 CREATE FUNCTION MADLIB_SCHEMA.gamma_pdf( |
| <a name="l00579"></a>00579 x DOUBLE PRECISION, |
| <a name="l00580"></a>00580 shape DOUBLE PRECISION, |
| <a name="l00581"></a><a class="code" href="prob_8sql__in.html#ab6760b0486bad2f1ab0635eb59404e7c">00581</a> scale DOUBLE PRECISION |
| <a name="l00582"></a>00582 ) RETURNS DOUBLE PRECISION |
| <a name="l00583"></a>00583 AS 'MODULE_PATHNAME<span class="stringliteral">'</span> |
| <a name="l00584"></a>00584 <span class="stringliteral">LANGUAGE C</span> |
| <a name="l00585"></a>00585 <span class="stringliteral">IMMUTABLE STRICT;</span> |
| <a name="l00586"></a>00586 <span class="stringliteral"></span><span class="comment"></span> |
| <a name="l00587"></a>00587 <span class="comment">/**</span> |
| <a name="l00588"></a>00588 <span class="comment"> * @brief Gamma quantile function</span> |
| <a name="l00589"></a>00589 <span class="comment"> *</span> |
| <a name="l00590"></a>00590 <span class="comment"> * @param p Probability \f$ p \in [0,1] \f$</span> |
| <a name="l00591"></a>00591 <span class="comment"> * @param shape Shape \f$ k > 0 \f$</span> |
| <a name="l00592"></a>00592 <span class="comment"> * @param scale Scale \f$ \theta > 0 \f$</span> |
| <a name="l00593"></a>00593 <span class="comment"> * @return \f$ x \f$ such that \f$ p = \Pr[X \leq x] \f$ where \f$ X \f$ is</span> |
| <a name="l00594"></a>00594 <span class="comment"> * a gamma distributed random variable with shape and scale parameters</span> |
| <a name="l00595"></a>00595 <span class="comment"> * \f$ k \f$ and \f$ \theta \f$, respectively</span> |
| <a name="l00596"></a>00596 <span class="comment"> */</span> |
| <a name="l00597"></a>00597 CREATE FUNCTION MADLIB_SCHEMA.gamma_quantile( |
| <a name="l00598"></a>00598 p DOUBLE PRECISION, |
| <a name="l00599"></a>00599 shape DOUBLE PRECISION, |
| <a name="l00600"></a><a class="code" href="prob_8sql__in.html#a6c37e3bda2596accbb46525321a328c4">00600</a> scale DOUBLE PRECISION |
| <a name="l00601"></a>00601 ) RETURNS DOUBLE PRECISION |
| <a name="l00602"></a>00602 AS 'MODULE_PATHNAME<span class="stringliteral">'</span> |
| <a name="l00603"></a>00603 <span class="stringliteral">LANGUAGE C</span> |
| <a name="l00604"></a>00604 <span class="stringliteral">IMMUTABLE STRICT;</span> |
| <a name="l00605"></a>00605 <span class="stringliteral"></span> |
| <a name="l00606"></a>00606 <span class="stringliteral"></span><span class="comment"></span> |
| <a name="l00607"></a>00607 <span class="comment">/**</span> |
| <a name="l00608"></a>00608 <span class="comment"> * @brief Geometric cumulative distribution function</span> |
| <a name="l00609"></a>00609 <span class="comment"> *</span> |
| <a name="l00610"></a>00610 <span class="comment"> * @param x Random variate \f$ x \f$</span> |
| <a name="l00611"></a>00611 <span class="comment"> * @param sp Success probability \f$ \mathit{sp} \in [0,1] \f$</span> |
| <a name="l00612"></a>00612 <span class="comment"> * @return \f$ \Pr[X \leq x] \f$ where \f$ X \f$ is a geometrically distributed</span> |
| <a name="l00613"></a>00613 <span class="comment"> * random variable with success probability \f$ \mathit{sp} \f$.</span> |
| <a name="l00614"></a>00614 <span class="comment"> */</span> |
| <a name="l00615"></a>00615 CREATE FUNCTION MADLIB_SCHEMA.geometric_cdf( |
| <a name="l00616"></a>00616 x DOUBLE PRECISION, |
| <a name="l00617"></a>00617 sp DOUBLE PRECISION |
| <a name="l00618"></a>00618 ) RETURNS DOUBLE PRECISION |
| <a name="l00619"></a><a class="code" href="prob_8sql__in.html#ac48bbd491bd34831415705c3a0b7bf29">00619</a> AS 'MODULE_PATHNAME<span class="stringliteral">'</span> |
| <a name="l00620"></a>00620 <span class="stringliteral">LANGUAGE C</span> |
| <a name="l00621"></a>00621 <span class="stringliteral">IMMUTABLE STRICT;</span> |
| <a name="l00622"></a>00622 <span class="stringliteral"></span><span class="comment"></span> |
| <a name="l00623"></a>00623 <span class="comment">/**</span> |
| <a name="l00624"></a>00624 <span class="comment"> * @brief Geometric probability mass function</span> |
| <a name="l00625"></a>00625 <span class="comment"> *</span> |
| <a name="l00626"></a>00626 <span class="comment"> * @param x Random variate \f$ x \f$</span> |
| <a name="l00627"></a>00627 <span class="comment"> * @param sp Success probability \f$ \mathit{sp} \in [0,1] \f$</span> |
| <a name="l00628"></a>00628 <span class="comment"> * @return \f$ f(x) \f$ where \f$ f \f$ is the probability mass function of a</span> |
| <a name="l00629"></a>00629 <span class="comment"> * geometrically distributed random variable with success probability</span> |
| <a name="l00630"></a>00630 <span class="comment"> * \f$ \mathit{sp} \f$</span> |
| <a name="l00631"></a>00631 <span class="comment"> */</span> |
| <a name="l00632"></a>00632 CREATE FUNCTION MADLIB_SCHEMA.geometric_pmf( |
| <a name="l00633"></a>00633 x INT4, |
| <a name="l00634"></a>00634 sp DOUBLE PRECISION |
| <a name="l00635"></a>00635 ) RETURNS DOUBLE PRECISION |
| <a name="l00636"></a>00636 AS 'MODULE_PATHNAME<span class="stringliteral">'</span> |
| <a name="l00637"></a><a class="code" href="prob_8sql__in.html#a00879bdf7d48ceddedb3b4cc33511497">00637</a> <span class="stringliteral">LANGUAGE C</span> |
| <a name="l00638"></a>00638 <span class="stringliteral">IMMUTABLE STRICT;</span> |
| <a name="l00639"></a>00639 <span class="stringliteral"></span><span class="comment"></span> |
| <a name="l00640"></a>00640 <span class="comment">/**</span> |
| <a name="l00641"></a>00641 <span class="comment"> * @brief Geometric quantile function</span> |
| <a name="l00642"></a>00642 <span class="comment"> *</span> |
| <a name="l00643"></a>00643 <span class="comment"> * @param p Probability \f$ p \in [0,1] \f$</span> |
| <a name="l00644"></a>00644 <span class="comment"> * @param sp Success probability \f$ \mathit{sp} \in [0,1] \f$</span> |
| <a name="l00645"></a>00645 <span class="comment"> * @return If \f$ p < 0.5 \f$ the maximum \f$ x \f$ such that</span> |
| <a name="l00646"></a>00646 <span class="comment"> * \f$ p \geq \Pr[X \leq x] \f$. If \f$ p \geq 0.5 \f$ the minimum \f$ x \f$</span> |
| <a name="l00647"></a>00647 <span class="comment"> * such that \f$ p \leq \Pr[X \leq x] \f$. Here, \f$ X \f$ is a</span> |
| <a name="l00648"></a>00648 <span class="comment"> * geometrically distributed random variable with success probability</span> |
| <a name="l00649"></a>00649 <span class="comment"> * \f$ \mathit{sp} \f$.</span> |
| <a name="l00650"></a>00650 <span class="comment"> */</span> |
| <a name="l00651"></a>00651 CREATE FUNCTION MADLIB_SCHEMA.geometric_quantile( |
| <a name="l00652"></a>00652 p DOUBLE PRECISION, |
| <a name="l00653"></a>00653 sp DOUBLE PRECISION |
| <a name="l00654"></a><a class="code" href="prob_8sql__in.html#a5e08db93bd448a1e2164e106ce5781a4">00654</a> ) RETURNS DOUBLE PRECISION |
| <a name="l00655"></a>00655 AS 'MODULE_PATHNAME<span class="stringliteral">'</span> |
| <a name="l00656"></a>00656 <span class="stringliteral">LANGUAGE C</span> |
| <a name="l00657"></a>00657 <span class="stringliteral">IMMUTABLE STRICT;</span> |
| <a name="l00658"></a>00658 <span class="stringliteral"></span> |
| <a name="l00659"></a>00659 <span class="stringliteral"></span><span class="comment"></span> |
| <a name="l00660"></a>00660 <span class="comment">/**</span> |
| <a name="l00661"></a>00661 <span class="comment"> * @brief Hypergeometric cumulative distribution function</span> |
| <a name="l00662"></a>00662 <span class="comment"> *</span> |
| <a name="l00663"></a>00663 <span class="comment"> * @param x Random variate \f$ x \f$</span> |
| <a name="l00664"></a>00664 <span class="comment"> * @param r Number \f$ r \in \{ 0, 1, \dots, N \} \f$ of items with</span> |
| <a name="l00665"></a>00665 <span class="comment"> * distinct property (sometimes called the number of <em>success states</em></span> |
| <a name="l00666"></a>00666 <span class="comment"> * in population)</span> |
| <a name="l00667"></a>00667 <span class="comment"> * @param n Number \f$ n \in \{ 0, 1, \dots, N \} \f$ of draws (without</span> |
| <a name="l00668"></a>00668 <span class="comment"> * replacement)</span> |
| <a name="l00669"></a>00669 <span class="comment"> * @param N Total number \f$ N \in \mathbb N \f$ of items</span> |
| <a name="l00670"></a>00670 <span class="comment"> * @return \f$ \Pr[X \leq x] \f$ where \f$ X \f$ is a hypergeometrically</span> |
| <a name="l00671"></a>00671 <span class="comment"> * distributed random variable with parameters \f$ r, n, N \f$</span> |
| <a name="l00672"></a>00672 <span class="comment"> *</span> |
| <a name="l00673"></a><a class="code" href="prob_8sql__in.html#a62674ca958aec0533cdf0a74a1dadea9">00673</a> <span class="comment"> * @internal Boost error messages refer to parameters 'r', 'n', 'N', so for now</span> |
| <a name="l00674"></a>00674 <span class="comment"> * we use the same identifiers for our function definition.</span> |
| <a name="l00675"></a>00675 <span class="comment"> */</span> |
| <a name="l00676"></a>00676 CREATE FUNCTION MADLIB_SCHEMA.hypergeometric_cdf( |
| <a name="l00677"></a>00677 x DOUBLE PRECISION, |
| <a name="l00678"></a>00678 r INT4, |
| <a name="l00679"></a>00679 n INT4, |
| <a name="l00680"></a>00680 "N" INT4 |
| <a name="l00681"></a>00681 ) RETURNS DOUBLE PRECISION |
| <a name="l00682"></a>00682 AS 'MODULE_PATHNAME<span class="stringliteral">'</span> |
| <a name="l00683"></a>00683 <span class="stringliteral">LANGUAGE C</span> |
| <a name="l00684"></a>00684 <span class="stringliteral">IMMUTABLE STRICT;</span> |
| <a name="l00685"></a>00685 <span class="stringliteral"></span><span class="comment"></span> |
| <a name="l00686"></a>00686 <span class="comment">/**</span> |
| <a name="l00687"></a>00687 <span class="comment"> * @brief Hypergeometric probability mass function</span> |
| <a name="l00688"></a>00688 <span class="comment"> *</span> |
| <a name="l00689"></a>00689 <span class="comment"> * @param x Random variate \f$ x \f$</span> |
| <a name="l00690"></a>00690 <span class="comment"> * @param r Number \f$ r \in \{ 0, 1, \dots, N \} \f$ of items with</span> |
| <a name="l00691"></a>00691 <span class="comment"> * distinct property (sometimes called the number of <em>success states</em></span> |
| <a name="l00692"></a>00692 <span class="comment"> * in population)</span> |
| <a name="l00693"></a>00693 <span class="comment"> * @param n Number \f$ n \in \{ 0, 1, \dots, N \} \f$ of draws (without</span> |
| <a name="l00694"></a>00694 <span class="comment"> * replacement)</span> |
| <a name="l00695"></a>00695 <span class="comment"> * @param N Total number \f$ N \in \mathbb N \f$ of items</span> |
| <a name="l00696"></a>00696 <span class="comment"> * @return \f$ f(x) \f$ where \f$ f \f$ is the probability mass function of</span> |
| <a name="l00697"></a>00697 <span class="comment"> * a hypergeometrically distributed random variable with parameters</span> |
| <a name="l00698"></a><a class="code" href="prob_8sql__in.html#a5c48e7fa2fc7bcbc69c7f4da663d457f">00698</a> <span class="comment"> * \f$ r, n, N \f$</span> |
| <a name="l00699"></a>00699 <span class="comment"> */</span> |
| <a name="l00700"></a>00700 CREATE FUNCTION MADLIB_SCHEMA.hypergeometric_pmf( |
| <a name="l00701"></a>00701 x INT4, |
| <a name="l00702"></a>00702 r INT4, |
| <a name="l00703"></a>00703 n INT4, |
| <a name="l00704"></a>00704 "N" INT4 |
| <a name="l00705"></a>00705 ) RETURNS DOUBLE PRECISION |
| <a name="l00706"></a>00706 AS 'MODULE_PATHNAME<span class="stringliteral">'</span> |
| <a name="l00707"></a>00707 <span class="stringliteral">LANGUAGE C</span> |
| <a name="l00708"></a>00708 <span class="stringliteral">IMMUTABLE STRICT;</span> |
| <a name="l00709"></a>00709 <span class="stringliteral"></span> |
| <a name="l00710"></a>00710 <span class="stringliteral"></span><span class="comment"></span> |
| <a name="l00711"></a>00711 <span class="comment">/**</span> |
| <a name="l00712"></a>00712 <span class="comment"> * @brief Hypergeometric quantile function</span> |
| <a name="l00713"></a>00713 <span class="comment"> *</span> |
| <a name="l00714"></a>00714 <span class="comment"> * @param p Probability \f$ p \in [0,1] \f$</span> |
| <a name="l00715"></a>00715 <span class="comment"> * @param r Number \f$ r \in \{ 0, 1, \dots, N \} \f$ of items with</span> |
| <a name="l00716"></a>00716 <span class="comment"> * distinct property (sometimes called the number of <em>success states</em></span> |
| <a name="l00717"></a>00717 <span class="comment"> * in population)</span> |
| <a name="l00718"></a>00718 <span class="comment"> * @param n Number \f$ n \in \{ 0, 1, \dots, N \} \f$ of draws (without</span> |
| <a name="l00719"></a>00719 <span class="comment"> * replacement)</span> |
| <a name="l00720"></a>00720 <span class="comment"> * @param N Total number \f$ N \in \mathbb N \f$ of items</span> |
| <a name="l00721"></a>00721 <span class="comment"> * @return \f$ x \f$ such that \f$ p = \Pr[X \leq x] \f$ where \f$ X \f$ is</span> |
| <a name="l00722"></a><a class="code" href="prob_8sql__in.html#afbd2f8d9fb30fb179f59cc14f1fd8d6d">00722</a> <span class="comment"> * a hypergeometrically distributed random variable with parameters</span> |
| <a name="l00723"></a>00723 <span class="comment"> * \f$ r, n, N \f$</span> |
| <a name="l00724"></a>00724 <span class="comment"> */</span> |
| <a name="l00725"></a>00725 CREATE FUNCTION MADLIB_SCHEMA.hypergeometric_quantile( |
| <a name="l00726"></a>00726 p DOUBLE PRECISION, |
| <a name="l00727"></a>00727 r INT4, |
| <a name="l00728"></a>00728 n INT4, |
| <a name="l00729"></a>00729 "N" INT4 |
| <a name="l00730"></a>00730 ) RETURNS DOUBLE PRECISION |
| <a name="l00731"></a>00731 AS 'MODULE_PATHNAME<span class="stringliteral">'</span> |
| <a name="l00732"></a>00732 <span class="stringliteral">LANGUAGE C</span> |
| <a name="l00733"></a>00733 <span class="stringliteral">IMMUTABLE STRICT;</span> |
| <a name="l00734"></a>00734 <span class="stringliteral"></span> |
| <a name="l00735"></a>00735 <span class="stringliteral"></span><span class="comment"></span> |
| <a name="l00736"></a>00736 <span class="comment">/**</span> |
| <a name="l00737"></a>00737 <span class="comment"> * @brief Inverse Gamma cumulative distribution function</span> |
| <a name="l00738"></a>00738 <span class="comment"> *</span> |
| <a name="l00739"></a>00739 <span class="comment"> * @param x Random variate \f$ x \f$</span> |
| <a name="l00740"></a>00740 <span class="comment"> * @param shape Shape \f$ \alpha > 0 \f$</span> |
| <a name="l00741"></a>00741 <span class="comment"> * @param scale Scale \f$ \beta > 0 \f$</span> |
| <a name="l00742"></a>00742 <span class="comment"> * @return \f$ \Pr[X \leq x] \f$ where \f$ X \f$ is an inverse-gamma distributed</span> |
| <a name="l00743"></a>00743 <span class="comment"> * random variable with shape and scale parameters \f$ \alpha \f$ and</span> |
| <a name="l00744"></a>00744 <span class="comment"> * \f$ \beta \f$, respectively</span> |
| <a name="l00745"></a>00745 <span class="comment"> */</span> |
| <a name="l00746"></a>00746 CREATE FUNCTION MADLIB_SCHEMA.inverse_gamma_cdf( |
| <a name="l00747"></a><a class="code" href="prob_8sql__in.html#a813cc27fe097e797ed0fb6022c7bb79a">00747</a> x DOUBLE PRECISION, |
| <a name="l00748"></a>00748 shape DOUBLE PRECISION, |
| <a name="l00749"></a>00749 scale DOUBLE PRECISION |
| <a name="l00750"></a>00750 ) RETURNS DOUBLE PRECISION |
| <a name="l00751"></a>00751 AS 'MODULE_PATHNAME<span class="stringliteral">'</span> |
| <a name="l00752"></a>00752 <span class="stringliteral">LANGUAGE C</span> |
| <a name="l00753"></a>00753 <span class="stringliteral">IMMUTABLE STRICT;</span> |
| <a name="l00754"></a>00754 <span class="stringliteral"></span><span class="comment"></span> |
| <a name="l00755"></a>00755 <span class="comment">/**</span> |
| <a name="l00756"></a>00756 <span class="comment"> * @brief Inverse Gamma probability density function</span> |
| <a name="l00757"></a>00757 <span class="comment"> *</span> |
| <a name="l00758"></a>00758 <span class="comment"> * @param x Random variate \f$ x \f$</span> |
| <a name="l00759"></a>00759 <span class="comment"> * @param shape Shape \f$ \alpha > 0 \f$</span> |
| <a name="l00760"></a>00760 <span class="comment"> * @param scale Scale \f$ \beta > 0 \f$</span> |
| <a name="l00761"></a>00761 <span class="comment"> * @return \f$ f(x) \f$ where \f$ f \f$ is the probability density function of</span> |
| <a name="l00762"></a>00762 <span class="comment"> * an inverse-gamma distributed random variable with shape and scale</span> |
| <a name="l00763"></a>00763 <span class="comment"> * parameters \f$ \alpha \f$ and \f$ \beta \f$, respectively</span> |
| <a name="l00764"></a>00764 <span class="comment"> */</span> |
| <a name="l00765"></a>00765 CREATE FUNCTION MADLIB_SCHEMA.inverse_gamma_pdf( |
| <a name="l00766"></a>00766 x DOUBLE PRECISION, |
| <a name="l00767"></a>00767 shape DOUBLE PRECISION, |
| <a name="l00768"></a><a class="code" href="prob_8sql__in.html#a85e9c16aa2c6973ddeb7883a5f153d93">00768</a> scale DOUBLE PRECISION |
| <a name="l00769"></a>00769 ) RETURNS DOUBLE PRECISION |
| <a name="l00770"></a>00770 AS 'MODULE_PATHNAME<span class="stringliteral">'</span> |
| <a name="l00771"></a>00771 <span class="stringliteral">LANGUAGE C</span> |
| <a name="l00772"></a>00772 <span class="stringliteral">IMMUTABLE STRICT;</span> |
| <a name="l00773"></a>00773 <span class="stringliteral"></span><span class="comment"></span> |
| <a name="l00774"></a>00774 <span class="comment">/**</span> |
| <a name="l00775"></a>00775 <span class="comment"> * @brief Inverse Gamma quantile function</span> |
| <a name="l00776"></a>00776 <span class="comment"> *</span> |
| <a name="l00777"></a>00777 <span class="comment"> * @param p Probability \f$ p \in [0,1] \f$</span> |
| <a name="l00778"></a>00778 <span class="comment"> * @param shape Shape \f$ \alpha > 0 \f$</span> |
| <a name="l00779"></a>00779 <span class="comment"> * @param scale Scale \f$ \beta > 0 \f$</span> |
| <a name="l00780"></a>00780 <span class="comment"> * @return \f$ x \f$ such that \f$ p = \Pr[X \leq x] \f$ where \f$ X \f$ is</span> |
| <a name="l00781"></a>00781 <span class="comment"> * an inverse-gamma distributed random variable with shape and scale</span> |
| <a name="l00782"></a>00782 <span class="comment"> * parameters \f$ \alpha \f$ and \f$ \beta \f$, respectively</span> |
| <a name="l00783"></a>00783 <span class="comment"> */</span> |
| <a name="l00784"></a>00784 CREATE FUNCTION MADLIB_SCHEMA.inverse_gamma_quantile( |
| <a name="l00785"></a>00785 p DOUBLE PRECISION, |
| <a name="l00786"></a>00786 shape DOUBLE PRECISION, |
| <a name="l00787"></a><a class="code" href="prob_8sql__in.html#a126211c2172a43a654288fa72a2349f9">00787</a> scale DOUBLE PRECISION |
| <a name="l00788"></a>00788 ) RETURNS DOUBLE PRECISION |
| <a name="l00789"></a>00789 AS 'MODULE_PATHNAME<span class="stringliteral">'</span> |
| <a name="l00790"></a>00790 <span class="stringliteral">LANGUAGE C</span> |
| <a name="l00791"></a>00791 <span class="stringliteral">IMMUTABLE STRICT;</span> |
| <a name="l00792"></a>00792 <span class="stringliteral"></span> |
| <a name="l00793"></a>00793 <span class="stringliteral"></span><span class="comment"></span> |
| <a name="l00794"></a>00794 <span class="comment">/**</span> |
| <a name="l00795"></a>00795 <span class="comment"> * @brief Kolmogorov cumulative distribution function</span> |
| <a name="l00796"></a>00796 <span class="comment"> *</span> |
| <a name="l00797"></a>00797 <span class="comment"> * @param x Random variate \f$ x \f$</span> |
| <a name="l00798"></a>00798 <span class="comment"> * @return \f$ \Pr[X \leq x] \f$ where \f$ X \f$ is a Kolmogorov distributed</span> |
| <a name="l00799"></a>00799 <span class="comment"> * random variable</span> |
| <a name="l00800"></a>00800 <span class="comment"> *</span> |
| <a name="l00801"></a>00801 <span class="comment"> * @sa Kolmogorov-Smirnov test: ks_test()</span> |
| <a name="l00802"></a>00802 <span class="comment"> */</span> |
| <a name="l00803"></a>00803 CREATE FUNCTION MADLIB_SCHEMA.kolmogorov_cdf( |
| <a name="l00804"></a>00804 x DOUBLE PRECISION |
| <a name="l00805"></a>00805 ) RETURNS DOUBLE PRECISION |
| <a name="l00806"></a><a class="code" href="prob_8sql__in.html#a5876aae01f14729866d4fd52918a65ba">00806</a> AS 'MODULE_PATHNAME<span class="stringliteral">'</span> |
| <a name="l00807"></a>00807 <span class="stringliteral">LANGUAGE C</span> |
| <a name="l00808"></a>00808 <span class="stringliteral">IMMUTABLE STRICT;</span> |
| <a name="l00809"></a>00809 <span class="stringliteral"></span> |
| <a name="l00810"></a>00810 <span class="stringliteral"></span><span class="comment"></span> |
| <a name="l00811"></a>00811 <span class="comment">/**</span> |
| <a name="l00812"></a>00812 <span class="comment"> * @brief Laplace cumulative distribution function</span> |
| <a name="l00813"></a>00813 <span class="comment"> *</span> |
| <a name="l00814"></a>00814 <span class="comment"> * @param x Random variate \f$ x \f$</span> |
| <a name="l00815"></a>00815 <span class="comment"> * @param mean Mean \f$ \mu \f$</span> |
| <a name="l00816"></a>00816 <span class="comment"> * @param scale Scale \f$ b > 0 \f$</span> |
| <a name="l00817"></a>00817 <span class="comment"> * @return \f$ \Pr[X \leq x] \f$ where \f$ X \f$ is a Laplace-distributed random</span> |
| <a name="l00818"></a>00818 <span class="comment"> * variable with mean \f$ \mu \f$ and variance \f$ 2 b^2 \f$</span> |
| <a name="l00819"></a>00819 <span class="comment"> */</span> |
| <a name="l00820"></a>00820 CREATE FUNCTION MADLIB_SCHEMA.laplace_cdf( |
| <a name="l00821"></a>00821 x DOUBLE PRECISION, |
| <a name="l00822"></a>00822 mean DOUBLE PRECISION, |
| <a name="l00823"></a>00823 scale DOUBLE PRECISION |
| <a name="l00824"></a>00824 ) RETURNS DOUBLE PRECISION |
| <a name="l00825"></a><a class="code" href="prob_8sql__in.html#aeef43f74f583bdff17bd074d9c0d9607">00825</a> AS 'MODULE_PATHNAME<span class="stringliteral">'</span> |
| <a name="l00826"></a>00826 <span class="stringliteral">LANGUAGE C</span> |
| <a name="l00827"></a>00827 <span class="stringliteral">IMMUTABLE STRICT;</span> |
| <a name="l00828"></a>00828 <span class="stringliteral"></span><span class="comment"></span> |
| <a name="l00829"></a>00829 <span class="comment">/**</span> |
| <a name="l00830"></a>00830 <span class="comment"> * @brief Laplace probability density function</span> |
| <a name="l00831"></a>00831 <span class="comment"> *</span> |
| <a name="l00832"></a>00832 <span class="comment"> * @param x Random variate \f$ x \f$</span> |
| <a name="l00833"></a>00833 <span class="comment"> * @param mean Mean \f$ \mu \f$</span> |
| <a name="l00834"></a>00834 <span class="comment"> * @param scale Scale \f$ b > 0 \f$</span> |
| <a name="l00835"></a>00835 <span class="comment"> * @return \f$ f(x) \f$ where \f$ f \f$ is the probability density function of</span> |
| <a name="l00836"></a>00836 <span class="comment"> * a Laplace-distributed random variable with mean \f$ \mu \f$ and variance</span> |
| <a name="l00837"></a>00837 <span class="comment"> * \f$ 2 b^2 \f$</span> |
| <a name="l00838"></a>00838 <span class="comment"> */</span> |
| <a name="l00839"></a>00839 CREATE FUNCTION MADLIB_SCHEMA.laplace_pdf( |
| <a name="l00840"></a>00840 x DOUBLE PRECISION, |
| <a name="l00841"></a>00841 mean DOUBLE PRECISION, |
| <a name="l00842"></a><a class="code" href="prob_8sql__in.html#a64e197de8da3761acdeec9db7e211703">00842</a> scale DOUBLE PRECISION |
| <a name="l00843"></a>00843 ) RETURNS DOUBLE PRECISION |
| <a name="l00844"></a>00844 AS 'MODULE_PATHNAME<span class="stringliteral">'</span> |
| <a name="l00845"></a>00845 <span class="stringliteral">LANGUAGE C</span> |
| <a name="l00846"></a>00846 <span class="stringliteral">IMMUTABLE STRICT;</span> |
| <a name="l00847"></a>00847 <span class="stringliteral"></span><span class="comment"></span> |
| <a name="l00848"></a>00848 <span class="comment">/**</span> |
| <a name="l00849"></a>00849 <span class="comment"> * @brief Laplace quantile function</span> |
| <a name="l00850"></a>00850 <span class="comment"> *</span> |
| <a name="l00851"></a>00851 <span class="comment"> * @param p Probability \f$ p \in [0,1] \f$</span> |
| <a name="l00852"></a>00852 <span class="comment"> * @param mean Mean \f$ \mu \f$</span> |
| <a name="l00853"></a>00853 <span class="comment"> * @param scale Scale \f$ b > 0 \f$</span> |
| <a name="l00854"></a>00854 <span class="comment"> * @return \f$ x \f$ such that \f$ p = \Pr[X \leq x] \f$ where \f$ X \f$ is a</span> |
| <a name="l00855"></a>00855 <span class="comment"> * Laplace-distributed random variable with mean \f$ \mu \f$ and variance</span> |
| <a name="l00856"></a>00856 <span class="comment"> * \f$ 2 b^2 \f$</span> |
| <a name="l00857"></a>00857 <span class="comment"> */</span> |
| <a name="l00858"></a>00858 CREATE FUNCTION MADLIB_SCHEMA.laplace_quantile( |
| <a name="l00859"></a>00859 p DOUBLE PRECISION, |
| <a name="l00860"></a>00860 mean DOUBLE PRECISION, |
| <a name="l00861"></a><a class="code" href="prob_8sql__in.html#a750278ad29d514793f76e159b773f410">00861</a> scale DOUBLE PRECISION |
| <a name="l00862"></a>00862 ) RETURNS DOUBLE PRECISION |
| <a name="l00863"></a>00863 AS 'MODULE_PATHNAME<span class="stringliteral">'</span> |
| <a name="l00864"></a>00864 <span class="stringliteral">LANGUAGE C</span> |
| <a name="l00865"></a>00865 <span class="stringliteral">IMMUTABLE STRICT;</span> |
| <a name="l00866"></a>00866 <span class="stringliteral"></span> |
| <a name="l00867"></a>00867 <span class="stringliteral"></span><span class="comment"></span> |
| <a name="l00868"></a>00868 <span class="comment">/**</span> |
| <a name="l00869"></a>00869 <span class="comment"> * @brief Logistic cumulative distribution function</span> |
| <a name="l00870"></a>00870 <span class="comment"> *</span> |
| <a name="l00871"></a>00871 <span class="comment"> * @param x Random variate \f$ x \f$</span> |
| <a name="l00872"></a>00872 <span class="comment"> * @param mean Mean \f$ \mu \f$</span> |
| <a name="l00873"></a>00873 <span class="comment"> * @param scale Scale \f$ s > 0 \f$</span> |
| <a name="l00874"></a>00874 <span class="comment"> * @return \f$ \Pr[X \leq x] \f$ where \f$ X \f$ is a logistically distributed</span> |
| <a name="l00875"></a>00875 <span class="comment"> * random variable with mean \f$ \mu \f$ and scale parameter \f$ s \f$</span> |
| <a name="l00876"></a>00876 <span class="comment"> */</span> |
| <a name="l00877"></a>00877 CREATE FUNCTION MADLIB_SCHEMA.logistic_cdf( |
| <a name="l00878"></a>00878 x DOUBLE PRECISION, |
| <a name="l00879"></a>00879 mean DOUBLE PRECISION, |
| <a name="l00880"></a><a class="code" href="prob_8sql__in.html#a77f94fc43d4777fc4f68d18e29454a81">00880</a> scale DOUBLE PRECISION |
| <a name="l00881"></a>00881 ) RETURNS DOUBLE PRECISION |
| <a name="l00882"></a>00882 AS 'MODULE_PATHNAME<span class="stringliteral">'</span> |
| <a name="l00883"></a>00883 <span class="stringliteral">LANGUAGE C</span> |
| <a name="l00884"></a>00884 <span class="stringliteral">IMMUTABLE STRICT;</span> |
| <a name="l00885"></a>00885 <span class="stringliteral"></span><span class="comment"></span> |
| <a name="l00886"></a>00886 <span class="comment">/**</span> |
| <a name="l00887"></a>00887 <span class="comment"> * @brief Logistic probability density function</span> |
| <a name="l00888"></a>00888 <span class="comment"> *</span> |
| <a name="l00889"></a>00889 <span class="comment"> * @param x Random variate \f$ x \f$</span> |
| <a name="l00890"></a>00890 <span class="comment"> * @param mean Mean \f$ \mu \f$</span> |
| <a name="l00891"></a>00891 <span class="comment"> * @param scale Scale \f$ s > 0 \f$</span> |
| <a name="l00892"></a>00892 <span class="comment"> * @return \f$ f(x) \f$ where \f$ f \f$ is the probability density function of</span> |
| <a name="l00893"></a>00893 <span class="comment"> * a logistically distributed random variable with mean \f$ \mu \f$ and</span> |
| <a name="l00894"></a>00894 <span class="comment"> * scale parameter \f$ s \f$</span> |
| <a name="l00895"></a>00895 <span class="comment"> */</span> |
| <a name="l00896"></a>00896 CREATE FUNCTION MADLIB_SCHEMA.logistic_pdf( |
| <a name="l00897"></a>00897 x DOUBLE PRECISION, |
| <a name="l00898"></a>00898 mean DOUBLE PRECISION, |
| <a name="l00899"></a><a class="code" href="prob_8sql__in.html#a140f674876813d5e786a4d8ba8d75c87">00899</a> scale DOUBLE PRECISION |
| <a name="l00900"></a>00900 ) RETURNS DOUBLE PRECISION |
| <a name="l00901"></a>00901 AS 'MODULE_PATHNAME<span class="stringliteral">'</span> |
| <a name="l00902"></a>00902 <span class="stringliteral">LANGUAGE C</span> |
| <a name="l00903"></a>00903 <span class="stringliteral">IMMUTABLE STRICT;</span> |
| <a name="l00904"></a>00904 <span class="stringliteral"></span><span class="comment"></span> |
| <a name="l00905"></a>00905 <span class="comment">/**</span> |
| <a name="l00906"></a>00906 <span class="comment"> * @brief Logistic quantile function</span> |
| <a name="l00907"></a>00907 <span class="comment"> *</span> |
| <a name="l00908"></a>00908 <span class="comment"> * @param p Probability \f$ p \in [0,1] \f$</span> |
| <a name="l00909"></a>00909 <span class="comment"> * @param mean Mean \f$ \mu \f$</span> |
| <a name="l00910"></a>00910 <span class="comment"> * @param scale Scale \f$ s > 0 \f$</span> |
| <a name="l00911"></a>00911 <span class="comment"> * @return \f$ x \f$ such that \f$ p = \Pr[X \leq x] \f$ where \f$ X \f$ is</span> |
| <a name="l00912"></a>00912 <span class="comment"> * a logistically distributed random variable with mean \f$ \mu \f$ and</span> |
| <a name="l00913"></a>00913 <span class="comment"> * scale parameter \f$ s \f$</span> |
| <a name="l00914"></a>00914 <span class="comment"> */</span> |
| <a name="l00915"></a>00915 CREATE FUNCTION MADLIB_SCHEMA.logistic_quantile( |
| <a name="l00916"></a>00916 p DOUBLE PRECISION, |
| <a name="l00917"></a>00917 mean DOUBLE PRECISION, |
| <a name="l00918"></a><a class="code" href="prob_8sql__in.html#afa38eb6c61d3c9825d5c172e6c17dbf7">00918</a> scale DOUBLE PRECISION |
| <a name="l00919"></a>00919 ) RETURNS DOUBLE PRECISION |
| <a name="l00920"></a>00920 AS 'MODULE_PATHNAME<span class="stringliteral">'</span> |
| <a name="l00921"></a>00921 <span class="stringliteral">LANGUAGE C</span> |
| <a name="l00922"></a>00922 <span class="stringliteral">IMMUTABLE STRICT;</span> |
| <a name="l00923"></a>00923 <span class="stringliteral"></span> |
| <a name="l00924"></a>00924 <span class="stringliteral"></span><span class="comment"></span> |
| <a name="l00925"></a>00925 <span class="comment">/**</span> |
| <a name="l00926"></a>00926 <span class="comment"> * @brief Log-normal cumulative distribution function</span> |
| <a name="l00927"></a>00927 <span class="comment"> *</span> |
| <a name="l00928"></a>00928 <span class="comment"> * @param x Random variate \f$ x \f$</span> |
| <a name="l00929"></a>00929 <span class="comment"> * @param location Location \f$ m \f$</span> |
| <a name="l00930"></a>00930 <span class="comment"> * @param scale Scale \f$ s > 0 \f$</span> |
| <a name="l00931"></a>00931 <span class="comment"> * @return \f$ \Pr[X \leq x] \f$ where \f$ X \f$ is a lognormally distributed</span> |
| <a name="l00932"></a>00932 <span class="comment"> * random variable with location and scale parameters \f$ m \f$ and</span> |
| <a name="l00933"></a>00933 <span class="comment"> * \f$ s \f$, respectively</span> |
| <a name="l00934"></a>00934 <span class="comment"> */</span> |
| <a name="l00935"></a>00935 CREATE FUNCTION MADLIB_SCHEMA.lognormal_cdf( |
| <a name="l00936"></a>00936 x DOUBLE PRECISION, |
| <a name="l00937"></a><a class="code" href="prob_8sql__in.html#a5a77a0bc5884af2a914a955174892ae2">00937</a> location DOUBLE PRECISION, |
| <a name="l00938"></a>00938 scale DOUBLE PRECISION |
| <a name="l00939"></a>00939 ) RETURNS DOUBLE PRECISION |
| <a name="l00940"></a>00940 AS 'MODULE_PATHNAME<span class="stringliteral">'</span> |
| <a name="l00941"></a>00941 <span class="stringliteral">LANGUAGE C</span> |
| <a name="l00942"></a>00942 <span class="stringliteral">IMMUTABLE STRICT;</span> |
| <a name="l00943"></a>00943 <span class="stringliteral"></span><span class="comment"></span> |
| <a name="l00944"></a>00944 <span class="comment">/**</span> |
| <a name="l00945"></a>00945 <span class="comment"> * @brief Log-normal probability density function</span> |
| <a name="l00946"></a>00946 <span class="comment"> *</span> |
| <a name="l00947"></a>00947 <span class="comment"> * @param x Random variate \f$ x \f$</span> |
| <a name="l00948"></a>00948 <span class="comment"> * @param location Location \f$ m \f$</span> |
| <a name="l00949"></a>00949 <span class="comment"> * @param scale Scale \f$ s > 0 \f$</span> |
| <a name="l00950"></a>00950 <span class="comment"> * @return \f$ f(x) \f$ where \f$ f \f$ is the probability density function of</span> |
| <a name="l00951"></a>00951 <span class="comment"> * a lognormally distributed random variable with location and scale</span> |
| <a name="l00952"></a>00952 <span class="comment"> * parameters \f$ m \f$ and \f$ s \f$, respectively</span> |
| <a name="l00953"></a>00953 <span class="comment"> */</span> |
| <a name="l00954"></a>00954 CREATE FUNCTION MADLIB_SCHEMA.lognormal_pdf( |
| <a name="l00955"></a>00955 x DOUBLE PRECISION, |
| <a name="l00956"></a>00956 location DOUBLE PRECISION, |
| <a name="l00957"></a><a class="code" href="prob_8sql__in.html#a4c05b347f8feb64e1236d21b850af61e">00957</a> scale DOUBLE PRECISION |
| <a name="l00958"></a>00958 ) RETURNS DOUBLE PRECISION |
| <a name="l00959"></a>00959 AS 'MODULE_PATHNAME<span class="stringliteral">'</span> |
| <a name="l00960"></a>00960 <span class="stringliteral">LANGUAGE C</span> |
| <a name="l00961"></a>00961 <span class="stringliteral">IMMUTABLE STRICT;</span> |
| <a name="l00962"></a>00962 <span class="stringliteral"></span><span class="comment"></span> |
| <a name="l00963"></a>00963 <span class="comment">/**</span> |
| <a name="l00964"></a>00964 <span class="comment"> * @brief Log-normal quantile function</span> |
| <a name="l00965"></a>00965 <span class="comment"> *</span> |
| <a name="l00966"></a>00966 <span class="comment"> * @param p Probability \f$ p \in [0,1] \f$</span> |
| <a name="l00967"></a>00967 <span class="comment"> * @param location Location \f$ m \f$</span> |
| <a name="l00968"></a>00968 <span class="comment"> * @param scale Scale \f$ s > 0 \f$</span> |
| <a name="l00969"></a>00969 <span class="comment"> * @return \f$ x \f$ such that \f$ p = \Pr[X \leq x] \f$ where \f$ X \f$ is</span> |
| <a name="l00970"></a>00970 <span class="comment"> * a lognormally distributed random variable with location and scale</span> |
| <a name="l00971"></a>00971 <span class="comment"> * parameters \f$ m \f$ and \f$ s \f$, respectively</span> |
| <a name="l00972"></a>00972 <span class="comment"> */</span> |
| <a name="l00973"></a>00973 CREATE FUNCTION MADLIB_SCHEMA.lognormal_quantile( |
| <a name="l00974"></a>00974 p DOUBLE PRECISION, |
| <a name="l00975"></a>00975 location DOUBLE PRECISION, |
| <a name="l00976"></a><a class="code" href="prob_8sql__in.html#a7370b797bf450f9aa54d4fea4d64d611">00976</a> scale DOUBLE PRECISION |
| <a name="l00977"></a>00977 ) RETURNS DOUBLE PRECISION |
| <a name="l00978"></a>00978 AS 'MODULE_PATHNAME<span class="stringliteral">'</span> |
| <a name="l00979"></a>00979 <span class="stringliteral">LANGUAGE C</span> |
| <a name="l00980"></a>00980 <span class="stringliteral">IMMUTABLE STRICT;</span> |
| <a name="l00981"></a>00981 <span class="stringliteral"></span> |
| <a name="l00982"></a>00982 <span class="stringliteral"></span><span class="comment"></span> |
| <a name="l00983"></a>00983 <span class="comment">/**</span> |
| <a name="l00984"></a>00984 <span class="comment"> * @brief Negative binomial cumulative distribution function</span> |
| <a name="l00985"></a>00985 <span class="comment"> *</span> |
| <a name="l00986"></a>00986 <span class="comment"> * @param x Random variate \f$ x \f$</span> |
| <a name="l00987"></a>00987 <span class="comment"> * @param r Total number \f$ r > 0 \f$ of successes in \f$ x + r \f$ trials</span> |
| <a name="l00988"></a>00988 <span class="comment"> * (assuming success in the last trial)</span> |
| <a name="l00989"></a>00989 <span class="comment"> * @param sp Success probability \f$ \mathit{sp} \in (0,1] \f$ in each trial</span> |
| <a name="l00990"></a>00990 <span class="comment"> * @return \f$ \Pr[X \leq x] \f$ where \f$ X \f$ is a negative-binomially</span> |
| <a name="l00991"></a>00991 <span class="comment"> * distributed random variable with parameters \f$ r, \mathit{sp} \f$</span> |
| <a name="l00992"></a>00992 <span class="comment"> */</span> |
| <a name="l00993"></a>00993 CREATE FUNCTION MADLIB_SCHEMA.negative_binomial_cdf( |
| <a name="l00994"></a>00994 x DOUBLE PRECISION, |
| <a name="l00995"></a><a class="code" href="prob_8sql__in.html#aab3a6de990ae5a81834274a1cf9cad8f">00995</a> r DOUBLE PRECISION, |
| <a name="l00996"></a>00996 sp DOUBLE PRECISION |
| <a name="l00997"></a>00997 ) RETURNS DOUBLE PRECISION |
| <a name="l00998"></a>00998 AS 'MODULE_PATHNAME<span class="stringliteral">'</span> |
| <a name="l00999"></a>00999 <span class="stringliteral">LANGUAGE C</span> |
| <a name="l01000"></a>01000 <span class="stringliteral">IMMUTABLE STRICT;</span> |
| <a name="l01001"></a>01001 <span class="stringliteral"></span><span class="comment"></span> |
| <a name="l01002"></a>01002 <span class="comment">/**</span> |
| <a name="l01003"></a>01003 <span class="comment"> * @brief Negative binomial probability mass function</span> |
| <a name="l01004"></a>01004 <span class="comment"> *</span> |
| <a name="l01005"></a>01005 <span class="comment"> * @param x Random variate \f$ x \f$</span> |
| <a name="l01006"></a>01006 <span class="comment"> * @param r Total number \f$ r > 0 \f$ of successes in \f$ x + r \f$ trials</span> |
| <a name="l01007"></a>01007 <span class="comment"> * (assuming success in the last trial)</span> |
| <a name="l01008"></a>01008 <span class="comment"> * @param sp Success probability \f$ \mathit{sp} \in (0,1] \f$ in each trial</span> |
| <a name="l01009"></a>01009 <span class="comment"> * @return \f$ f(x) \f$ where \f$ f \f$ is the probability mass function of</span> |
| <a name="l01010"></a>01010 <span class="comment"> * a negative-binomially distributed random variable with parameters</span> |
| <a name="l01011"></a>01011 <span class="comment"> * \f$ r, \mathit{sp} \f$</span> |
| <a name="l01012"></a>01012 <span class="comment"> */</span> |
| <a name="l01013"></a>01013 CREATE FUNCTION MADLIB_SCHEMA.negative_binomial_pmf( |
| <a name="l01014"></a>01014 x INT4, |
| <a name="l01015"></a><a class="code" href="prob_8sql__in.html#ad0a7e4474f828869fb90e62f8e6f04d7">01015</a> r DOUBLE PRECISION, |
| <a name="l01016"></a>01016 sp DOUBLE PRECISION |
| <a name="l01017"></a>01017 ) RETURNS DOUBLE PRECISION |
| <a name="l01018"></a>01018 AS 'MODULE_PATHNAME<span class="stringliteral">'</span> |
| <a name="l01019"></a>01019 <span class="stringliteral">LANGUAGE C</span> |
| <a name="l01020"></a>01020 <span class="stringliteral">IMMUTABLE STRICT;</span> |
| <a name="l01021"></a>01021 <span class="stringliteral"></span><span class="comment"></span> |
| <a name="l01022"></a>01022 <span class="comment">/**</span> |
| <a name="l01023"></a>01023 <span class="comment"> * @brief Negative binomial quantile function</span> |
| <a name="l01024"></a>01024 <span class="comment"> *</span> |
| <a name="l01025"></a>01025 <span class="comment"> * @param p Probability \f$ p \in [0,1] \f$</span> |
| <a name="l01026"></a>01026 <span class="comment"> * @param r Total number \f$ r > 0 \f$ of successes in \f$ x + r \f$ trials</span> |
| <a name="l01027"></a>01027 <span class="comment"> * (assuming success in the last trial)</span> |
| <a name="l01028"></a>01028 <span class="comment"> * @param sp Success probability \f$ \mathit{sp} \in (0,1] \f$ in each trial</span> |
| <a name="l01029"></a>01029 <span class="comment"> * @return If \f$ p < 0.5 \f$ the maximum \f$ x \f$ such that</span> |
| <a name="l01030"></a>01030 <span class="comment"> * \f$ p \geq \Pr[X \leq x] \f$. If \f$ p \geq 0.5 \f$ the minimum \f$ x \f$</span> |
| <a name="l01031"></a>01031 <span class="comment"> * such that \f$ p \leq \Pr[X \leq x] \f$. Here, \f$ X \f$ is</span> |
| <a name="l01032"></a>01032 <span class="comment"> * a negative-binomially distributed random variable with parameters</span> |
| <a name="l01033"></a>01033 <span class="comment"> * \f$ r, \mathit{sp} \f$</span> |
| <a name="l01034"></a>01034 <span class="comment"> */</span> |
| <a name="l01035"></a><a class="code" href="prob_8sql__in.html#ab9cbc30424eba30f2df2a32a7e45f138">01035</a> CREATE FUNCTION MADLIB_SCHEMA.negative_binomial_quantile( |
| <a name="l01036"></a>01036 p DOUBLE PRECISION, |
| <a name="l01037"></a>01037 r DOUBLE PRECISION, |
| <a name="l01038"></a>01038 sp DOUBLE PRECISION |
| <a name="l01039"></a>01039 ) RETURNS DOUBLE PRECISION |
| <a name="l01040"></a>01040 AS 'MODULE_PATHNAME<span class="stringliteral">'</span> |
| <a name="l01041"></a>01041 <span class="stringliteral">LANGUAGE C</span> |
| <a name="l01042"></a>01042 <span class="stringliteral">IMMUTABLE STRICT;</span> |
| <a name="l01043"></a>01043 <span class="stringliteral"></span> |
| <a name="l01044"></a>01044 <span class="stringliteral"></span><span class="comment"></span> |
| <a name="l01045"></a>01045 <span class="comment">/**</span> |
| <a name="l01046"></a>01046 <span class="comment"> * @brief Noncentral beta cumulative distribution function</span> |
| <a name="l01047"></a>01047 <span class="comment"> *</span> |
| <a name="l01048"></a>01048 <span class="comment"> * @param x Random variate \f$ x \f$</span> |
| <a name="l01049"></a>01049 <span class="comment"> * @param alpha Shape \f$ \alpha > 0 \f$</span> |
| <a name="l01050"></a>01050 <span class="comment"> * @param beta Shape \f$ \beta > 0 \f$</span> |
| <a name="l01051"></a>01051 <span class="comment"> * @param ncp Noncentrality parameter \f$ \delta \geq 0 \f$</span> |
| <a name="l01052"></a>01052 <span class="comment"> * @return \f$ \Pr[X \leq x] \f$ where \f$ X \f$ is a noncentral-beta</span> |
| <a name="l01053"></a>01053 <span class="comment"> * distributed random variable with shape parameters \f$ shape_1 \f$ and</span> |
| <a name="l01054"></a>01054 <span class="comment"> * \f$ shape_2 \f$ and noncentrality parameter \f$ \delta \f$</span> |
| <a name="l01055"></a>01055 <span class="comment"> */</span> |
| <a name="l01056"></a>01056 CREATE FUNCTION MADLIB_SCHEMA.non_central_beta_cdf( |
| <a name="l01057"></a><a class="code" href="prob_8sql__in.html#ad9e541de8b41da2e7b7434f862db4845">01057</a> x DOUBLE PRECISION, |
| <a name="l01058"></a>01058 alpha DOUBLE PRECISION, |
| <a name="l01059"></a>01059 beta DOUBLE PRECISION, |
| <a name="l01060"></a>01060 ncp DOUBLE PRECISION |
| <a name="l01061"></a>01061 ) RETURNS DOUBLE PRECISION |
| <a name="l01062"></a>01062 AS 'MODULE_PATHNAME<span class="stringliteral">'</span> |
| <a name="l01063"></a>01063 <span class="stringliteral">LANGUAGE C</span> |
| <a name="l01064"></a>01064 <span class="stringliteral">IMMUTABLE STRICT;</span> |
| <a name="l01065"></a>01065 <span class="stringliteral"></span><span class="comment"></span> |
| <a name="l01066"></a>01066 <span class="comment">/**</span> |
| <a name="l01067"></a>01067 <span class="comment"> * @brief Noncentral beta probability density function</span> |
| <a name="l01068"></a>01068 <span class="comment"> *</span> |
| <a name="l01069"></a>01069 <span class="comment"> * @param x Random variate \f$ x \f$</span> |
| <a name="l01070"></a>01070 <span class="comment"> * @param alpha Shape \f$ \alpha > 0 \f$</span> |
| <a name="l01071"></a>01071 <span class="comment"> * @param beta Shape \f$ \beta > 0 \f$</span> |
| <a name="l01072"></a>01072 <span class="comment"> * @param ncp Noncentrality parameter \f$ \delta \geq 0 \f$</span> |
| <a name="l01073"></a>01073 <span class="comment"> * @return \f$ f(x) \f$ where \f$ f \f$ is the probability density function of</span> |
| <a name="l01074"></a>01074 <span class="comment"> * a noncentral-beta distributed random variable with shape parameters</span> |
| <a name="l01075"></a>01075 <span class="comment"> * \f$ shape_1 \f$ and \f$ shape_2 \f$ and noncentrality parameter</span> |
| <a name="l01076"></a>01076 <span class="comment"> * \f$ \delta \f$</span> |
| <a name="l01077"></a>01077 <span class="comment"> */</span> |
| <a name="l01078"></a><a class="code" href="prob_8sql__in.html#a1361569bd86e41f796c70f8cb277010e">01078</a> CREATE FUNCTION MADLIB_SCHEMA.non_central_beta_pdf( |
| <a name="l01079"></a>01079 x DOUBLE PRECISION, |
| <a name="l01080"></a>01080 alpha DOUBLE PRECISION, |
| <a name="l01081"></a>01081 beta DOUBLE PRECISION, |
| <a name="l01082"></a>01082 ncp DOUBLE PRECISION |
| <a name="l01083"></a>01083 ) RETURNS DOUBLE PRECISION |
| <a name="l01084"></a>01084 AS 'MODULE_PATHNAME<span class="stringliteral">'</span> |
| <a name="l01085"></a>01085 <span class="stringliteral">LANGUAGE C</span> |
| <a name="l01086"></a>01086 <span class="stringliteral">IMMUTABLE STRICT;</span> |
| <a name="l01087"></a>01087 <span class="stringliteral"></span><span class="comment"></span> |
| <a name="l01088"></a>01088 <span class="comment">/**</span> |
| <a name="l01089"></a>01089 <span class="comment"> * @brief Noncentral beta quantile function</span> |
| <a name="l01090"></a>01090 <span class="comment"> *</span> |
| <a name="l01091"></a>01091 <span class="comment"> * @param p Probability \f$ p \in [0,1] \f$</span> |
| <a name="l01092"></a>01092 <span class="comment"> * @param alpha Shape \f$ \alpha > 0 \f$</span> |
| <a name="l01093"></a>01093 <span class="comment"> * @param beta Shape \f$ \beta > 0 \f$</span> |
| <a name="l01094"></a>01094 <span class="comment"> * @param ncp Noncentrality parameter \f$ \delta \geq 0 \f$</span> |
| <a name="l01095"></a>01095 <span class="comment"> * @return \f$ x \f$ such that \f$ p = \Pr[X \leq x] \f$ where \f$ X \f$ is</span> |
| <a name="l01096"></a>01096 <span class="comment"> * a noncentral-beta distributed random variable with shape parameters</span> |
| <a name="l01097"></a>01097 <span class="comment"> * \f$ shape_1 \f$ and \f$ shape_2 \f$ and noncentrality parameter</span> |
| <a name="l01098"></a>01098 <span class="comment"> * \f$ \delta \f$</span> |
| <a name="l01099"></a>01099 <span class="comment"> */</span> |
| <a name="l01100"></a><a class="code" href="prob_8sql__in.html#ad4a12c083054f0e2d316ae76c9aaeef7">01100</a> CREATE FUNCTION MADLIB_SCHEMA.non_central_beta_quantile( |
| <a name="l01101"></a>01101 p DOUBLE PRECISION, |
| <a name="l01102"></a>01102 alpha DOUBLE PRECISION, |
| <a name="l01103"></a>01103 beta DOUBLE PRECISION, |
| <a name="l01104"></a>01104 ncp DOUBLE PRECISION |
| <a name="l01105"></a>01105 ) RETURNS DOUBLE PRECISION |
| <a name="l01106"></a>01106 AS 'MODULE_PATHNAME<span class="stringliteral">'</span> |
| <a name="l01107"></a>01107 <span class="stringliteral">LANGUAGE C</span> |
| <a name="l01108"></a>01108 <span class="stringliteral">IMMUTABLE STRICT;</span> |
| <a name="l01109"></a>01109 <span class="stringliteral"></span> |
| <a name="l01110"></a>01110 <span class="stringliteral"></span><span class="comment"></span> |
| <a name="l01111"></a>01111 <span class="comment">/**</span> |
| <a name="l01112"></a>01112 <span class="comment"> * @brief Noncentral chi-squared cumulative distribution function</span> |
| <a name="l01113"></a>01113 <span class="comment"> *</span> |
| <a name="l01114"></a>01114 <span class="comment"> * @param x Random variate \f$ x \f$</span> |
| <a name="l01115"></a>01115 <span class="comment"> * @param df Degrees of freedom \f$ \nu > 0 \f$</span> |
| <a name="l01116"></a>01116 <span class="comment"> * @param ncp The noncentrality parameter \f$ \lambda \geq 0 \f$</span> |
| <a name="l01117"></a>01117 <span class="comment"> * @return \f$ \Pr[X \leq x] \f$ where \f$ X \f$ is a noncentral-chi-squared</span> |
| <a name="l01118"></a>01118 <span class="comment"> * distributed random variable with \f$ \nu \f$ degrees of freedom and</span> |
| <a name="l01119"></a>01119 <span class="comment"> * noncentrality parameter \f$ \lambda \f$</span> |
| <a name="l01120"></a>01120 <span class="comment"> */</span> |
| <a name="l01121"></a>01121 CREATE FUNCTION MADLIB_SCHEMA.non_central_chi_squared_cdf( |
| <a name="l01122"></a><a class="code" href="prob_8sql__in.html#a3073b409eaee3faa6d43df014662c279">01122</a> x DOUBLE PRECISION, |
| <a name="l01123"></a>01123 df DOUBLE PRECISION, |
| <a name="l01124"></a>01124 ncp DOUBLE PRECISION |
| <a name="l01125"></a>01125 ) RETURNS DOUBLE PRECISION |
| <a name="l01126"></a>01126 AS 'MODULE_PATHNAME<span class="stringliteral">'</span> |
| <a name="l01127"></a>01127 <span class="stringliteral">LANGUAGE C</span> |
| <a name="l01128"></a>01128 <span class="stringliteral">IMMUTABLE STRICT;</span> |
| <a name="l01129"></a>01129 <span class="stringliteral"></span><span class="comment"></span> |
| <a name="l01130"></a>01130 <span class="comment">/**</span> |
| <a name="l01131"></a>01131 <span class="comment"> * @brief Noncentral chi-squared distribution probability density function</span> |
| <a name="l01132"></a>01132 <span class="comment"> *</span> |
| <a name="l01133"></a>01133 <span class="comment"> * @param x Random variate \f$ x \f$</span> |
| <a name="l01134"></a>01134 <span class="comment"> * @param df Degrees of freedom \f$ \nu > 0 \f$</span> |
| <a name="l01135"></a>01135 <span class="comment"> * @param ncp The noncentrality parameter \f$ \lambda \geq 0 \f$</span> |
| <a name="l01136"></a>01136 <span class="comment"> * @return \f$ f(x) \f$ where \f$ f \f$ is the probability density function of</span> |
| <a name="l01137"></a>01137 <span class="comment"> * a noncentral-chi-squared distributed random variable with \f$ \nu \f$</span> |
| <a name="l01138"></a>01138 <span class="comment"> * degrees of freedom and noncentrality parameter \f$ \lambda \f$</span> |
| <a name="l01139"></a>01139 <span class="comment"> */</span> |
| <a name="l01140"></a>01140 CREATE FUNCTION MADLIB_SCHEMA.non_central_chi_squared_pdf( |
| <a name="l01141"></a>01141 x DOUBLE PRECISION, |
| <a name="l01142"></a>01142 df DOUBLE PRECISION, |
| <a name="l01143"></a><a class="code" href="prob_8sql__in.html#ab4b7d2cf10bb031328dcc34c6ff494ad">01143</a> ncp DOUBLE PRECISION |
| <a name="l01144"></a>01144 ) RETURNS DOUBLE PRECISION |
| <a name="l01145"></a>01145 AS 'MODULE_PATHNAME<span class="stringliteral">'</span> |
| <a name="l01146"></a>01146 <span class="stringliteral">LANGUAGE C</span> |
| <a name="l01147"></a>01147 <span class="stringliteral">IMMUTABLE STRICT;</span> |
| <a name="l01148"></a>01148 <span class="stringliteral"></span><span class="comment"></span> |
| <a name="l01149"></a>01149 <span class="comment">/**</span> |
| <a name="l01150"></a>01150 <span class="comment"> * @brief Noncentral chi-squared distribution quantile function</span> |
| <a name="l01151"></a>01151 <span class="comment"> *</span> |
| <a name="l01152"></a>01152 <span class="comment"> * @param p Probability \f$ p \in [0,1] \f$</span> |
| <a name="l01153"></a>01153 <span class="comment"> * @param df Degrees of freedom \f$ \nu > 0 \f$</span> |
| <a name="l01154"></a>01154 <span class="comment"> * @param ncp The noncentrality parameter \f$ \lambda \geq 0 \f$</span> |
| <a name="l01155"></a>01155 <span class="comment"> * @return \f$ x \f$ such that \f$ p = \Pr[X \leq x] \f$ where \f$ X \f$ is a</span> |
| <a name="l01156"></a>01156 <span class="comment"> * noncentral-chi-squared distributed random variable with \f$ \nu \f$</span> |
| <a name="l01157"></a>01157 <span class="comment"> * degrees of freedom and noncentrality parameter \f$ \lambda \f$</span> |
| <a name="l01158"></a>01158 <span class="comment"> */</span> |
| <a name="l01159"></a>01159 CREATE FUNCTION MADLIB_SCHEMA.non_central_chi_squared_quantile( |
| <a name="l01160"></a>01160 p DOUBLE PRECISION, |
| <a name="l01161"></a>01161 df DOUBLE PRECISION, |
| <a name="l01162"></a><a class="code" href="prob_8sql__in.html#aa7a563183224593d1e0d623a3c5489d8">01162</a> ncp DOUBLE PRECISION |
| <a name="l01163"></a>01163 ) RETURNS DOUBLE PRECISION |
| <a name="l01164"></a>01164 AS 'MODULE_PATHNAME<span class="stringliteral">'</span> |
| <a name="l01165"></a>01165 <span class="stringliteral">LANGUAGE C</span> |
| <a name="l01166"></a>01166 <span class="stringliteral">IMMUTABLE STRICT;</span> |
| <a name="l01167"></a>01167 <span class="stringliteral"></span> |
| <a name="l01168"></a>01168 <span class="stringliteral"></span><span class="comment"></span> |
| <a name="l01169"></a>01169 <span class="comment">/**</span> |
| <a name="l01170"></a>01170 <span class="comment"> * @brief Noncentral Fisher F cumulative distribution function</span> |
| <a name="l01171"></a>01171 <span class="comment"> *</span> |
| <a name="l01172"></a>01172 <span class="comment"> * @param x Random variate \f$ x \f$</span> |
| <a name="l01173"></a>01173 <span class="comment"> * @param df1 Degrees of freedom in numerator \f$ \nu_1 > 0 \f$</span> |
| <a name="l01174"></a>01174 <span class="comment"> * @param df2 Degrees of freedom in denominator \f$ \nu_1 > 0 \f$</span> |
| <a name="l01175"></a>01175 <span class="comment"> * @param ncp The noncentrality parameter \f$ \lambda \geq 0 \f$</span> |
| <a name="l01176"></a>01176 <span class="comment"> * @return \f$ \Pr[X \leq x] \f$ where \f$ X \f$ is a</span> |
| <a name="l01177"></a>01177 <span class="comment"> * noncentral Fisher F-distributed random variable with parameters</span> |
| <a name="l01178"></a>01178 <span class="comment"> * \f$ \nu_1, \nu_2, \lambda \f$</span> |
| <a name="l01179"></a>01179 <span class="comment"> */</span> |
| <a name="l01180"></a>01180 CREATE FUNCTION MADLIB_SCHEMA.non_central_f_cdf( |
| <a name="l01181"></a><a class="code" href="prob_8sql__in.html#ad694e29187b629ae683ef1235d2b9270">01181</a> x DOUBLE PRECISION, |
| <a name="l01182"></a>01182 df1 DOUBLE PRECISION, |
| <a name="l01183"></a>01183 df2 DOUBLE PRECISION, |
| <a name="l01184"></a>01184 ncp DOUBLE PRECISION |
| <a name="l01185"></a>01185 ) RETURNS DOUBLE PRECISION |
| <a name="l01186"></a>01186 AS 'MODULE_PATHNAME<span class="stringliteral">'</span> |
| <a name="l01187"></a>01187 <span class="stringliteral">LANGUAGE C</span> |
| <a name="l01188"></a>01188 <span class="stringliteral">IMMUTABLE STRICT;</span> |
| <a name="l01189"></a>01189 <span class="stringliteral"></span><span class="comment"></span> |
| <a name="l01190"></a>01190 <span class="comment">/**</span> |
| <a name="l01191"></a>01191 <span class="comment"> * @brief Noncentral Fisher F probability density function</span> |
| <a name="l01192"></a>01192 <span class="comment"> *</span> |
| <a name="l01193"></a>01193 <span class="comment"> * @param x Random variate \f$ x \f$</span> |
| <a name="l01194"></a>01194 <span class="comment"> * @param df1 Degrees of freedom in numerator \f$ \nu_1 > 0 \f$</span> |
| <a name="l01195"></a>01195 <span class="comment"> * @param df2 Degrees of freedom in denominator \f$ \nu_1 > 0 \f$</span> |
| <a name="l01196"></a>01196 <span class="comment"> * @param ncp The noncentrality parameter \f$ \lambda \geq 0 \f$</span> |
| <a name="l01197"></a>01197 <span class="comment"> * @return \f$ f(x) \f$ where \f$ f \f$ is the probability density function of a</span> |
| <a name="l01198"></a>01198 <span class="comment"> * noncentral Fisher F-distributed random variable with parameters</span> |
| <a name="l01199"></a>01199 <span class="comment"> * \f$ \nu_1, \nu_2, \lambda \f$</span> |
| <a name="l01200"></a>01200 <span class="comment"> */</span> |
| <a name="l01201"></a>01201 CREATE FUNCTION MADLIB_SCHEMA.non_central_f_pdf( |
| <a name="l01202"></a><a class="code" href="prob_8sql__in.html#a00051df630007b530ce86b4ab44a0434">01202</a> x DOUBLE PRECISION, |
| <a name="l01203"></a>01203 df1 DOUBLE PRECISION, |
| <a name="l01204"></a>01204 df2 DOUBLE PRECISION, |
| <a name="l01205"></a>01205 ncp DOUBLE PRECISION |
| <a name="l01206"></a>01206 ) RETURNS DOUBLE PRECISION |
| <a name="l01207"></a>01207 AS 'MODULE_PATHNAME<span class="stringliteral">'</span> |
| <a name="l01208"></a>01208 <span class="stringliteral">LANGUAGE C</span> |
| <a name="l01209"></a>01209 <span class="stringliteral">IMMUTABLE STRICT;</span> |
| <a name="l01210"></a>01210 <span class="stringliteral"></span><span class="comment"></span> |
| <a name="l01211"></a>01211 <span class="comment">/**</span> |
| <a name="l01212"></a>01212 <span class="comment"> * @brief Noncentral Fisher F quantile function</span> |
| <a name="l01213"></a>01213 <span class="comment"> *</span> |
| <a name="l01214"></a>01214 <span class="comment"> * @param p Probability \f$ p \in [0,1] \f$</span> |
| <a name="l01215"></a>01215 <span class="comment"> * @param df1 Degrees of freedom in numerator \f$ \nu_1 > 0 \f$</span> |
| <a name="l01216"></a>01216 <span class="comment"> * @param df2 Degrees of freedom in denominator \f$ \nu_1 > 0 \f$</span> |
| <a name="l01217"></a>01217 <span class="comment"> * @param ncp The noncentrality parameter \f$ \lambda \geq 0 \f$</span> |
| <a name="l01218"></a>01218 <span class="comment"> * @return \f$ x \f$ such that \f$ p = \Pr[X \leq x] \f$ where \f$ X \f$ is a</span> |
| <a name="l01219"></a>01219 <span class="comment"> * noncentral Fisher F-distributed random variable with parameters</span> |
| <a name="l01220"></a>01220 <span class="comment"> * \f$ \nu_1, \nu_2, \lambda \f$</span> |
| <a name="l01221"></a>01221 <span class="comment"> */</span> |
| <a name="l01222"></a>01222 CREATE FUNCTION MADLIB_SCHEMA.non_central_f_quantile( |
| <a name="l01223"></a><a class="code" href="prob_8sql__in.html#a3d94edcf90fca1fa52671293a9ea9c2f">01223</a> p DOUBLE PRECISION, |
| <a name="l01224"></a>01224 df1 DOUBLE PRECISION, |
| <a name="l01225"></a>01225 df2 DOUBLE PRECISION, |
| <a name="l01226"></a>01226 ncp DOUBLE PRECISION |
| <a name="l01227"></a>01227 ) RETURNS DOUBLE PRECISION |
| <a name="l01228"></a>01228 AS 'MODULE_PATHNAME<span class="stringliteral">'</span> |
| <a name="l01229"></a>01229 <span class="stringliteral">LANGUAGE C</span> |
| <a name="l01230"></a>01230 <span class="stringliteral">IMMUTABLE STRICT;</span> |
| <a name="l01231"></a>01231 <span class="stringliteral"></span> |
| <a name="l01232"></a>01232 <span class="stringliteral"></span><span class="comment"></span> |
| <a name="l01233"></a>01233 <span class="comment">/**</span> |
| <a name="l01234"></a>01234 <span class="comment"> * @brief Noncentral Student-t cumulative distribution function</span> |
| <a name="l01235"></a>01235 <span class="comment"> *</span> |
| <a name="l01236"></a>01236 <span class="comment"> * @param x Random variate \f$ x \f$</span> |
| <a name="l01237"></a>01237 <span class="comment"> * @param df Degrees of freedom \f$ \nu > 0 \f$</span> |
| <a name="l01238"></a>01238 <span class="comment"> * @param ncp Noncentrality parameter \f$ \delta \f$</span> |
| <a name="l01239"></a>01239 <span class="comment"> * @return \f$ \Pr[X \leq x] \f$ where \f$ X \f$ is a noncentral Student's</span> |
| <a name="l01240"></a>01240 <span class="comment"> * t-distributed random variable with \f$ \nu \f$ degrees of freedom and</span> |
| <a name="l01241"></a>01241 <span class="comment"> * noncentrality parameter \f$ \delta \f$</span> |
| <a name="l01242"></a>01242 <span class="comment"> */</span> |
| <a name="l01243"></a>01243 CREATE FUNCTION MADLIB_SCHEMA.non_central_t_cdf( |
| <a name="l01244"></a><a class="code" href="prob_8sql__in.html#a92b2a978db480a6c78cfb708107ecb92">01244</a> x DOUBLE PRECISION, |
| <a name="l01245"></a>01245 df DOUBLE PRECISION, |
| <a name="l01246"></a>01246 ncp DOUBLE PRECISION |
| <a name="l01247"></a>01247 ) RETURNS DOUBLE PRECISION |
| <a name="l01248"></a>01248 AS 'MODULE_PATHNAME<span class="stringliteral">'</span> |
| <a name="l01249"></a>01249 <span class="stringliteral">LANGUAGE C</span> |
| <a name="l01250"></a>01250 <span class="stringliteral">IMMUTABLE STRICT;</span> |
| <a name="l01251"></a>01251 <span class="stringliteral"></span><span class="comment"></span> |
| <a name="l01252"></a>01252 <span class="comment">/**</span> |
| <a name="l01253"></a>01253 <span class="comment"> * @brief Noncentral Student-t probability density function</span> |
| <a name="l01254"></a>01254 <span class="comment"> *</span> |
| <a name="l01255"></a>01255 <span class="comment"> * @param x Random variate \f$ x \f$</span> |
| <a name="l01256"></a>01256 <span class="comment"> * @param df Degrees of freedom \f$ \nu > 0 \f$</span> |
| <a name="l01257"></a>01257 <span class="comment"> * @param ncp Noncentrality parameter \f$ \delta \f$</span> |
| <a name="l01258"></a>01258 <span class="comment"> * @return \f$ x \f$ such that \f$ p = \Pr[X \leq x] \f$ where \f$ X \f$ is a</span> |
| <a name="l01259"></a>01259 <span class="comment"> * noncentral Student's t-distributed random variable with \f$ \nu \f$</span> |
| <a name="l01260"></a>01260 <span class="comment"> * degrees of freedom and noncentrality parameter \f$ \delta \f$</span> |
| <a name="l01261"></a>01261 <span class="comment"> */</span> |
| <a name="l01262"></a>01262 CREATE FUNCTION MADLIB_SCHEMA.non_central_t_pdf( |
| <a name="l01263"></a>01263 x DOUBLE PRECISION, |
| <a name="l01264"></a>01264 df DOUBLE PRECISION, |
| <a name="l01265"></a><a class="code" href="prob_8sql__in.html#afaf4374d2720b230a54713e21ecb1955">01265</a> ncp DOUBLE PRECISION |
| <a name="l01266"></a>01266 ) RETURNS DOUBLE PRECISION |
| <a name="l01267"></a>01267 AS 'MODULE_PATHNAME<span class="stringliteral">'</span> |
| <a name="l01268"></a>01268 <span class="stringliteral">LANGUAGE C</span> |
| <a name="l01269"></a>01269 <span class="stringliteral">IMMUTABLE STRICT;</span> |
| <a name="l01270"></a>01270 <span class="stringliteral"></span><span class="comment"></span> |
| <a name="l01271"></a>01271 <span class="comment">/**</span> |
| <a name="l01272"></a>01272 <span class="comment"> * @brief Noncentral Student-t quantile function</span> |
| <a name="l01273"></a>01273 <span class="comment"> *</span> |
| <a name="l01274"></a>01274 <span class="comment"> * @param p Probability \f$ p \in [0,1] \f$</span> |
| <a name="l01275"></a>01275 <span class="comment"> * @param df Degrees of freedom \f$ \nu > 0 \f$</span> |
| <a name="l01276"></a>01276 <span class="comment"> * @param ncp Noncentrality parameter \f$ \delta \f$</span> |
| <a name="l01277"></a>01277 <span class="comment"> * @return \f$ x \f$ such that \f$ p = \Pr[X \leq x] \f$ where \f$ X \f$ is a</span> |
| <a name="l01278"></a>01278 <span class="comment"> * noncentral Student's t-distributed random variable with \f$ \nu \f$</span> |
| <a name="l01279"></a>01279 <span class="comment"> * degrees of freedom and noncentrality parameter \f$ \delta \f$</span> |
| <a name="l01280"></a>01280 <span class="comment"> */</span> |
| <a name="l01281"></a>01281 CREATE FUNCTION MADLIB_SCHEMA.non_central_t_quantile( |
| <a name="l01282"></a>01282 p DOUBLE PRECISION, |
| <a name="l01283"></a>01283 df DOUBLE PRECISION, |
| <a name="l01284"></a><a class="code" href="prob_8sql__in.html#a4799e3bb68a496d9bc1ef1ea85265409">01284</a> ncp DOUBLE PRECISION |
| <a name="l01285"></a>01285 ) RETURNS DOUBLE PRECISION |
| <a name="l01286"></a>01286 AS 'MODULE_PATHNAME<span class="stringliteral">'</span> |
| <a name="l01287"></a>01287 <span class="stringliteral">LANGUAGE C</span> |
| <a name="l01288"></a>01288 <span class="stringliteral">IMMUTABLE STRICT;</span> |
| <a name="l01289"></a>01289 <span class="stringliteral"></span> |
| <a name="l01290"></a>01290 <span class="stringliteral"></span><span class="comment"></span> |
| <a name="l01291"></a>01291 <span class="comment">/**</span> |
| <a name="l01292"></a>01292 <span class="comment"> * @brief Normal cumulative distribution function</span> |
| <a name="l01293"></a>01293 <span class="comment"> *</span> |
| <a name="l01294"></a>01294 <span class="comment"> * @param x Random variate \f$ x \f$</span> |
| <a name="l01295"></a>01295 <span class="comment"> * @param mean Mean \f$ \mu \f$</span> |
| <a name="l01296"></a>01296 <span class="comment"> * @param sd Standard deviation \f$ \sigma > 0 \f$</span> |
| <a name="l01297"></a>01297 <span class="comment"> * @return \f$ \Pr[X \leq x] \f$ where \f$ T \f$ is a normally distributed</span> |
| <a name="l01298"></a>01298 <span class="comment"> * random variable with mean \f$ \mu \f$ and variance \f$ \sigma^2 \f$</span> |
| <a name="l01299"></a>01299 <span class="comment"> */</span> |
| <a name="l01300"></a>01300 CREATE FUNCTION MADLIB_SCHEMA.normal_cdf( |
| <a name="l01301"></a>01301 x DOUBLE PRECISION, |
| <a name="l01302"></a>01302 mean DOUBLE PRECISION /*+ DEFAULT 0 */, |
| <a name="l01303"></a><a class="code" href="prob_8sql__in.html#af50865aba2ece2e23b2af461a02f7d12">01303</a> sd DOUBLE PRECISION /*+ DEFAULT 1 */ |
| <a name="l01304"></a>01304 ) RETURNS DOUBLE PRECISION |
| <a name="l01305"></a>01305 AS 'MODULE_PATHNAME<span class="stringliteral">'</span> |
| <a name="l01306"></a>01306 <span class="stringliteral">LANGUAGE C</span> |
| <a name="l01307"></a>01307 <span class="stringliteral">IMMUTABLE STRICT;</span> |
| <a name="l01308"></a>01308 <span class="stringliteral"></span> |
| <a name="l01309"></a>01309 <span class="stringliteral">CREATE FUNCTION MADLIB_SCHEMA.normal_cdf(</span> |
| <a name="l01310"></a>01310 <span class="stringliteral"> x DOUBLE PRECISION,</span> |
| <a name="l01311"></a>01311 <span class="stringliteral"> mean DOUBLE PRECISION</span> |
| <a name="l01312"></a>01312 <span class="stringliteral">) RETURNS DOUBLE PRECISION</span> |
| <a name="l01313"></a>01313 <span class="stringliteral">IMMUTABLE</span> |
| <a name="l01314"></a>01314 <span class="stringliteral">STRICT</span> |
| <a name="l01315"></a>01315 <span class="stringliteral">LANGUAGE sql AS $$</span> |
| <a name="l01316"></a>01316 <span class="stringliteral"> SELECT MADLIB_SCHEMA.normal_cdf($1, $2, 1)</span> |
| <a name="l01317"></a>01317 <span class="stringliteral">$$;</span> |
| <a name="l01318"></a>01318 <span class="stringliteral"></span> |
| <a name="l01319"></a>01319 <span class="stringliteral">CREATE FUNCTION MADLIB_SCHEMA.normal_cdf(</span> |
| <a name="l01320"></a>01320 <span class="stringliteral"> x DOUBLE PRECISION</span> |
| <a name="l01321"></a>01321 <span class="stringliteral">) RETURNS DOUBLE PRECISION</span> |
| <a name="l01322"></a><a class="code" href="prob_8sql__in.html#aebcd34ad7b1ca4b31d9699112c9a3b90">01322</a> <span class="stringliteral">IMMUTABLE</span> |
| <a name="l01323"></a>01323 <span class="stringliteral">STRICT</span> |
| <a name="l01324"></a>01324 <span class="stringliteral">LANGUAGE sql AS $$</span> |
| <a name="l01325"></a>01325 <span class="stringliteral"> SELECT MADLIB_SCHEMA.normal_cdf($1, 0, 1)</span> |
| <a name="l01326"></a>01326 <span class="stringliteral">$$;</span> |
| <a name="l01327"></a>01327 <span class="stringliteral"></span><span class="comment"></span> |
| <a name="l01328"></a>01328 <span class="comment">/**</span> |
| <a name="l01329"></a>01329 <span class="comment"> * @brief Normal probability density function</span> |
| <a name="l01330"></a>01330 <span class="comment"> *</span> |
| <a name="l01331"></a>01331 <span class="comment"> * @param x Random variate \f$ x \f$</span> |
| <a name="l01332"></a>01332 <span class="comment"> * @param mean Mean \f$ \mu \f$</span> |
| <a name="l01333"></a>01333 <span class="comment"> * @param sd Standard deviation \f$ \sigma > 0 \f$</span> |
| <a name="l01334"></a>01334 <span class="comment"> * @return \f$ f(x) \f$ where \f$ f \f$ is the probability density function of</span> |
| <a name="l01335"></a>01335 <span class="comment"> * a normally distributed random variable with mean \f$ \mu \f$ and</span> |
| <a name="l01336"></a>01336 <span class="comment"> * variance \f$ \sigma^2 \f$</span> |
| <a name="l01337"></a>01337 <span class="comment"> */</span> |
| <a name="l01338"></a>01338 CREATE FUNCTION MADLIB_SCHEMA.normal_pdf( |
| <a name="l01339"></a>01339 x DOUBLE PRECISION, |
| <a name="l01340"></a>01340 mean DOUBLE PRECISION /*+ DEFAULT 0 */, |
| <a name="l01341"></a>01341 sd DOUBLE PRECISION /*+ DEFAULT 1 */ |
| <a name="l01342"></a>01342 ) RETURNS DOUBLE PRECISION |
| <a name="l01343"></a>01343 AS 'MODULE_PATHNAME<span class="stringliteral">'</span> |
| <a name="l01344"></a>01344 <span class="stringliteral">LANGUAGE C</span> |
| <a name="l01345"></a>01345 <span class="stringliteral">IMMUTABLE STRICT;</span> |
| <a name="l01346"></a>01346 <span class="stringliteral"></span> |
| <a name="l01347"></a>01347 <span class="stringliteral">CREATE FUNCTION MADLIB_SCHEMA.normal_pdf(</span> |
| <a name="l01348"></a>01348 <span class="stringliteral"> x DOUBLE PRECISION,</span> |
| <a name="l01349"></a>01349 <span class="stringliteral"> mean DOUBLE PRECISION</span> |
| <a name="l01350"></a>01350 <span class="stringliteral">) RETURNS DOUBLE PRECISION</span> |
| <a name="l01351"></a>01351 <span class="stringliteral">IMMUTABLE</span> |
| <a name="l01352"></a>01352 <span class="stringliteral">STRICT</span> |
| <a name="l01353"></a>01353 <span class="stringliteral">LANGUAGE sql AS $$</span> |
| <a name="l01354"></a>01354 <span class="stringliteral"> SELECT MADLIB_SCHEMA.normal_pdf($1, $2, 1)</span> |
| <a name="l01355"></a>01355 <span class="stringliteral">$$;</span> |
| <a name="l01356"></a>01356 <span class="stringliteral"></span> |
| <a name="l01357"></a>01357 <span class="stringliteral">CREATE FUNCTION MADLIB_SCHEMA.normal_pdf(</span> |
| <a name="l01358"></a>01358 <span class="stringliteral"> x DOUBLE PRECISION</span> |
| <a name="l01359"></a>01359 <span class="stringliteral">) RETURNS DOUBLE PRECISION</span> |
| <a name="l01360"></a><a class="code" href="prob_8sql__in.html#a63f555f36385d86e229cdca223e39567">01360</a> <span class="stringliteral">IMMUTABLE</span> |
| <a name="l01361"></a>01361 <span class="stringliteral">STRICT</span> |
| <a name="l01362"></a>01362 <span class="stringliteral">LANGUAGE sql AS $$</span> |
| <a name="l01363"></a>01363 <span class="stringliteral"> SELECT MADLIB_SCHEMA.normal_pdf($1, 0, 1)</span> |
| <a name="l01364"></a>01364 <span class="stringliteral">$$;</span> |
| <a name="l01365"></a>01365 <span class="stringliteral"></span><span class="comment"></span> |
| <a name="l01366"></a>01366 <span class="comment">/**</span> |
| <a name="l01367"></a>01367 <span class="comment"> * @brief Normal quantile function</span> |
| <a name="l01368"></a>01368 <span class="comment"> *</span> |
| <a name="l01369"></a>01369 <span class="comment"> * @param p Probability \f$ p \in [0,1] \f$</span> |
| <a name="l01370"></a>01370 <span class="comment"> * @param mean Mean \f$ \mu \f$</span> |
| <a name="l01371"></a>01371 <span class="comment"> * @param sd Standard deviation \f$ \sigma > 0 \f$</span> |
| <a name="l01372"></a>01372 <span class="comment"> * @return \f$ x \f$ such that \f$ p = \Pr[X \leq x] \f$ where \f$ X \f$ is a</span> |
| <a name="l01373"></a>01373 <span class="comment"> * normally distributed random variable with mean \f$ \mu \f$ and</span> |
| <a name="l01374"></a>01374 <span class="comment"> * variance \f$ \sigma^2 \f$</span> |
| <a name="l01375"></a>01375 <span class="comment"> */</span> |
| <a name="l01376"></a>01376 CREATE FUNCTION MADLIB_SCHEMA.normal_quantile( |
| <a name="l01377"></a>01377 p DOUBLE PRECISION, |
| <a name="l01378"></a>01378 mean DOUBLE PRECISION /*+ DEFAULT 0 */, |
| <a name="l01379"></a>01379 sd DOUBLE PRECISION /*+ DEFAULT 1 */ |
| <a name="l01380"></a>01380 ) RETURNS DOUBLE PRECISION |
| <a name="l01381"></a>01381 AS 'MODULE_PATHNAME<span class="stringliteral">'</span> |
| <a name="l01382"></a>01382 <span class="stringliteral">LANGUAGE C</span> |
| <a name="l01383"></a>01383 <span class="stringliteral">IMMUTABLE STRICT;</span> |
| <a name="l01384"></a>01384 <span class="stringliteral"></span> |
| <a name="l01385"></a>01385 <span class="stringliteral">CREATE FUNCTION MADLIB_SCHEMA.normal_quantile(</span> |
| <a name="l01386"></a>01386 <span class="stringliteral"> p DOUBLE PRECISION,</span> |
| <a name="l01387"></a>01387 <span class="stringliteral"> mean DOUBLE PRECISION</span> |
| <a name="l01388"></a>01388 <span class="stringliteral">) RETURNS DOUBLE PRECISION</span> |
| <a name="l01389"></a>01389 <span class="stringliteral">IMMUTABLE</span> |
| <a name="l01390"></a>01390 <span class="stringliteral">STRICT</span> |
| <a name="l01391"></a>01391 <span class="stringliteral">LANGUAGE sql AS $$</span> |
| <a name="l01392"></a>01392 <span class="stringliteral"> SELECT MADLIB_SCHEMA.normal_quantile($1, $2, 1)</span> |
| <a name="l01393"></a>01393 <span class="stringliteral">$$;</span> |
| <a name="l01394"></a>01394 <span class="stringliteral"></span> |
| <a name="l01395"></a>01395 <span class="stringliteral">CREATE FUNCTION MADLIB_SCHEMA.normal_quantile(</span> |
| <a name="l01396"></a>01396 <span class="stringliteral"> p DOUBLE PRECISION</span> |
| <a name="l01397"></a>01397 <span class="stringliteral">) RETURNS DOUBLE PRECISION</span> |
| <a name="l01398"></a><a class="code" href="prob_8sql__in.html#a53d56b672fe4cd1277cb5eac5de5118f">01398</a> <span class="stringliteral">IMMUTABLE</span> |
| <a name="l01399"></a>01399 <span class="stringliteral">STRICT</span> |
| <a name="l01400"></a>01400 <span class="stringliteral">LANGUAGE sql AS $$</span> |
| <a name="l01401"></a>01401 <span class="stringliteral"> SELECT MADLIB_SCHEMA.normal_quantile($1, 0, 1)</span> |
| <a name="l01402"></a>01402 <span class="stringliteral">$$;</span> |
| <a name="l01403"></a>01403 <span class="stringliteral"></span> |
| <a name="l01404"></a>01404 <span class="stringliteral"></span><span class="comment"></span> |
| <a name="l01405"></a>01405 <span class="comment">/**</span> |
| <a name="l01406"></a>01406 <span class="comment"> * @brief Pareto cumulative distribution function</span> |
| <a name="l01407"></a>01407 <span class="comment"> *</span> |
| <a name="l01408"></a>01408 <span class="comment"> * @param x Random variate \f$ x \f$</span> |
| <a name="l01409"></a>01409 <span class="comment"> * @param scale Scale \f$ \beta > 0 \f$</span> |
| <a name="l01410"></a>01410 <span class="comment"> * @param shape Shape \f$ \alpha > 0 \f$</span> |
| <a name="l01411"></a>01411 <span class="comment"> * @return \f$ \Pr[X \leq x] \f$ where \f$ X \f$ is a Pareto-distributed random</span> |
| <a name="l01412"></a>01412 <span class="comment"> * variable with shape and scale parameters \f$ \alpha \f$ and</span> |
| <a name="l01413"></a>01413 <span class="comment"> * \f$ \beta \f$, respectively</span> |
| <a name="l01414"></a>01414 <span class="comment"> */</span> |
| <a name="l01415"></a>01415 CREATE FUNCTION MADLIB_SCHEMA.pareto_cdf( |
| <a name="l01416"></a>01416 x DOUBLE PRECISION, |
| <a name="l01417"></a>01417 scale DOUBLE PRECISION, |
| <a name="l01418"></a>01418 shape DOUBLE PRECISION |
| <a name="l01419"></a>01419 ) RETURNS DOUBLE PRECISION |
| <a name="l01420"></a>01420 AS 'MODULE_PATHNAME<span class="stringliteral">'</span> |
| <a name="l01421"></a>01421 <span class="stringliteral">LANGUAGE C</span> |
| <a name="l01422"></a>01422 <span class="stringliteral">IMMUTABLE STRICT;</span> |
| <a name="l01423"></a>01423 <span class="stringliteral"></span><span class="comment"></span> |
| <a name="l01424"></a>01424 <span class="comment">/**</span> |
| <a name="l01425"></a>01425 <span class="comment"> * @brief Pareto probability density function</span> |
| <a name="l01426"></a>01426 <span class="comment"> *</span> |
| <a name="l01427"></a>01427 <span class="comment"> * @param x Random variate \f$ x \f$</span> |
| <a name="l01428"></a>01428 <span class="comment"> * @param scale Scale \f$ \beta > 0 \f$</span> |
| <a name="l01429"></a>01429 <span class="comment"> * @param shape Shape \f$ \alpha > 0 \f$</span> |
| <a name="l01430"></a>01430 <span class="comment"> * @return \f$ f(x) \f$ where \f$ f \f$ is the probability density function of</span> |
| <a name="l01431"></a>01431 <span class="comment"> * a Pareto-distributed random variable with shape and scale parameters</span> |
| <a name="l01432"></a>01432 <span class="comment"> * \f$ \alpha \f$ and \f$ \beta \f$, respectively</span> |
| <a name="l01433"></a>01433 <span class="comment"> */</span> |
| <a name="l01434"></a>01434 CREATE FUNCTION MADLIB_SCHEMA.pareto_pdf( |
| <a name="l01435"></a>01435 x DOUBLE PRECISION, |
| <a name="l01436"></a>01436 scale DOUBLE PRECISION, |
| <a name="l01437"></a><a class="code" href="prob_8sql__in.html#aa1a42ebd68f20f65bc1784b427721b5d">01437</a> shape DOUBLE PRECISION |
| <a name="l01438"></a>01438 ) RETURNS DOUBLE PRECISION |
| <a name="l01439"></a>01439 AS 'MODULE_PATHNAME<span class="stringliteral">'</span> |
| <a name="l01440"></a>01440 <span class="stringliteral">LANGUAGE C</span> |
| <a name="l01441"></a>01441 <span class="stringliteral">IMMUTABLE STRICT;</span> |
| <a name="l01442"></a>01442 <span class="stringliteral"></span><span class="comment"></span> |
| <a name="l01443"></a>01443 <span class="comment">/**</span> |
| <a name="l01444"></a>01444 <span class="comment"> * @brief Pareto quantile function</span> |
| <a name="l01445"></a>01445 <span class="comment"> *</span> |
| <a name="l01446"></a>01446 <span class="comment"> * @param p Probability \f$ p \in [0,1] \f$</span> |
| <a name="l01447"></a>01447 <span class="comment"> * @param scale Scale \f$ \beta > 0 \f$</span> |
| <a name="l01448"></a>01448 <span class="comment"> * @param shape Shape \f$ \alpha > 0 \f$</span> |
| <a name="l01449"></a>01449 <span class="comment"> * @return \f$ x \f$ such that \f$ p = \Pr[X \leq x] \f$ where \f$ X \f$ is a</span> |
| <a name="l01450"></a>01450 <span class="comment"> * Pareto-distributed random variable with shape and scale parameters</span> |
| <a name="l01451"></a>01451 <span class="comment"> * \f$ \alpha \f$ and \f$ \beta \f$, respectively</span> |
| <a name="l01452"></a>01452 <span class="comment"> */</span> |
| <a name="l01453"></a>01453 CREATE FUNCTION MADLIB_SCHEMA.pareto_quantile( |
| <a name="l01454"></a>01454 p DOUBLE PRECISION, |
| <a name="l01455"></a>01455 scale DOUBLE PRECISION, |
| <a name="l01456"></a><a class="code" href="prob_8sql__in.html#a22c56a6e48bc442435b13afac2a1eb37">01456</a> shape DOUBLE PRECISION |
| <a name="l01457"></a>01457 ) RETURNS DOUBLE PRECISION |
| <a name="l01458"></a>01458 AS 'MODULE_PATHNAME<span class="stringliteral">'</span> |
| <a name="l01459"></a>01459 <span class="stringliteral">LANGUAGE C</span> |
| <a name="l01460"></a>01460 <span class="stringliteral">IMMUTABLE STRICT;</span> |
| <a name="l01461"></a>01461 <span class="stringliteral"></span> |
| <a name="l01462"></a>01462 <span class="stringliteral"></span><span class="comment"></span> |
| <a name="l01463"></a>01463 <span class="comment">/**</span> |
| <a name="l01464"></a>01464 <span class="comment"> * @brief Poisson cumulative distribution function</span> |
| <a name="l01465"></a>01465 <span class="comment"> *</span> |
| <a name="l01466"></a>01466 <span class="comment"> * @param x Random variate \f$ x \f$</span> |
| <a name="l01467"></a>01467 <span class="comment"> * @param mean Average occurrence rate \f$ \lambda > 0 \f$</span> |
| <a name="l01468"></a>01468 <span class="comment"> * @return \f$ \Pr[X \leq x] \f$ where \f$ X \f$ is a Poisson distributed random</span> |
| <a name="l01469"></a>01469 <span class="comment"> * variable with mean \f$ \lambda \f$</span> |
| <a name="l01470"></a>01470 <span class="comment"> */</span> |
| <a name="l01471"></a>01471 CREATE FUNCTION MADLIB_SCHEMA.poisson_cdf( |
| <a name="l01472"></a>01472 x DOUBLE PRECISION, |
| <a name="l01473"></a>01473 mean DOUBLE PRECISION |
| <a name="l01474"></a>01474 ) RETURNS DOUBLE PRECISION |
| <a name="l01475"></a><a class="code" href="prob_8sql__in.html#a77779e2b5fa951189ccba6806c503c4d">01475</a> AS 'MODULE_PATHNAME<span class="stringliteral">'</span> |
| <a name="l01476"></a>01476 <span class="stringliteral">LANGUAGE C</span> |
| <a name="l01477"></a>01477 <span class="stringliteral">IMMUTABLE STRICT;</span> |
| <a name="l01478"></a>01478 <span class="stringliteral"></span><span class="comment"></span> |
| <a name="l01479"></a>01479 <span class="comment">/**</span> |
| <a name="l01480"></a>01480 <span class="comment"> * @brief Poisson probability mass function</span> |
| <a name="l01481"></a>01481 <span class="comment"> *</span> |
| <a name="l01482"></a>01482 <span class="comment"> * @param x Random variate \f$ x \f$</span> |
| <a name="l01483"></a>01483 <span class="comment"> * @param mean Average occurrence rate \f$ \lambda > 0 \f$</span> |
| <a name="l01484"></a>01484 <span class="comment"> * @return \f$ f(x) \f$ where \f$ f \f$ is the probability mass function of a</span> |
| <a name="l01485"></a>01485 <span class="comment"> * Poisson distributed random variable with mean \f$ \lambda \f$</span> |
| <a name="l01486"></a>01486 <span class="comment"> */</span> |
| <a name="l01487"></a>01487 CREATE FUNCTION MADLIB_SCHEMA.poisson_pmf( |
| <a name="l01488"></a>01488 x INT4, |
| <a name="l01489"></a>01489 mean DOUBLE PRECISION |
| <a name="l01490"></a>01490 ) RETURNS DOUBLE PRECISION |
| <a name="l01491"></a>01491 AS 'MODULE_PATHNAME<span class="stringliteral">'</span> |
| <a name="l01492"></a>01492 <span class="stringliteral">LANGUAGE C</span> |
| <a name="l01493"></a><a class="code" href="prob_8sql__in.html#ae0b4313d9fe730d6efb3f7c44206f345">01493</a> <span class="stringliteral">IMMUTABLE STRICT;</span> |
| <a name="l01494"></a>01494 <span class="stringliteral"></span><span class="comment"></span> |
| <a name="l01495"></a>01495 <span class="comment">/**</span> |
| <a name="l01496"></a>01496 <span class="comment"> * @brief Poisson quantile function</span> |
| <a name="l01497"></a>01497 <span class="comment"> *</span> |
| <a name="l01498"></a>01498 <span class="comment"> * @param p Probability \f$ p \in [0,1] \f$</span> |
| <a name="l01499"></a>01499 <span class="comment"> * @param mean Average occurrence rate \f$ \lambda > 0 \f$</span> |
| <a name="l01500"></a>01500 <span class="comment"> * @return If \f$ p < 0.5 \f$ the maximum \f$ x \f$ such that</span> |
| <a name="l01501"></a>01501 <span class="comment"> * \f$ p \geq \Pr[X \leq x] \f$. If \f$ p \geq 0.5 \f$ the minimum \f$ x \f$</span> |
| <a name="l01502"></a>01502 <span class="comment"> * such that \f$ p \leq \Pr[X \leq x] \f$. Here, \f$ X \f$ is a</span> |
| <a name="l01503"></a>01503 <span class="comment"> * Poisson distributed random variable with mean \f$ \lambda \f$</span> |
| <a name="l01504"></a>01504 <span class="comment"> */</span> |
| <a name="l01505"></a>01505 CREATE FUNCTION MADLIB_SCHEMA.poisson_quantile( |
| <a name="l01506"></a>01506 p DOUBLE PRECISION, |
| <a name="l01507"></a>01507 mean DOUBLE PRECISION |
| <a name="l01508"></a>01508 ) RETURNS DOUBLE PRECISION |
| <a name="l01509"></a><a class="code" href="prob_8sql__in.html#a82f1edc27261021c73cd080ff2677a9f">01509</a> AS 'MODULE_PATHNAME<span class="stringliteral">'</span> |
| <a name="l01510"></a>01510 <span class="stringliteral">LANGUAGE C</span> |
| <a name="l01511"></a>01511 <span class="stringliteral">IMMUTABLE STRICT;</span> |
| <a name="l01512"></a>01512 <span class="stringliteral"></span> |
| <a name="l01513"></a>01513 <span class="stringliteral"></span><span class="comment"></span> |
| <a name="l01514"></a>01514 <span class="comment">/**</span> |
| <a name="l01515"></a>01515 <span class="comment"> * @brief Rayleigh cumulative distribution function</span> |
| <a name="l01516"></a>01516 <span class="comment"> *</span> |
| <a name="l01517"></a>01517 <span class="comment"> * @param x Random variate \f$ x \f$</span> |
| <a name="l01518"></a>01518 <span class="comment"> * @param scale Scale \f$ \sigma > 0 \f$</span> |
| <a name="l01519"></a>01519 <span class="comment"> * @return \f$ \Pr[X \leq x] \f$ where \f$ X \f$ is a Rayleigh-distributed</span> |
| <a name="l01520"></a>01520 <span class="comment"> * random variable with parameter \f$ \sigma \f$</span> |
| <a name="l01521"></a>01521 <span class="comment"> */</span> |
| <a name="l01522"></a>01522 CREATE FUNCTION MADLIB_SCHEMA.rayleigh_cdf( |
| <a name="l01523"></a>01523 x DOUBLE PRECISION, |
| <a name="l01524"></a>01524 scale DOUBLE PRECISION |
| <a name="l01525"></a>01525 ) RETURNS DOUBLE PRECISION |
| <a name="l01526"></a>01526 AS 'MODULE_PATHNAME<span class="stringliteral">'</span> |
| <a name="l01527"></a><a class="code" href="prob_8sql__in.html#a032d26db18b2ee1034085f5521939c61">01527</a> <span class="stringliteral">LANGUAGE C</span> |
| <a name="l01528"></a>01528 <span class="stringliteral">IMMUTABLE STRICT;</span> |
| <a name="l01529"></a>01529 <span class="stringliteral"></span><span class="comment"></span> |
| <a name="l01530"></a>01530 <span class="comment">/**</span> |
| <a name="l01531"></a>01531 <span class="comment"> * @brief Rayleigh probability density function</span> |
| <a name="l01532"></a>01532 <span class="comment"> *</span> |
| <a name="l01533"></a>01533 <span class="comment"> * @param x Random variate \f$ x \f$</span> |
| <a name="l01534"></a>01534 <span class="comment"> * @param scale Scale \f$ \sigma > 0 \f$</span> |
| <a name="l01535"></a>01535 <span class="comment"> * @return \f$ f(x) \f$ where \f$ f \f$ is the probability density function of</span> |
| <a name="l01536"></a>01536 <span class="comment"> * a Rayleigh-distributed random variable with parameter \f$ \sigma \f$</span> |
| <a name="l01537"></a>01537 <span class="comment"> */</span> |
| <a name="l01538"></a>01538 CREATE FUNCTION MADLIB_SCHEMA.rayleigh_pdf( |
| <a name="l01539"></a>01539 x DOUBLE PRECISION, |
| <a name="l01540"></a>01540 scale DOUBLE PRECISION |
| <a name="l01541"></a>01541 ) RETURNS DOUBLE PRECISION |
| <a name="l01542"></a>01542 AS 'MODULE_PATHNAME<span class="stringliteral">'</span> |
| <a name="l01543"></a>01543 <span class="stringliteral">LANGUAGE C</span> |
| <a name="l01544"></a><a class="code" href="prob_8sql__in.html#aab0ddb8a5348cfa387d777043a3cb6d0">01544</a> <span class="stringliteral">IMMUTABLE STRICT;</span> |
| <a name="l01545"></a>01545 <span class="stringliteral"></span><span class="comment"></span> |
| <a name="l01546"></a>01546 <span class="comment">/**</span> |
| <a name="l01547"></a>01547 <span class="comment"> * @brief Rayleigh quantile function</span> |
| <a name="l01548"></a>01548 <span class="comment"> *</span> |
| <a name="l01549"></a>01549 <span class="comment"> * @param p Probability \f$ p \in [0,1] \f$</span> |
| <a name="l01550"></a>01550 <span class="comment"> * @param scale Scale \f$ \sigma > 0 \f$</span> |
| <a name="l01551"></a>01551 <span class="comment"> * @return \f$ x \f$ such that \f$ p = \Pr[X \leq x] \f$ where \f$ X \f$ is a</span> |
| <a name="l01552"></a>01552 <span class="comment"> * Rayleigh-distributed random variable with parameter \f$ \sigma \f$</span> |
| <a name="l01553"></a>01553 <span class="comment"> */</span> |
| <a name="l01554"></a>01554 CREATE FUNCTION MADLIB_SCHEMA.rayleigh_quantile( |
| <a name="l01555"></a>01555 p DOUBLE PRECISION, |
| <a name="l01556"></a>01556 scale DOUBLE PRECISION |
| <a name="l01557"></a>01557 ) RETURNS DOUBLE PRECISION |
| <a name="l01558"></a>01558 AS 'MODULE_PATHNAME<span class="stringliteral">'</span> |
| <a name="l01559"></a>01559 <span class="stringliteral">LANGUAGE C</span> |
| <a name="l01560"></a><a class="code" href="prob_8sql__in.html#a798541736d9255bdd5c0bd94924d47bc">01560</a> <span class="stringliteral">IMMUTABLE STRICT;</span> |
| <a name="l01561"></a>01561 <span class="stringliteral"></span> |
| <a name="l01562"></a>01562 <span class="stringliteral"></span><span class="comment"></span> |
| <a name="l01563"></a>01563 <span class="comment">/**</span> |
| <a name="l01564"></a>01564 <span class="comment"> * @brief Student's t cumulative distribution function</span> |
| <a name="l01565"></a>01565 <span class="comment"> *</span> |
| <a name="l01566"></a>01566 <span class="comment"> * @param x Random variate \f$ x \f$</span> |
| <a name="l01567"></a>01567 <span class="comment"> * @param df Degrees of freedom \f$ \nu > 0 \f$</span> |
| <a name="l01568"></a>01568 <span class="comment"> * @return \f$ \Pr[X \leq x] \f$ where \f$ X \f$ is a Student's t-distributed</span> |
| <a name="l01569"></a>01569 <span class="comment"> * random variable with \f$ \nu \f$ degrees of freedom</span> |
| <a name="l01570"></a>01570 <span class="comment"> */</span> |
| <a name="l01571"></a>01571 CREATE FUNCTION MADLIB_SCHEMA.students_t_cdf( |
| <a name="l01572"></a>01572 x DOUBLE PRECISION, |
| <a name="l01573"></a>01573 df DOUBLE PRECISION |
| <a name="l01574"></a>01574 ) RETURNS DOUBLE PRECISION |
| <a name="l01575"></a>01575 AS 'MODULE_PATHNAME<span class="stringliteral">'</span> |
| <a name="l01576"></a><a class="code" href="prob_8sql__in.html#acd6757acab1683c735e2b57901494336">01576</a> <span class="stringliteral">LANGUAGE C</span> |
| <a name="l01577"></a>01577 <span class="stringliteral">IMMUTABLE STRICT;</span> |
| <a name="l01578"></a>01578 <span class="stringliteral"></span><span class="comment"></span> |
| <a name="l01579"></a>01579 <span class="comment">/**</span> |
| <a name="l01580"></a>01580 <span class="comment"> * @brief Student's t probability density function</span> |
| <a name="l01581"></a>01581 <span class="comment"> *</span> |
| <a name="l01582"></a>01582 <span class="comment"> * @param x Random variate \f$ x \f$</span> |
| <a name="l01583"></a>01583 <span class="comment"> * @param df Degrees of freedom \f$ \nu > 0 \f$</span> |
| <a name="l01584"></a>01584 <span class="comment"> * @return \f$ f(x) \f$ where \f$ f \f$ is the probability density function of</span> |
| <a name="l01585"></a>01585 <span class="comment"> * a Stundent's t-distributed random variable with \f$ \nu \f$ degrees of</span> |
| <a name="l01586"></a>01586 <span class="comment"> * freedom</span> |
| <a name="l01587"></a>01587 <span class="comment"> */</span> |
| <a name="l01588"></a>01588 CREATE FUNCTION MADLIB_SCHEMA.students_t_pdf( |
| <a name="l01589"></a>01589 x DOUBLE PRECISION, |
| <a name="l01590"></a>01590 df DOUBLE PRECISION |
| <a name="l01591"></a>01591 ) RETURNS DOUBLE PRECISION |
| <a name="l01592"></a>01592 AS 'MODULE_PATHNAME<span class="stringliteral">'</span> |
| <a name="l01593"></a><a class="code" href="prob_8sql__in.html#a5322531131074c23a2dbf067ee504ef7">01593</a> <span class="stringliteral">LANGUAGE C</span> |
| <a name="l01594"></a>01594 <span class="stringliteral">IMMUTABLE STRICT;</span> |
| <a name="l01595"></a>01595 <span class="stringliteral"></span><span class="comment"></span> |
| <a name="l01596"></a>01596 <span class="comment">/**</span> |
| <a name="l01597"></a>01597 <span class="comment"> * @brief Student's t quantile function</span> |
| <a name="l01598"></a>01598 <span class="comment"> *</span> |
| <a name="l01599"></a>01599 <span class="comment"> * @param p Probability \f$ p \in [0,1] \f$</span> |
| <a name="l01600"></a>01600 <span class="comment"> * @param df Degrees of freedom \f$ \nu > 0 \f$</span> |
| <a name="l01601"></a>01601 <span class="comment"> * @return \f$ x \f$ such that \f$ p = \Pr[X \leq x] \f$ where \f$ X \f$ is a</span> |
| <a name="l01602"></a>01602 <span class="comment"> * Student's t-distributed random variable with \f$ \nu \f$ degrees of</span> |
| <a name="l01603"></a>01603 <span class="comment"> * freedom</span> |
| <a name="l01604"></a>01604 <span class="comment"> */</span> |
| <a name="l01605"></a>01605 CREATE FUNCTION MADLIB_SCHEMA.students_t_quantile( |
| <a name="l01606"></a>01606 p DOUBLE PRECISION, |
| <a name="l01607"></a>01607 df DOUBLE PRECISION |
| <a name="l01608"></a>01608 ) RETURNS DOUBLE PRECISION |
| <a name="l01609"></a>01609 AS 'MODULE_PATHNAME<span class="stringliteral">'</span> |
| <a name="l01610"></a><a class="code" href="prob_8sql__in.html#a8815c21670fff9d31946553a84b845b1">01610</a> <span class="stringliteral">LANGUAGE C</span> |
| <a name="l01611"></a>01611 <span class="stringliteral">IMMUTABLE STRICT;</span> |
| <a name="l01612"></a>01612 <span class="stringliteral"></span> |
| <a name="l01613"></a>01613 <span class="stringliteral"></span><span class="comment"></span> |
| <a name="l01614"></a>01614 <span class="comment">/**</span> |
| <a name="l01615"></a>01615 <span class="comment"> * @brief Triangular cumulative distribution function</span> |
| <a name="l01616"></a>01616 <span class="comment"> *</span> |
| <a name="l01617"></a>01617 <span class="comment"> * @param x Random variate \f$ x \f$</span> |
| <a name="l01618"></a>01618 <span class="comment"> * @param lower Lower bound \f$ a \f$</span> |
| <a name="l01619"></a>01619 <span class="comment"> * @param mode Mode \f$ c \geq a \f$</span> |
| <a name="l01620"></a>01620 <span class="comment"> * @param upper Upper bound \f$ b \geq c \f$, where \f$ b > a \f$</span> |
| <a name="l01621"></a>01621 <span class="comment"> * @return \f$ \Pr[X \leq x] \f$ where \f$ X \f$ is a triangular distributed</span> |
| <a name="l01622"></a>01622 <span class="comment"> * random variable with parameters \f$ a, b, c \f$</span> |
| <a name="l01623"></a>01623 <span class="comment"> */</span> |
| <a name="l01624"></a>01624 CREATE FUNCTION MADLIB_SCHEMA.triangular_cdf( |
| <a name="l01625"></a>01625 x DOUBLE PRECISION, |
| <a name="l01626"></a>01626 lower DOUBLE PRECISION, |
| <a name="l01627"></a><a class="code" href="prob_8sql__in.html#a7d64add02af21a95d73502b2dd466a75">01627</a> mode DOUBLE PRECISION, |
| <a name="l01628"></a>01628 upper DOUBLE PRECISION |
| <a name="l01629"></a>01629 ) RETURNS DOUBLE PRECISION |
| <a name="l01630"></a>01630 AS 'MODULE_PATHNAME<span class="stringliteral">'</span> |
| <a name="l01631"></a>01631 <span class="stringliteral">LANGUAGE C</span> |
| <a name="l01632"></a>01632 <span class="stringliteral">IMMUTABLE STRICT;</span> |
| <a name="l01633"></a>01633 <span class="stringliteral"></span><span class="comment"></span> |
| <a name="l01634"></a>01634 <span class="comment">/**</span> |
| <a name="l01635"></a>01635 <span class="comment"> * @brief Triangular probability density function</span> |
| <a name="l01636"></a>01636 <span class="comment"> *</span> |
| <a name="l01637"></a>01637 <span class="comment"> * @param x Random variate \f$ x \f$</span> |
| <a name="l01638"></a>01638 <span class="comment"> * @param lower Lower bound \f$ a \f$</span> |
| <a name="l01639"></a>01639 <span class="comment"> * @param mode Mode \f$ c \geq a \f$</span> |
| <a name="l01640"></a>01640 <span class="comment"> * @param upper Upper bound \f$ b \geq c \f$, where \f$ b > a \f$</span> |
| <a name="l01641"></a>01641 <span class="comment"> * @return \f$ f(x) \f$ where \f$ f \f$ is the probability density function of</span> |
| <a name="l01642"></a>01642 <span class="comment"> * a triangular distributed random variable with parameters \f$ a, b, c \f$</span> |
| <a name="l01643"></a>01643 <span class="comment"> */</span> |
| <a name="l01644"></a>01644 CREATE FUNCTION MADLIB_SCHEMA.triangular_pdf( |
| <a name="l01645"></a>01645 x DOUBLE PRECISION, |
| <a name="l01646"></a><a class="code" href="prob_8sql__in.html#abf9c7d870bcfe68cacaa421749bbdf35">01646</a> lower DOUBLE PRECISION, |
| <a name="l01647"></a>01647 mode DOUBLE PRECISION, |
| <a name="l01648"></a>01648 upper DOUBLE PRECISION |
| <a name="l01649"></a>01649 ) RETURNS DOUBLE PRECISION |
| <a name="l01650"></a>01650 AS 'MODULE_PATHNAME<span class="stringliteral">'</span> |
| <a name="l01651"></a>01651 <span class="stringliteral">LANGUAGE C</span> |
| <a name="l01652"></a>01652 <span class="stringliteral">IMMUTABLE STRICT;</span> |
| <a name="l01653"></a>01653 <span class="stringliteral"></span><span class="comment"></span> |
| <a name="l01654"></a>01654 <span class="comment">/**</span> |
| <a name="l01655"></a>01655 <span class="comment"> * @brief Triangular quantile function</span> |
| <a name="l01656"></a>01656 <span class="comment"> *</span> |
| <a name="l01657"></a>01657 <span class="comment"> * @param p Probability \f$ p \in [0,1] \f$</span> |
| <a name="l01658"></a>01658 <span class="comment"> * @param lower Lower bound \f$ a \f$</span> |
| <a name="l01659"></a>01659 <span class="comment"> * @param mode Mode \f$ c \geq a \f$</span> |
| <a name="l01660"></a>01660 <span class="comment"> * @param upper Upper bound \f$ b \geq c \f$, where \f$ b > a \f$</span> |
| <a name="l01661"></a>01661 <span class="comment"> * @return \f$ x \f$ such that \f$ p = \Pr[X \leq x] \f$ where \f$ X \f$ is a</span> |
| <a name="l01662"></a>01662 <span class="comment"> * trianbular distributed random variable with parameters \f$ a, b, c \f$</span> |
| <a name="l01663"></a>01663 <span class="comment"> */</span> |
| <a name="l01664"></a>01664 CREATE FUNCTION MADLIB_SCHEMA.triangular_quantile( |
| <a name="l01665"></a>01665 p DOUBLE PRECISION, |
| <a name="l01666"></a><a class="code" href="prob_8sql__in.html#a0c511b9748b2f7a21fe56aaf5f66d188">01666</a> lower DOUBLE PRECISION, |
| <a name="l01667"></a>01667 mode DOUBLE PRECISION, |
| <a name="l01668"></a>01668 upper DOUBLE PRECISION |
| <a name="l01669"></a>01669 ) RETURNS DOUBLE PRECISION |
| <a name="l01670"></a>01670 AS 'MODULE_PATHNAME<span class="stringliteral">'</span> |
| <a name="l01671"></a>01671 <span class="stringliteral">LANGUAGE C</span> |
| <a name="l01672"></a>01672 <span class="stringliteral">IMMUTABLE STRICT;</span> |
| <a name="l01673"></a>01673 <span class="stringliteral"></span> |
| <a name="l01674"></a>01674 <span class="stringliteral"></span><span class="comment"></span> |
| <a name="l01675"></a>01675 <span class="comment">/**</span> |
| <a name="l01676"></a>01676 <span class="comment"> * @brief Uniform cumulative distribution function</span> |
| <a name="l01677"></a>01677 <span class="comment"> *</span> |
| <a name="l01678"></a>01678 <span class="comment"> * @param x Random variate \f$ x \f$</span> |
| <a name="l01679"></a>01679 <span class="comment"> * @param lower Lower bound \f$ a \f$</span> |
| <a name="l01680"></a>01680 <span class="comment"> * @param upper Upper bound \f$ b \f$</span> |
| <a name="l01681"></a>01681 <span class="comment"> * @return \f$ \Pr[X \leq x] \f$ where \f$ X \f$ is a uniform distributed random</span> |
| <a name="l01682"></a>01682 <span class="comment"> * variable with support \f$ [a, b] \f$</span> |
| <a name="l01683"></a>01683 <span class="comment"> */</span> |
| <a name="l01684"></a>01684 CREATE FUNCTION MADLIB_SCHEMA.uniform_cdf( |
| <a name="l01685"></a>01685 x DOUBLE PRECISION, |
| <a name="l01686"></a><a class="code" href="prob_8sql__in.html#a4777540ab1b003ff92d484c4bc26af27">01686</a> lower DOUBLE PRECISION, |
| <a name="l01687"></a>01687 upper DOUBLE PRECISION |
| <a name="l01688"></a>01688 ) RETURNS DOUBLE PRECISION |
| <a name="l01689"></a>01689 AS 'MODULE_PATHNAME<span class="stringliteral">'</span> |
| <a name="l01690"></a>01690 <span class="stringliteral">LANGUAGE C</span> |
| <a name="l01691"></a>01691 <span class="stringliteral">IMMUTABLE STRICT;</span> |
| <a name="l01692"></a>01692 <span class="stringliteral"></span><span class="comment"></span> |
| <a name="l01693"></a>01693 <span class="comment">/**</span> |
| <a name="l01694"></a>01694 <span class="comment"> * @brief Uniform probability density function</span> |
| <a name="l01695"></a>01695 <span class="comment"> *</span> |
| <a name="l01696"></a>01696 <span class="comment"> * @param x Random variate \f$ x \f$</span> |
| <a name="l01697"></a>01697 <span class="comment"> * @param lower Lower bound \f$ a \f$</span> |
| <a name="l01698"></a>01698 <span class="comment"> * @param upper Upper bound \f$ b \f$</span> |
| <a name="l01699"></a>01699 <span class="comment"> * @return \f$ f(x) \f$ where \f$ f \f$ is the probability density function of</span> |
| <a name="l01700"></a>01700 <span class="comment"> * a uniform distributed random variable with support \f$ [a, b] \f$</span> |
| <a name="l01701"></a>01701 <span class="comment"> */</span> |
| <a name="l01702"></a>01702 CREATE FUNCTION MADLIB_SCHEMA.uniform_pdf( |
| <a name="l01703"></a>01703 x DOUBLE PRECISION, |
| <a name="l01704"></a>01704 lower DOUBLE PRECISION, |
| <a name="l01705"></a>01705 upper DOUBLE PRECISION |
| <a name="l01706"></a><a class="code" href="prob_8sql__in.html#aa3a05f4f2e0ef9eb65e828261ecfbed9">01706</a> ) RETURNS DOUBLE PRECISION |
| <a name="l01707"></a>01707 AS 'MODULE_PATHNAME<span class="stringliteral">'</span> |
| <a name="l01708"></a>01708 <span class="stringliteral">LANGUAGE C</span> |
| <a name="l01709"></a>01709 <span class="stringliteral">IMMUTABLE STRICT;</span> |
| <a name="l01710"></a>01710 <span class="stringliteral"></span><span class="comment"></span> |
| <a name="l01711"></a>01711 <span class="comment">/**</span> |
| <a name="l01712"></a>01712 <span class="comment"> * @brief Uniform quantile function</span> |
| <a name="l01713"></a>01713 <span class="comment"> *</span> |
| <a name="l01714"></a>01714 <span class="comment"> * @param p Probability \f$ p \in [0,1] \f$</span> |
| <a name="l01715"></a>01715 <span class="comment"> * @param lower Lower bound \f$ a \f$</span> |
| <a name="l01716"></a>01716 <span class="comment"> * @param upper Upper bound \f$ b \f$</span> |
| <a name="l01717"></a>01717 <span class="comment"> * @return \f$ x \f$ such that \f$ p = \Pr[X \leq x] \f$ where \f$ X \f$ is a</span> |
| <a name="l01718"></a>01718 <span class="comment"> * uniform distributed random variable with support \f$ [a, b] \f$</span> |
| <a name="l01719"></a>01719 <span class="comment"> */</span> |
| <a name="l01720"></a>01720 CREATE FUNCTION MADLIB_SCHEMA.uniform_quantile( |
| <a name="l01721"></a>01721 p DOUBLE PRECISION, |
| <a name="l01722"></a>01722 lower DOUBLE PRECISION, |
| <a name="l01723"></a>01723 upper DOUBLE PRECISION |
| <a name="l01724"></a><a class="code" href="prob_8sql__in.html#ab90fa34d90a9c75747a34c3f210df239">01724</a> ) RETURNS DOUBLE PRECISION |
| <a name="l01725"></a>01725 AS 'MODULE_PATHNAME<span class="stringliteral">'</span> |
| <a name="l01726"></a>01726 <span class="stringliteral">LANGUAGE C</span> |
| <a name="l01727"></a>01727 <span class="stringliteral">IMMUTABLE STRICT;</span> |
| <a name="l01728"></a>01728 <span class="stringliteral"></span> |
| <a name="l01729"></a>01729 <span class="stringliteral"></span><span class="comment"></span> |
| <a name="l01730"></a>01730 <span class="comment">/**</span> |
| <a name="l01731"></a>01731 <span class="comment"> * @brief Weibull cumulative distribution function</span> |
| <a name="l01732"></a>01732 <span class="comment"> *</span> |
| <a name="l01733"></a>01733 <span class="comment"> * @param x Random variate \f$ x \f$</span> |
| <a name="l01734"></a>01734 <span class="comment"> * @param shape Shape \f$ \alpha > 0 \f$</span> |
| <a name="l01735"></a>01735 <span class="comment"> * @param scale Scale \f$ \beta > 0 \f$</span> |
| <a name="l01736"></a>01736 <span class="comment"> * @return \f$ \Pr[X \leq x] \f$ where \f$ X \f$ is a weibull distributed random</span> |
| <a name="l01737"></a>01737 <span class="comment"> * variable with shape and scale parameters \f$ \alpha \f$ and</span> |
| <a name="l01738"></a>01738 <span class="comment"> * \f$ \beta \f$, respectively</span> |
| <a name="l01739"></a>01739 <span class="comment"> */</span> |
| <a name="l01740"></a>01740 CREATE FUNCTION MADLIB_SCHEMA.weibull_cdf( |
| <a name="l01741"></a>01741 x DOUBLE PRECISION, |
| <a name="l01742"></a><a class="code" href="prob_8sql__in.html#a629587a0fdefb588d28b15517ae5cc04">01742</a> shape DOUBLE PRECISION, |
| <a name="l01743"></a>01743 scale DOUBLE PRECISION |
| <a name="l01744"></a>01744 ) RETURNS DOUBLE PRECISION |
| <a name="l01745"></a>01745 AS 'MODULE_PATHNAME<span class="stringliteral">'</span> |
| <a name="l01746"></a>01746 <span class="stringliteral">LANGUAGE C</span> |
| <a name="l01747"></a>01747 <span class="stringliteral">IMMUTABLE STRICT;</span> |
| <a name="l01748"></a>01748 <span class="stringliteral"></span><span class="comment"></span> |
| <a name="l01749"></a>01749 <span class="comment">/**</span> |
| <a name="l01750"></a>01750 <span class="comment"> * @brief Weibull probability density function</span> |
| <a name="l01751"></a>01751 <span class="comment"> *</span> |
| <a name="l01752"></a>01752 <span class="comment"> * @param x Random variate \f$ x \f$</span> |
| <a name="l01753"></a>01753 <span class="comment"> * @param shape Shape \f$ \alpha > 0 \f$</span> |
| <a name="l01754"></a>01754 <span class="comment"> * @param scale Scale \f$ \beta > 0 \f$</span> |
| <a name="l01755"></a>01755 <span class="comment"> * @return \f$ f(x) \f$ where \f$ f \f$ is the probability density function of</span> |
| <a name="l01756"></a>01756 <span class="comment"> * a weibull distributed random variable with shape and scale parameters</span> |
| <a name="l01757"></a>01757 <span class="comment"> * \f$ \alpha \f$ and \f$ \beta \f$, respectively</span> |
| <a name="l01758"></a>01758 <span class="comment"> */</span> |
| <a name="l01759"></a>01759 CREATE FUNCTION MADLIB_SCHEMA.weibull_pdf( |
| <a name="l01760"></a>01760 x DOUBLE PRECISION, |
| <a name="l01761"></a>01761 shape DOUBLE PRECISION, |
| <a name="l01762"></a><a class="code" href="prob_8sql__in.html#a50e4a1883588cd7a4c1ff1017399e4af">01762</a> scale DOUBLE PRECISION |
| <a name="l01763"></a>01763 ) RETURNS DOUBLE PRECISION |
| <a name="l01764"></a>01764 AS 'MODULE_PATHNAME<span class="stringliteral">'</span> |
| <a name="l01765"></a>01765 <span class="stringliteral">LANGUAGE C</span> |
| <a name="l01766"></a>01766 <span class="stringliteral">IMMUTABLE STRICT;</span> |
| <a name="l01767"></a>01767 <span class="stringliteral"></span><span class="comment"></span> |
| <a name="l01768"></a>01768 <span class="comment">/**</span> |
| <a name="l01769"></a>01769 <span class="comment"> * @brief Weibull quantile function</span> |
| <a name="l01770"></a>01770 <span class="comment"> *</span> |
| <a name="l01771"></a>01771 <span class="comment"> * @param p Probability \f$ p \in [0,1] \f$</span> |
| <a name="l01772"></a>01772 <span class="comment"> * @param shape Shape \f$ \alpha > 0 \f$</span> |
| <a name="l01773"></a>01773 <span class="comment"> * @param scale Scale \f$ \beta > 0 \f$</span> |
| <a name="l01774"></a>01774 <span class="comment"> * @return \f$ x \f$ such that \f$ p = \Pr[X \leq x] \f$ where \f$ X \f$ is a</span> |
| <a name="l01775"></a>01775 <span class="comment"> * weibull distributed random variable with shape and scale parameters</span> |
| <a name="l01776"></a>01776 <span class="comment"> * \f$ \alpha \f$ and \f$ \beta \f$, respectively</span> |
| <a name="l01777"></a>01777 <span class="comment"> */</span> |
| <a name="l01778"></a>01778 CREATE FUNCTION MADLIB_SCHEMA.weibull_quantile( |
| <a name="l01779"></a>01779 p DOUBLE PRECISION, |
| <a name="l01780"></a>01780 shape DOUBLE PRECISION, |
| <a name="l01781"></a><a class="code" href="prob_8sql__in.html#a81a876ae2b8598f060dadb179b9324d2">01781</a> scale DOUBLE PRECISION |
| <a name="l01782"></a>01782 ) RETURNS DOUBLE PRECISION |
| <a name="l01783"></a>01783 AS 'MODULE_PATHNAME<span class="stringliteral">'</span> |
| <a name="l01784"></a>01784 <span class="stringliteral">LANGUAGE C</span> |
| <a name="l01785"></a>01785 <span class="stringliteral">IMMUTABLE STRICT;</span> |
| </pre></div></div> |
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