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| <li class="navelem"><a class="el" href="dir_bdd9a5d540de89e9fe90efdfc6973a4f.html">common</a></li><li class="navelem"><a class="el" href="dir_11fbc4217d50ab21044e5ad6614aede5.html">include</a></li> </ul> |
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| <div class="headertitle"><div class="title">bounds_binomial_proportions.hpp</div></div> |
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| <div class="contents"> |
| <div class="fragment"><div class="line"><a id="l00001" name="l00001"></a><span class="lineno"> 1</span><span class="comment">/*</span></div> |
| <div class="line"><a id="l00002" name="l00002"></a><span class="lineno"> 2</span><span class="comment"> * Licensed to the Apache Software Foundation (ASF) under one</span></div> |
| <div class="line"><a id="l00003" name="l00003"></a><span class="lineno"> 3</span><span class="comment"> * or more contributor license agreements. See the NOTICE file</span></div> |
| <div class="line"><a id="l00004" name="l00004"></a><span class="lineno"> 4</span><span class="comment"> * distributed with this work for additional information</span></div> |
| <div class="line"><a id="l00005" name="l00005"></a><span class="lineno"> 5</span><span class="comment"> * regarding copyright ownership. The ASF licenses this file</span></div> |
| <div class="line"><a id="l00006" name="l00006"></a><span class="lineno"> 6</span><span class="comment"> * to you under the Apache License, Version 2.0 (the</span></div> |
| <div class="line"><a id="l00007" name="l00007"></a><span class="lineno"> 7</span><span class="comment"> * "License"); you may not use this file except in compliance</span></div> |
| <div class="line"><a id="l00008" name="l00008"></a><span class="lineno"> 8</span><span class="comment"> * with the License. You may obtain a copy of the License at</span></div> |
| <div class="line"><a id="l00009" name="l00009"></a><span class="lineno"> 9</span><span class="comment"> *</span></div> |
| <div class="line"><a id="l00010" name="l00010"></a><span class="lineno"> 10</span><span class="comment"> * http://www.apache.org/licenses/LICENSE-2.0</span></div> |
| <div class="line"><a id="l00011" name="l00011"></a><span class="lineno"> 11</span><span class="comment"> *</span></div> |
| <div class="line"><a id="l00012" name="l00012"></a><span class="lineno"> 12</span><span class="comment"> * Unless required by applicable law or agreed to in writing,</span></div> |
| <div class="line"><a id="l00013" name="l00013"></a><span class="lineno"> 13</span><span class="comment"> * software distributed under the License is distributed on an</span></div> |
| <div class="line"><a id="l00014" name="l00014"></a><span class="lineno"> 14</span><span class="comment"> * "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY</span></div> |
| <div class="line"><a id="l00015" name="l00015"></a><span class="lineno"> 15</span><span class="comment"> * KIND, either express or implied. See the License for the</span></div> |
| <div class="line"><a id="l00016" name="l00016"></a><span class="lineno"> 16</span><span class="comment"> * specific language governing permissions and limitations</span></div> |
| <div class="line"><a id="l00017" name="l00017"></a><span class="lineno"> 17</span><span class="comment"> * under the License.</span></div> |
| <div class="line"><a id="l00018" name="l00018"></a><span class="lineno"> 18</span><span class="comment"> */</span></div> |
| <div class="line"><a id="l00019" name="l00019"></a><span class="lineno"> 19</span> </div> |
| <div class="line"><a id="l00020" name="l00020"></a><span class="lineno"> 20</span><span class="preprocessor">#ifndef _BOUNDS_BINOMIAL_PROPORTIONS_HPP_</span></div> |
| <div class="line"><a id="l00021" name="l00021"></a><span class="lineno"> 21</span><span class="preprocessor">#define _BOUNDS_BINOMIAL_PROPORTIONS_HPP_</span></div> |
| <div class="line"><a id="l00022" name="l00022"></a><span class="lineno"> 22</span> </div> |
| <div class="line"><a id="l00023" name="l00023"></a><span class="lineno"> 23</span><span class="preprocessor">#include <cmath></span></div> |
| <div class="line"><a id="l00024" name="l00024"></a><span class="lineno"> 24</span><span class="preprocessor">#include <stdexcept></span></div> |
| <div class="line"><a id="l00025" name="l00025"></a><span class="lineno"> 25</span> </div> |
| <div class="line"><a id="l00026" name="l00026"></a><span class="lineno"> 26</span><span class="keyword">namespace </span><a class="code hl_namespace" href="namespacedatasketches.html">datasketches</a> {</div> |
| <div class="line"><a id="l00027" name="l00027"></a><span class="lineno"> 27</span> </div> |
| <div class="foldopen" id="foldopen00081" data-start="{" data-end="};"> |
| <div class="line"><a id="l00081" name="l00081"></a><span class="lineno"><a class="line" href="classdatasketches_1_1bounds__binomial__proportions.html"> 81</a></span><span class="keyword">class </span><a class="code hl_class" href="classdatasketches_1_1bounds__binomial__proportions.html">bounds_binomial_proportions</a> { <span class="comment">// confidence intervals for binomial proportions</span></div> |
| <div class="line"><a id="l00082" name="l00082"></a><span class="lineno"> 82</span> </div> |
| <div class="line"><a id="l00083" name="l00083"></a><span class="lineno"> 83</span><span class="keyword">public</span>:</div> |
| <div class="foldopen" id="foldopen00113" data-start="{" data-end="}"> |
| <div class="line"><a id="l00113" name="l00113"></a><span class="lineno"><a class="line" href="classdatasketches_1_1bounds__binomial__proportions.html#aeaf7a3842e7bc82772b1dc33891f8c50"> 113</a></span> <span class="keyword">static</span> <span class="keyword">inline</span> <span class="keywordtype">double</span> <a class="code hl_function" href="classdatasketches_1_1bounds__binomial__proportions.html#aeaf7a3842e7bc82772b1dc33891f8c50">approximate_lower_bound_on_p</a>(uint64_t n, uint64_t k, <span class="keywordtype">double</span> num_std_devs) {</div> |
| <div class="line"><a id="l00114" name="l00114"></a><span class="lineno"> 114</span> check_inputs(n, k);</div> |
| <div class="line"><a id="l00115" name="l00115"></a><span class="lineno"> 115</span> <span class="keywordflow">if</span> (n == 0) { <span class="keywordflow">return</span> 0.0; } <span class="comment">// the coin was never flipped, so we know nothing</span></div> |
| <div class="line"><a id="l00116" name="l00116"></a><span class="lineno"> 116</span> <span class="keywordflow">else</span> <span class="keywordflow">if</span> (k == 0) { <span class="keywordflow">return</span> 0.0; }</div> |
| <div class="line"><a id="l00117" name="l00117"></a><span class="lineno"> 117</span> <span class="keywordflow">else</span> <span class="keywordflow">if</span> (k == 1) { <span class="keywordflow">return</span> (exact_lower_bound_on_p_k_eq_1(n, delta_of_num_stdevs(num_std_devs))); }</div> |
| <div class="line"><a id="l00118" name="l00118"></a><span class="lineno"> 118</span> <span class="keywordflow">else</span> <span class="keywordflow">if</span> (k == n) { <span class="keywordflow">return</span> (exact_lower_bound_on_p_k_eq_n(n, delta_of_num_stdevs(num_std_devs))); }</div> |
| <div class="line"><a id="l00119" name="l00119"></a><span class="lineno"> 119</span> <span class="keywordflow">else</span> {</div> |
| <div class="line"><a id="l00120" name="l00120"></a><span class="lineno"> 120</span> <span class="keywordtype">double</span> x = abramowitz_stegun_formula_26p5p22((n - k) + 1.0, <span class="keyword">static_cast<</span><span class="keywordtype">double</span><span class="keyword">></span>(k), (-1.0 * num_std_devs));</div> |
| <div class="line"><a id="l00121" name="l00121"></a><span class="lineno"> 121</span> <span class="keywordflow">return</span> (1.0 - x); <span class="comment">// which is p</span></div> |
| <div class="line"><a id="l00122" name="l00122"></a><span class="lineno"> 122</span> }</div> |
| <div class="line"><a id="l00123" name="l00123"></a><span class="lineno"> 123</span> }</div> |
| </div> |
| <div class="line"><a id="l00124" name="l00124"></a><span class="lineno"> 124</span> </div> |
| <div class="foldopen" id="foldopen00148" data-start="{" data-end="}"> |
| <div class="line"><a id="l00148" name="l00148"></a><span class="lineno"><a class="line" href="classdatasketches_1_1bounds__binomial__proportions.html#a497df40100e75dd55e6f0cdccd90b60a"> 148</a></span> <span class="keyword">static</span> <span class="keyword">inline</span> <span class="keywordtype">double</span> <a class="code hl_function" href="classdatasketches_1_1bounds__binomial__proportions.html#a497df40100e75dd55e6f0cdccd90b60a">approximate_upper_bound_on_p</a>(uint64_t n, uint64_t k, <span class="keywordtype">double</span> num_std_devs) {</div> |
| <div class="line"><a id="l00149" name="l00149"></a><span class="lineno"> 149</span> check_inputs(n, k);</div> |
| <div class="line"><a id="l00150" name="l00150"></a><span class="lineno"> 150</span> <span class="keywordflow">if</span> (n == 0) { <span class="keywordflow">return</span> 1.0; } <span class="comment">// the coin was never flipped, so we know nothing</span></div> |
| <div class="line"><a id="l00151" name="l00151"></a><span class="lineno"> 151</span> <span class="keywordflow">else</span> <span class="keywordflow">if</span> (k == n) { <span class="keywordflow">return</span> 1.0; }</div> |
| <div class="line"><a id="l00152" name="l00152"></a><span class="lineno"> 152</span> <span class="keywordflow">else</span> <span class="keywordflow">if</span> (k == (n - 1)) {</div> |
| <div class="line"><a id="l00153" name="l00153"></a><span class="lineno"> 153</span> <span class="keywordflow">return</span> (exact_upper_bound_on_p_k_eq_minusone(n, delta_of_num_stdevs(num_std_devs)));</div> |
| <div class="line"><a id="l00154" name="l00154"></a><span class="lineno"> 154</span> }</div> |
| <div class="line"><a id="l00155" name="l00155"></a><span class="lineno"> 155</span> <span class="keywordflow">else</span> <span class="keywordflow">if</span> (k == 0) {</div> |
| <div class="line"><a id="l00156" name="l00156"></a><span class="lineno"> 156</span> <span class="keywordflow">return</span> (exact_upper_bound_on_p_k_eq_zero(n, delta_of_num_stdevs(num_std_devs)));</div> |
| <div class="line"><a id="l00157" name="l00157"></a><span class="lineno"> 157</span> }</div> |
| <div class="line"><a id="l00158" name="l00158"></a><span class="lineno"> 158</span> <span class="keywordflow">else</span> {</div> |
| <div class="line"><a id="l00159" name="l00159"></a><span class="lineno"> 159</span> <span class="keywordtype">double</span> x = abramowitz_stegun_formula_26p5p22(<span class="keyword">static_cast<</span><span class="keywordtype">double</span><span class="keyword">></span>(n - k), k + 1.0, num_std_devs);</div> |
| <div class="line"><a id="l00160" name="l00160"></a><span class="lineno"> 160</span> <span class="keywordflow">return</span> (1.0 - x); <span class="comment">// which is p</span></div> |
| <div class="line"><a id="l00161" name="l00161"></a><span class="lineno"> 161</span> }</div> |
| <div class="line"><a id="l00162" name="l00162"></a><span class="lineno"> 162</span> }</div> |
| </div> |
| <div class="line"><a id="l00163" name="l00163"></a><span class="lineno"> 163</span> </div> |
| <div class="foldopen" id="foldopen00170" data-start="{" data-end="}"> |
| <div class="line"><a id="l00170" name="l00170"></a><span class="lineno"><a class="line" href="classdatasketches_1_1bounds__binomial__proportions.html#a04e345ceea6646f2789a4fc8868c470d"> 170</a></span> <span class="keyword">static</span> <span class="keyword">inline</span> <span class="keywordtype">double</span> <a class="code hl_function" href="classdatasketches_1_1bounds__binomial__proportions.html#a04e345ceea6646f2789a4fc8868c470d">estimate_unknown_p</a>(uint64_t n, uint64_t k) {</div> |
| <div class="line"><a id="l00171" name="l00171"></a><span class="lineno"> 171</span> check_inputs(n, k);</div> |
| <div class="line"><a id="l00172" name="l00172"></a><span class="lineno"> 172</span> <span class="keywordflow">if</span> (n == 0) { <span class="keywordflow">return</span> 0.5; } <span class="comment">// the coin was never flipped, so we know nothing</span></div> |
| <div class="line"><a id="l00173" name="l00173"></a><span class="lineno"> 173</span> <span class="keywordflow">else</span> { <span class="keywordflow">return</span> ((<span class="keywordtype">double</span>) k / (<span class="keywordtype">double</span>) n); }</div> |
| <div class="line"><a id="l00174" name="l00174"></a><span class="lineno"> 174</span> }</div> |
| </div> |
| <div class="line"><a id="l00175" name="l00175"></a><span class="lineno"> 175</span> </div> |
| <div class="foldopen" id="foldopen00181" data-start="{" data-end="}"> |
| <div class="line"><a id="l00181" name="l00181"></a><span class="lineno"><a class="line" href="classdatasketches_1_1bounds__binomial__proportions.html#ab0c083907bbd0cf5c9532f7c094ae6ef"> 181</a></span> <span class="keyword">static</span> <span class="keyword">inline</span> <span class="keywordtype">double</span> <a class="code hl_function" href="classdatasketches_1_1bounds__binomial__proportions.html#ab0c083907bbd0cf5c9532f7c094ae6ef">erf</a>(<span class="keywordtype">double</span> x) {</div> |
| <div class="line"><a id="l00182" name="l00182"></a><span class="lineno"> 182</span> <span class="keywordflow">if</span> (x < 0.0) { <span class="keywordflow">return</span> (-1.0 * (erf_of_nonneg(-1.0 * x))); }</div> |
| <div class="line"><a id="l00183" name="l00183"></a><span class="lineno"> 183</span> <span class="keywordflow">else</span> { <span class="keywordflow">return</span> (erf_of_nonneg(x)); }</div> |
| <div class="line"><a id="l00184" name="l00184"></a><span class="lineno"> 184</span> }</div> |
| </div> |
| <div class="line"><a id="l00185" name="l00185"></a><span class="lineno"> 185</span> </div> |
| <div class="foldopen" id="foldopen00191" data-start="{" data-end="}"> |
| <div class="line"><a id="l00191" name="l00191"></a><span class="lineno"><a class="line" href="classdatasketches_1_1bounds__binomial__proportions.html#a842aac311b818d8b074f8d1c344b903a"> 191</a></span> <span class="keyword">static</span> <span class="keyword">inline</span> <span class="keywordtype">double</span> <a class="code hl_function" href="classdatasketches_1_1bounds__binomial__proportions.html#a842aac311b818d8b074f8d1c344b903a">normal_cdf</a>(<span class="keywordtype">double</span> x) {</div> |
| <div class="line"><a id="l00192" name="l00192"></a><span class="lineno"> 192</span> <span class="keywordflow">return</span> (0.5 * (1.0 + (<a class="code hl_function" href="classdatasketches_1_1bounds__binomial__proportions.html#ab0c083907bbd0cf5c9532f7c094ae6ef">erf</a>(x / (sqrt(2.0))))));</div> |
| <div class="line"><a id="l00193" name="l00193"></a><span class="lineno"> 193</span> }</div> |
| </div> |
| <div class="line"><a id="l00194" name="l00194"></a><span class="lineno"> 194</span> </div> |
| <div class="line"><a id="l00195" name="l00195"></a><span class="lineno"> 195</span><span class="keyword">private</span>:</div> |
| <div class="line"><a id="l00196" name="l00196"></a><span class="lineno"> 196</span> <span class="keyword">static</span> <span class="keyword">inline</span> <span class="keywordtype">void</span> check_inputs(uint64_t n, uint64_t k) {</div> |
| <div class="line"><a id="l00197" name="l00197"></a><span class="lineno"> 197</span> <span class="keywordflow">if</span> (k > n) { <span class="keywordflow">throw</span> std::invalid_argument(<span class="stringliteral">"K cannot exceed N"</span>); }</div> |
| <div class="line"><a id="l00198" name="l00198"></a><span class="lineno"> 198</span> }</div> |
| <div class="line"><a id="l00199" name="l00199"></a><span class="lineno"> 199</span> </div> |
| <div class="line"><a id="l00200" name="l00200"></a><span class="lineno"> 200</span> <span class="comment">//@formatter:off</span></div> |
| <div class="line"><a id="l00201" name="l00201"></a><span class="lineno"> 201</span> <span class="comment">// Abramowitz and Stegun formula 7.1.28, p. 88; Claims accuracy of about 7 decimal digits */</span></div> |
| <div class="line"><a id="l00202" name="l00202"></a><span class="lineno"> 202</span> <span class="keyword">static</span> <span class="keyword">inline</span> <span class="keywordtype">double</span> erf_of_nonneg(<span class="keywordtype">double</span> x) {</div> |
| <div class="line"><a id="l00203" name="l00203"></a><span class="lineno"> 203</span> <span class="comment">// The constants that appear below, formatted for easy checking against the book.</span></div> |
| <div class="line"><a id="l00204" name="l00204"></a><span class="lineno"> 204</span> <span class="comment">// a1 = 0.07052 30784</span></div> |
| <div class="line"><a id="l00205" name="l00205"></a><span class="lineno"> 205</span> <span class="comment">// a3 = 0.00927 05272</span></div> |
| <div class="line"><a id="l00206" name="l00206"></a><span class="lineno"> 206</span> <span class="comment">// a5 = 0.00027 65672</span></div> |
| <div class="line"><a id="l00207" name="l00207"></a><span class="lineno"> 207</span> <span class="comment">// a2 = 0.04228 20123</span></div> |
| <div class="line"><a id="l00208" name="l00208"></a><span class="lineno"> 208</span> <span class="comment">// a4 = 0.00015 20143</span></div> |
| <div class="line"><a id="l00209" name="l00209"></a><span class="lineno"> 209</span> <span class="comment">// a6 = 0.00004 30638</span></div> |
| <div class="line"><a id="l00210" name="l00210"></a><span class="lineno"> 210</span> <span class="keyword">static</span> <span class="keyword">const</span> <span class="keywordtype">double</span> a1 = 0.0705230784;</div> |
| <div class="line"><a id="l00211" name="l00211"></a><span class="lineno"> 211</span> <span class="keyword">static</span> <span class="keyword">const</span> <span class="keywordtype">double</span> a3 = 0.0092705272;</div> |
| <div class="line"><a id="l00212" name="l00212"></a><span class="lineno"> 212</span> <span class="keyword">static</span> <span class="keyword">const</span> <span class="keywordtype">double</span> a5 = 0.0002765672;</div> |
| <div class="line"><a id="l00213" name="l00213"></a><span class="lineno"> 213</span> <span class="keyword">static</span> <span class="keyword">const</span> <span class="keywordtype">double</span> a2 = 0.0422820123;</div> |
| <div class="line"><a id="l00214" name="l00214"></a><span class="lineno"> 214</span> <span class="keyword">static</span> <span class="keyword">const</span> <span class="keywordtype">double</span> a4 = 0.0001520143;</div> |
| <div class="line"><a id="l00215" name="l00215"></a><span class="lineno"> 215</span> <span class="keyword">static</span> <span class="keyword">const</span> <span class="keywordtype">double</span> a6 = 0.0000430638;</div> |
| <div class="line"><a id="l00216" name="l00216"></a><span class="lineno"> 216</span> <span class="keyword">const</span> <span class="keywordtype">double</span> x2 = x * x; <span class="comment">// x squared, x cubed, etc.</span></div> |
| <div class="line"><a id="l00217" name="l00217"></a><span class="lineno"> 217</span> <span class="keyword">const</span> <span class="keywordtype">double</span> x3 = x2 * x;</div> |
| <div class="line"><a id="l00218" name="l00218"></a><span class="lineno"> 218</span> <span class="keyword">const</span> <span class="keywordtype">double</span> x4 = x2 * x2;</div> |
| <div class="line"><a id="l00219" name="l00219"></a><span class="lineno"> 219</span> <span class="keyword">const</span> <span class="keywordtype">double</span> x5 = x2 * x3;</div> |
| <div class="line"><a id="l00220" name="l00220"></a><span class="lineno"> 220</span> <span class="keyword">const</span> <span class="keywordtype">double</span> x6 = x3 * x3;</div> |
| <div class="line"><a id="l00221" name="l00221"></a><span class="lineno"> 221</span> <span class="keyword">const</span> <span class="keywordtype">double</span> sum = ( 1.0</div> |
| <div class="line"><a id="l00222" name="l00222"></a><span class="lineno"> 222</span> + (a1 * x)</div> |
| <div class="line"><a id="l00223" name="l00223"></a><span class="lineno"> 223</span> + (a2 * x2)</div> |
| <div class="line"><a id="l00224" name="l00224"></a><span class="lineno"> 224</span> + (a3 * x3)</div> |
| <div class="line"><a id="l00225" name="l00225"></a><span class="lineno"> 225</span> + (a4 * x4)</div> |
| <div class="line"><a id="l00226" name="l00226"></a><span class="lineno"> 226</span> + (a5 * x5)</div> |
| <div class="line"><a id="l00227" name="l00227"></a><span class="lineno"> 227</span> + (a6 * x6) );</div> |
| <div class="line"><a id="l00228" name="l00228"></a><span class="lineno"> 228</span> <span class="keyword">const</span> <span class="keywordtype">double</span> sum2 = sum * sum; <span class="comment">// raise the sum to the 16th power</span></div> |
| <div class="line"><a id="l00229" name="l00229"></a><span class="lineno"> 229</span> <span class="keyword">const</span> <span class="keywordtype">double</span> sum4 = sum2 * sum2;</div> |
| <div class="line"><a id="l00230" name="l00230"></a><span class="lineno"> 230</span> <span class="keyword">const</span> <span class="keywordtype">double</span> sum8 = sum4 * sum4;</div> |
| <div class="line"><a id="l00231" name="l00231"></a><span class="lineno"> 231</span> <span class="keyword">const</span> <span class="keywordtype">double</span> sum16 = sum8 * sum8;</div> |
| <div class="line"><a id="l00232" name="l00232"></a><span class="lineno"> 232</span> <span class="keywordflow">return</span> (1.0 - (1.0 / sum16));</div> |
| <div class="line"><a id="l00233" name="l00233"></a><span class="lineno"> 233</span> }</div> |
| <div class="line"><a id="l00234" name="l00234"></a><span class="lineno"> 234</span> </div> |
| <div class="line"><a id="l00235" name="l00235"></a><span class="lineno"> 235</span> <span class="keyword">static</span> <span class="keyword">inline</span> <span class="keywordtype">double</span> delta_of_num_stdevs(<span class="keywordtype">double</span> kappa) {</div> |
| <div class="line"><a id="l00236" name="l00236"></a><span class="lineno"> 236</span> <span class="keywordflow">return</span> (<a class="code hl_function" href="classdatasketches_1_1bounds__binomial__proportions.html#a842aac311b818d8b074f8d1c344b903a">normal_cdf</a>(-1.0 * kappa));</div> |
| <div class="line"><a id="l00237" name="l00237"></a><span class="lineno"> 237</span> }</div> |
| <div class="line"><a id="l00238" name="l00238"></a><span class="lineno"> 238</span> </div> |
| <div class="line"><a id="l00239" name="l00239"></a><span class="lineno"> 239</span> <span class="comment">//@formatter:on</span></div> |
| <div class="line"><a id="l00240" name="l00240"></a><span class="lineno"> 240</span> <span class="comment">// Formula 26.5.22 on page 945 of Abramowitz & Stegun, which is an approximation</span></div> |
| <div class="line"><a id="l00241" name="l00241"></a><span class="lineno"> 241</span> <span class="comment">// of the inverse of the incomplete beta function I_x(a,b) = delta</span></div> |
| <div class="line"><a id="l00242" name="l00242"></a><span class="lineno"> 242</span> <span class="comment">// viewed as a scalar function of x.</span></div> |
| <div class="line"><a id="l00243" name="l00243"></a><span class="lineno"> 243</span> <span class="comment">// In other words, we specify delta, and it gives us x (with a and b held constant).</span></div> |
| <div class="line"><a id="l00244" name="l00244"></a><span class="lineno"> 244</span> <span class="comment">// However, delta is specified in an indirect way through yp which</span></div> |
| <div class="line"><a id="l00245" name="l00245"></a><span class="lineno"> 245</span> <span class="comment">// is the number of stdDevs that leaves delta probability in the right</span></div> |
| <div class="line"><a id="l00246" name="l00246"></a><span class="lineno"> 246</span> <span class="comment">// tail of a standard gaussian distribution.</span></div> |
| <div class="line"><a id="l00247" name="l00247"></a><span class="lineno"> 247</span> </div> |
| <div class="line"><a id="l00248" name="l00248"></a><span class="lineno"> 248</span> <span class="comment">// We point out that the variable names correspond to those in the book,</span></div> |
| <div class="line"><a id="l00249" name="l00249"></a><span class="lineno"> 249</span> <span class="comment">// and it is worth keeping it that way so that it will always be easy to verify</span></div> |
| <div class="line"><a id="l00250" name="l00250"></a><span class="lineno"> 250</span> <span class="comment">// that the formula was typed in correctly.</span></div> |
| <div class="line"><a id="l00251" name="l00251"></a><span class="lineno"> 251</span> </div> |
| <div class="line"><a id="l00252" name="l00252"></a><span class="lineno"> 252</span> <span class="keyword">static</span> <span class="keyword">inline</span> <span class="keywordtype">double</span> abramowitz_stegun_formula_26p5p22(<span class="keywordtype">double</span> a, <span class="keywordtype">double</span> b, <span class="keywordtype">double</span> yp) {</div> |
| <div class="line"><a id="l00253" name="l00253"></a><span class="lineno"> 253</span> <span class="keyword">const</span> <span class="keywordtype">double</span> b2m1 = (2.0 * b) - 1.0;</div> |
| <div class="line"><a id="l00254" name="l00254"></a><span class="lineno"> 254</span> <span class="keyword">const</span> <span class="keywordtype">double</span> a2m1 = (2.0 * a) - 1.0;</div> |
| <div class="line"><a id="l00255" name="l00255"></a><span class="lineno"> 255</span> <span class="keyword">const</span> <span class="keywordtype">double</span> lambda = ((yp * yp) - 3.0) / 6.0;</div> |
| <div class="line"><a id="l00256" name="l00256"></a><span class="lineno"> 256</span> <span class="keyword">const</span> <span class="keywordtype">double</span> htmp = (1.0 / a2m1) + (1.0 / b2m1);</div> |
| <div class="line"><a id="l00257" name="l00257"></a><span class="lineno"> 257</span> <span class="keyword">const</span> <span class="keywordtype">double</span> h = 2.0 / htmp;</div> |
| <div class="line"><a id="l00258" name="l00258"></a><span class="lineno"> 258</span> <span class="keyword">const</span> <span class="keywordtype">double</span> term1 = (yp * (sqrt(h + lambda))) / h;</div> |
| <div class="line"><a id="l00259" name="l00259"></a><span class="lineno"> 259</span> <span class="keyword">const</span> <span class="keywordtype">double</span> term2 = (1.0 / b2m1) - (1.0 / a2m1);</div> |
| <div class="line"><a id="l00260" name="l00260"></a><span class="lineno"> 260</span> <span class="keyword">const</span> <span class="keywordtype">double</span> term3 = (lambda + (5.0 / 6.0)) - (2.0 / (3.0 * h));</div> |
| <div class="line"><a id="l00261" name="l00261"></a><span class="lineno"> 261</span> <span class="keyword">const</span> <span class="keywordtype">double</span> w = term1 - (term2 * term3);</div> |
| <div class="line"><a id="l00262" name="l00262"></a><span class="lineno"> 262</span> <span class="keyword">const</span> <span class="keywordtype">double</span> xp = a / (a + (b * (exp(2.0 * w))));</div> |
| <div class="line"><a id="l00263" name="l00263"></a><span class="lineno"> 263</span> <span class="keywordflow">return</span> xp;</div> |
| <div class="line"><a id="l00264" name="l00264"></a><span class="lineno"> 264</span> }</div> |
| <div class="line"><a id="l00265" name="l00265"></a><span class="lineno"> 265</span> </div> |
| <div class="line"><a id="l00266" name="l00266"></a><span class="lineno"> 266</span> <span class="comment">// Formulas for some special cases.</span></div> |
| <div class="line"><a id="l00267" name="l00267"></a><span class="lineno"> 267</span> </div> |
| <div class="line"><a id="l00268" name="l00268"></a><span class="lineno"> 268</span> <span class="keyword">static</span> <span class="keyword">inline</span> <span class="keywordtype">double</span> exact_upper_bound_on_p_k_eq_zero(uint64_t n, <span class="keywordtype">double</span> delta) {</div> |
| <div class="line"><a id="l00269" name="l00269"></a><span class="lineno"> 269</span> <span class="keywordflow">return</span> (1.0 - pow(delta, (1.0 / n)));</div> |
| <div class="line"><a id="l00270" name="l00270"></a><span class="lineno"> 270</span> }</div> |
| <div class="line"><a id="l00271" name="l00271"></a><span class="lineno"> 271</span> </div> |
| <div class="line"><a id="l00272" name="l00272"></a><span class="lineno"> 272</span> <span class="keyword">static</span> <span class="keyword">inline</span> <span class="keywordtype">double</span> exact_lower_bound_on_p_k_eq_n(uint64_t n, <span class="keywordtype">double</span> delta) {</div> |
| <div class="line"><a id="l00273" name="l00273"></a><span class="lineno"> 273</span> <span class="keywordflow">return</span> (pow(delta, (1.0 / n)));</div> |
| <div class="line"><a id="l00274" name="l00274"></a><span class="lineno"> 274</span> }</div> |
| <div class="line"><a id="l00275" name="l00275"></a><span class="lineno"> 275</span> </div> |
| <div class="line"><a id="l00276" name="l00276"></a><span class="lineno"> 276</span> <span class="keyword">static</span> <span class="keyword">inline</span> <span class="keywordtype">double</span> exact_lower_bound_on_p_k_eq_1(uint64_t n, <span class="keywordtype">double</span> delta) {</div> |
| <div class="line"><a id="l00277" name="l00277"></a><span class="lineno"> 277</span> <span class="keywordflow">return</span> (1.0 - pow((1.0 - delta), (1.0 / n)));</div> |
| <div class="line"><a id="l00278" name="l00278"></a><span class="lineno"> 278</span> }</div> |
| <div class="line"><a id="l00279" name="l00279"></a><span class="lineno"> 279</span> </div> |
| <div class="line"><a id="l00280" name="l00280"></a><span class="lineno"> 280</span> <span class="keyword">static</span> <span class="keyword">inline</span> <span class="keywordtype">double</span> exact_upper_bound_on_p_k_eq_minusone(uint64_t n, <span class="keywordtype">double</span> delta) {</div> |
| <div class="line"><a id="l00281" name="l00281"></a><span class="lineno"> 281</span> <span class="keywordflow">return</span> (pow((1.0 - delta), (1.0 / n)));</div> |
| <div class="line"><a id="l00282" name="l00282"></a><span class="lineno"> 282</span> }</div> |
| <div class="line"><a id="l00283" name="l00283"></a><span class="lineno"> 283</span> </div> |
| <div class="line"><a id="l00284" name="l00284"></a><span class="lineno"> 284</span>};</div> |
| </div> |
| <div class="line"><a id="l00285" name="l00285"></a><span class="lineno"> 285</span> </div> |
| <div class="line"><a id="l00286" name="l00286"></a><span class="lineno"> 286</span>}</div> |
| <div class="line"><a id="l00287" name="l00287"></a><span class="lineno"> 287</span> </div> |
| <div class="line"><a id="l00288" name="l00288"></a><span class="lineno"> 288</span><span class="preprocessor">#endif </span><span class="comment">// _BOUNDS_BINOMIAL_PROPORTIONS_HPP_</span></div> |
| <div class="ttc" id="aclassdatasketches_1_1bounds__binomial__proportions_html"><div class="ttname"><a href="classdatasketches_1_1bounds__binomial__proportions.html">datasketches::bounds_binomial_proportions</a></div><div class="ttdoc">Confidence intervals for binomial proportions.</div><div class="ttdef"><b>Definition</b> bounds_binomial_proportions.hpp:81</div></div> |
| <div class="ttc" id="aclassdatasketches_1_1bounds__binomial__proportions_html_a04e345ceea6646f2789a4fc8868c470d"><div class="ttname"><a href="classdatasketches_1_1bounds__binomial__proportions.html#a04e345ceea6646f2789a4fc8868c470d">datasketches::bounds_binomial_proportions::estimate_unknown_p</a></div><div class="ttdeci">static double estimate_unknown_p(uint64_t n, uint64_t k)</div><div class="ttdoc">Computes an estimate of an unknown binomial proportion.</div><div class="ttdef"><b>Definition</b> bounds_binomial_proportions.hpp:170</div></div> |
| <div class="ttc" id="aclassdatasketches_1_1bounds__binomial__proportions_html_a497df40100e75dd55e6f0cdccd90b60a"><div class="ttname"><a href="classdatasketches_1_1bounds__binomial__proportions.html#a497df40100e75dd55e6f0cdccd90b60a">datasketches::bounds_binomial_proportions::approximate_upper_bound_on_p</a></div><div class="ttdeci">static double approximate_upper_bound_on_p(uint64_t n, uint64_t k, double num_std_devs)</div><div class="ttdoc">Computes upper bound of approximate Clopper-Pearson confidence interval for a binomial proportion.</div><div class="ttdef"><b>Definition</b> bounds_binomial_proportions.hpp:148</div></div> |
| <div class="ttc" id="aclassdatasketches_1_1bounds__binomial__proportions_html_a842aac311b818d8b074f8d1c344b903a"><div class="ttname"><a href="classdatasketches_1_1bounds__binomial__proportions.html#a842aac311b818d8b074f8d1c344b903a">datasketches::bounds_binomial_proportions::normal_cdf</a></div><div class="ttdeci">static double normal_cdf(double x)</div><div class="ttdoc">Computes an approximation to normal_cdf(x).</div><div class="ttdef"><b>Definition</b> bounds_binomial_proportions.hpp:191</div></div> |
| <div class="ttc" id="aclassdatasketches_1_1bounds__binomial__proportions_html_ab0c083907bbd0cf5c9532f7c094ae6ef"><div class="ttname"><a href="classdatasketches_1_1bounds__binomial__proportions.html#ab0c083907bbd0cf5c9532f7c094ae6ef">datasketches::bounds_binomial_proportions::erf</a></div><div class="ttdeci">static double erf(double x)</div><div class="ttdoc">Computes an approximation to the erf() function.</div><div class="ttdef"><b>Definition</b> bounds_binomial_proportions.hpp:181</div></div> |
| <div class="ttc" id="aclassdatasketches_1_1bounds__binomial__proportions_html_aeaf7a3842e7bc82772b1dc33891f8c50"><div class="ttname"><a href="classdatasketches_1_1bounds__binomial__proportions.html#aeaf7a3842e7bc82772b1dc33891f8c50">datasketches::bounds_binomial_proportions::approximate_lower_bound_on_p</a></div><div class="ttdeci">static double approximate_lower_bound_on_p(uint64_t n, uint64_t k, double num_std_devs)</div><div class="ttdoc">Computes lower bound of approximate Clopper-Pearson confidence interval for a binomial proportion.</div><div class="ttdef"><b>Definition</b> bounds_binomial_proportions.hpp:113</div></div> |
| <div class="ttc" id="anamespacedatasketches_html"><div class="ttname"><a href="namespacedatasketches.html">datasketches</a></div><div class="ttdoc">DataSketches namespace.</div><div class="ttdef"><b>Definition</b> binomial_bounds.hpp:38</div></div> |
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