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Added: dev/commons/statistics/1.0-RC1/site/xref/org/apache/commons/statistics/distribution/GeometricDistribution.html
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--- dev/commons/statistics/1.0-RC1/site/xref/org/apache/commons/statistics/distribution/GeometricDistribution.html (added)
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+<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd">
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+<head><meta http-equiv="content-type" content="text/html; charset=UTF-8" />
+<title>GeometricDistribution xref</title>
+<link type="text/css" rel="stylesheet" href="../../../../../stylesheet.css" />
+</head>
+<body>
+<div id="overview"><a href="../../../../../../apidocs/org/apache/commons/statistics/distribution/GeometricDistribution.html">View Javadoc</a></div><pre>
+<a class="jxr_linenumber" name="L1" href="#L1">1</a> <em class="jxr_comment">/*</em>
+<a class="jxr_linenumber" name="L2" href="#L2">2</a> <em class="jxr_comment"> * Licensed to the Apache Software Foundation (ASF) under one or more</em>
+<a class="jxr_linenumber" name="L3" href="#L3">3</a> <em class="jxr_comment"> * contributor license agreements. See the NOTICE file distributed with</em>
+<a class="jxr_linenumber" name="L4" href="#L4">4</a> <em class="jxr_comment"> * this work for additional information regarding copyright ownership.</em>
+<a class="jxr_linenumber" name="L5" href="#L5">5</a> <em class="jxr_comment"> * The ASF licenses this file to You under the Apache License, Version 2.0</em>
+<a class="jxr_linenumber" name="L6" href="#L6">6</a> <em class="jxr_comment"> * (the "License"); you may not use this file except in compliance with</em>
+<a class="jxr_linenumber" name="L7" href="#L7">7</a> <em class="jxr_comment"> * the License. You may obtain a copy of the License at</em>
+<a class="jxr_linenumber" name="L8" href="#L8">8</a> <em class="jxr_comment"> *</em>
+<a class="jxr_linenumber" name="L9" href="#L9">9</a> <em class="jxr_comment"> * <a href="http://www.apache.org/licenses/LICENSE-2.0" target="alexandria_uri">http://www.apache.org/licenses/LICENSE-2.0</a></em>
+<a class="jxr_linenumber" name="L10" href="#L10">10</a> <em class="jxr_comment"> *</em>
+<a class="jxr_linenumber" name="L11" href="#L11">11</a> <em class="jxr_comment"> * Unless required by applicable law or agreed to in writing, software</em>
+<a class="jxr_linenumber" name="L12" href="#L12">12</a> <em class="jxr_comment"> * distributed under the License is distributed on an "AS IS" BASIS,</em>
+<a class="jxr_linenumber" name="L13" href="#L13">13</a> <em class="jxr_comment"> * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.</em>
+<a class="jxr_linenumber" name="L14" href="#L14">14</a> <em class="jxr_comment"> * See the License for the specific language governing permissions and</em>
+<a class="jxr_linenumber" name="L15" href="#L15">15</a> <em class="jxr_comment"> * limitations under the License.</em>
+<a class="jxr_linenumber" name="L16" href="#L16">16</a> <em class="jxr_comment"> */</em>
+<a class="jxr_linenumber" name="L17" href="#L17">17</a> <strong class="jxr_keyword">package</strong> org.apache.commons.statistics.distribution;
+<a class="jxr_linenumber" name="L18" href="#L18">18</a>
+<a class="jxr_linenumber" name="L19" href="#L19">19</a> <strong class="jxr_keyword">import</strong> java.util.function.IntToDoubleFunction;
+<a class="jxr_linenumber" name="L20" href="#L20">20</a> <strong class="jxr_keyword">import</strong> org.apache.commons.rng.UniformRandomProvider;
+<a class="jxr_linenumber" name="L21" href="#L21">21</a> <strong class="jxr_keyword">import</strong> org.apache.commons.rng.sampling.distribution.GeometricSampler;
+<a class="jxr_linenumber" name="L22" href="#L22">22</a>
+<a class="jxr_linenumber" name="L23" href="#L23">23</a> <em class="jxr_javadoccomment">/**</em>
+<a class="jxr_linenumber" name="L24" href="#L24">24</a> <em class="jxr_javadoccomment"> * Implementation of the geometric distribution.</em>
+<a class="jxr_linenumber" name="L25" href="#L25">25</a> <em class="jxr_javadoccomment"> *</em>
+<a class="jxr_linenumber" name="L26" href="#L26">26</a> <em class="jxr_javadoccomment"> * <p>The probability mass function of \( X \) is:</em>
+<a class="jxr_linenumber" name="L27" href="#L27">27</a> <em class="jxr_javadoccomment"> *</em>
+<a class="jxr_linenumber" name="L28" href="#L28">28</a> <em class="jxr_javadoccomment"> * <p>\[ f(k; p) = (1-p)^k \, p \]</em>
+<a class="jxr_linenumber" name="L29" href="#L29">29</a> <em class="jxr_javadoccomment"> *</em>
+<a class="jxr_linenumber" name="L30" href="#L30">30</a> <em class="jxr_javadoccomment"> * <p>for \( p \in (0, 1] \) the probability of success and</em>
+<a class="jxr_linenumber" name="L31" href="#L31">31</a> <em class="jxr_javadoccomment"> * \( k \in \{0, 1, 2, \dots\} \) the number of failures.</em>
+<a class="jxr_linenumber" name="L32" href="#L32">32</a> <em class="jxr_javadoccomment"> *</em>
+<a class="jxr_linenumber" name="L33" href="#L33">33</a> <em class="jxr_javadoccomment"> * <p>This parameterization is used to model the number of failures until</em>
+<a class="jxr_linenumber" name="L34" href="#L34">34</a> <em class="jxr_javadoccomment"> * the first success.</em>
+<a class="jxr_linenumber" name="L35" href="#L35">35</a> <em class="jxr_javadoccomment"> *</em>
+<a class="jxr_linenumber" name="L36" href="#L36">36</a> <em class="jxr_javadoccomment"> * @see <a href="<a href="https://en.wikipedia.org/wiki/Geometric_distribution" target="alexandria_uri">https://en.wikipedia.org/wiki/Geometric_distribution</a>">Geometric distribution (Wikipedia)</a></em>
+<a class="jxr_linenumber" name="L37" href="#L37">37</a> <em class="jxr_javadoccomment"> * @see <a href="<a href="https://mathworld.wolfram.com/GeometricDistribution.html" target="alexandria_uri">https://mathworld.wolfram.com/GeometricDistribution.html</a>">Geometric distribution (MathWorld)</a></em>
+<a class="jxr_linenumber" name="L38" href="#L38">38</a> <em class="jxr_javadoccomment"> */</em>
+<a class="jxr_linenumber" name="L39" href="#L39">39</a> <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">class</strong> <a name="GeometricDistribution" href="../../../../../org/apache/commons/statistics/distribution/GeometricDistribution.html#GeometricDistribution">GeometricDistribution</a> <strong class="jxr_keyword">extends</strong> <a name="AbstractDiscreteDistribution" href="../../../../../org/apache/commons/statistics/distribution/AbstractDiscreteDistribution.html#AbstractDiscreteDistribution">AbstractDiscreteDistribution</a> {
+<a class="jxr_linenumber" name="L40" href="#L40">40</a> <em class="jxr_javadoccomment">/** 1/2. */</em>
+<a class="jxr_linenumber" name="L41" href="#L41">41</a> <strong class="jxr_keyword">private</strong> <strong class="jxr_keyword">static</strong> <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> HALF = 0.5;
+<a class="jxr_linenumber" name="L42" href="#L42">42</a>
+<a class="jxr_linenumber" name="L43" href="#L43">43</a> <em class="jxr_javadoccomment">/** The probability of success. */</em>
+<a class="jxr_linenumber" name="L44" href="#L44">44</a> <strong class="jxr_keyword">private</strong> <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> probabilityOfSuccess;
+<a class="jxr_linenumber" name="L45" href="#L45">45</a> <em class="jxr_javadoccomment">/** {@code log(p)} where p is the probability of success. */</em>
+<a class="jxr_linenumber" name="L46" href="#L46">46</a> <strong class="jxr_keyword">private</strong> <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> logProbabilityOfSuccess;
+<a class="jxr_linenumber" name="L47" href="#L47">47</a> <em class="jxr_javadoccomment">/** {@code log(1 - p)} where p is the probability of success. */</em>
+<a class="jxr_linenumber" name="L48" href="#L48">48</a> <strong class="jxr_keyword">private</strong> <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> log1mProbabilityOfSuccess;
+<a class="jxr_linenumber" name="L49" href="#L49">49</a> <em class="jxr_javadoccomment">/** Value of survival probability for x=0.</em>
+<a class="jxr_linenumber" name="L50" href="#L50">50</a> <em class="jxr_javadoccomment"> * Used in the survival functions. Equal to (1 - probability of success). */</em>
+<a class="jxr_linenumber" name="L51" href="#L51">51</a> <strong class="jxr_keyword">private</strong> <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> sf0;
+<a class="jxr_linenumber" name="L52" href="#L52">52</a> <em class="jxr_javadoccomment">/** Implementation of PMF(x). Assumes that {@code x > 0}. */</em>
+<a class="jxr_linenumber" name="L53" href="#L53">53</a> <strong class="jxr_keyword">private</strong> <strong class="jxr_keyword">final</strong> IntToDoubleFunction pmf;
+<a class="jxr_linenumber" name="L54" href="#L54">54</a>
+<a class="jxr_linenumber" name="L55" href="#L55">55</a> <em class="jxr_javadoccomment">/**</em>
+<a class="jxr_linenumber" name="L56" href="#L56">56</a> <em class="jxr_javadoccomment"> * @param p Probability of success.</em>
+<a class="jxr_linenumber" name="L57" href="#L57">57</a> <em class="jxr_javadoccomment"> */</em>
+<a class="jxr_linenumber" name="L58" href="#L58">58</a> <strong class="jxr_keyword">private</strong> <a name="GeometricDistribution" href="../../../../../org/apache/commons/statistics/distribution/GeometricDistribution.html#GeometricDistribution">GeometricDistribution</a>(<strong class="jxr_keyword">double</strong> p) {
+<a class="jxr_linenumber" name="L59" href="#L59">59</a> probabilityOfSuccess = p;
+<a class="jxr_linenumber" name="L60" href="#L60">60</a> logProbabilityOfSuccess = Math.log(p);
+<a class="jxr_linenumber" name="L61" href="#L61">61</a> log1mProbabilityOfSuccess = Math.log1p(-p);
+<a class="jxr_linenumber" name="L62" href="#L62">62</a> sf0 = 1 - p;
+<a class="jxr_linenumber" name="L63" href="#L63">63</a>
+<a class="jxr_linenumber" name="L64" href="#L64">64</a> <em class="jxr_comment">// Choose the PMF implementation.</em>
+<a class="jxr_linenumber" name="L65" href="#L65">65</a> <em class="jxr_comment">// When p >= 0.5 then 1 - p is exact and using the power function</em>
+<a class="jxr_linenumber" name="L66" href="#L66">66</a> <em class="jxr_comment">// is consistently more accurate than the use of the exponential function.</em>
+<a class="jxr_linenumber" name="L67" href="#L67">67</a> <em class="jxr_comment">// When p -> 0 then the exponential function avoids large error propagation</em>
+<a class="jxr_linenumber" name="L68" href="#L68">68</a> <em class="jxr_comment">// of the power function used with an inexact 1 - p.</em>
+<a class="jxr_linenumber" name="L69" href="#L69">69</a> <em class="jxr_comment">// Also compute the survival probability for use when x=0.</em>
+<a class="jxr_linenumber" name="L70" href="#L70">70</a> <strong class="jxr_keyword">if</strong> (p >= HALF) {
+<a class="jxr_linenumber" name="L71" href="#L71">71</a> pmf = x -> Math.pow(sf0, x) * probabilityOfSuccess;
+<a class="jxr_linenumber" name="L72" href="#L72">72</a> } <strong class="jxr_keyword">else</strong> {
+<a class="jxr_linenumber" name="L73" href="#L73">73</a> pmf = x -> Math.exp(log1mProbabilityOfSuccess * x) * probabilityOfSuccess;
+<a class="jxr_linenumber" name="L74" href="#L74">74</a> }
+<a class="jxr_linenumber" name="L75" href="#L75">75</a> }
+<a class="jxr_linenumber" name="L76" href="#L76">76</a>
+<a class="jxr_linenumber" name="L77" href="#L77">77</a> <em class="jxr_javadoccomment">/**</em>
+<a class="jxr_linenumber" name="L78" href="#L78">78</a> <em class="jxr_javadoccomment"> * Creates a geometric distribution.</em>
+<a class="jxr_linenumber" name="L79" href="#L79">79</a> <em class="jxr_javadoccomment"> *</em>
+<a class="jxr_linenumber" name="L80" href="#L80">80</a> <em class="jxr_javadoccomment"> * @param p Probability of success.</em>
+<a class="jxr_linenumber" name="L81" href="#L81">81</a> <em class="jxr_javadoccomment"> * @return the geometric distribution</em>
+<a class="jxr_linenumber" name="L82" href="#L82">82</a> <em class="jxr_javadoccomment"> * @throws IllegalArgumentException if {@code p <= 0} or {@code p > 1}.</em>
+<a class="jxr_linenumber" name="L83" href="#L83">83</a> <em class="jxr_javadoccomment"> */</em>
+<a class="jxr_linenumber" name="L84" href="#L84">84</a> <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">static</strong> <a name="GeometricDistribution" href="../../../../../org/apache/commons/statistics/distribution/GeometricDistribution.html#GeometricDistribution">GeometricDistribution</a> of(<strong class="jxr_keyword">double</strong> p) {
+<a class="jxr_linenumber" name="L85" href="#L85">85</a> <strong class="jxr_keyword">if</strong> (p <= 0 || p > 1) {
+<a class="jxr_linenumber" name="L86" href="#L86">86</a> <strong class="jxr_keyword">throw</strong> <strong class="jxr_keyword">new</strong> <a name="DistributionException" href="../../../../../org/apache/commons/statistics/distribution/DistributionException.html#DistributionException">DistributionException</a>(DistributionException.INVALID_NON_ZERO_PROBABILITY, p);
+<a class="jxr_linenumber" name="L87" href="#L87">87</a> }
+<a class="jxr_linenumber" name="L88" href="#L88">88</a> <strong class="jxr_keyword">return</strong> <strong class="jxr_keyword">new</strong> <a name="GeometricDistribution" href="../../../../../org/apache/commons/statistics/distribution/GeometricDistribution.html#GeometricDistribution">GeometricDistribution</a>(p);
+<a class="jxr_linenumber" name="L89" href="#L89">89</a> }
+<a class="jxr_linenumber" name="L90" href="#L90">90</a>
+<a class="jxr_linenumber" name="L91" href="#L91">91</a> <em class="jxr_javadoccomment">/**</em>
+<a class="jxr_linenumber" name="L92" href="#L92">92</a> <em class="jxr_javadoccomment"> * Gets the probability of success parameter of this distribution.</em>
+<a class="jxr_linenumber" name="L93" href="#L93">93</a> <em class="jxr_javadoccomment"> *</em>
+<a class="jxr_linenumber" name="L94" href="#L94">94</a> <em class="jxr_javadoccomment"> * @return the probability of success.</em>
+<a class="jxr_linenumber" name="L95" href="#L95">95</a> <em class="jxr_javadoccomment"> */</em>
+<a class="jxr_linenumber" name="L96" href="#L96">96</a> <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">double</strong> getProbabilityOfSuccess() {
+<a class="jxr_linenumber" name="L97" href="#L97">97</a> <strong class="jxr_keyword">return</strong> probabilityOfSuccess;
+<a class="jxr_linenumber" name="L98" href="#L98">98</a> }
+<a class="jxr_linenumber" name="L99" href="#L99">99</a>
+<a class="jxr_linenumber" name="L100" href="#L100">100</a> <em class="jxr_javadoccomment">/** {@inheritDoc} */</em>
+<a class="jxr_linenumber" name="L101" href="#L101">101</a> @Override
+<a class="jxr_linenumber" name="L102" href="#L102">102</a> <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">double</strong> probability(<strong class="jxr_keyword">int</strong> x) {
+<a class="jxr_linenumber" name="L103" href="#L103">103</a> <strong class="jxr_keyword">if</strong> (x <= 0) {
+<a class="jxr_linenumber" name="L104" href="#L104">104</a> <em class="jxr_comment">// Special case of x=0 exploiting cancellation.</em>
+<a class="jxr_linenumber" name="L105" href="#L105">105</a> <strong class="jxr_keyword">return</strong> x == 0 ? probabilityOfSuccess : 0;
+<a class="jxr_linenumber" name="L106" href="#L106">106</a> }
+<a class="jxr_linenumber" name="L107" href="#L107">107</a> <strong class="jxr_keyword">return</strong> pmf.applyAsDouble(x);
+<a class="jxr_linenumber" name="L108" href="#L108">108</a> }
+<a class="jxr_linenumber" name="L109" href="#L109">109</a>
+<a class="jxr_linenumber" name="L110" href="#L110">110</a> <em class="jxr_javadoccomment">/** {@inheritDoc} */</em>
+<a class="jxr_linenumber" name="L111" href="#L111">111</a> @Override
+<a class="jxr_linenumber" name="L112" href="#L112">112</a> <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">double</strong> logProbability(<strong class="jxr_keyword">int</strong> x) {
+<a class="jxr_linenumber" name="L113" href="#L113">113</a> <strong class="jxr_keyword">if</strong> (x <= 0) {
+<a class="jxr_linenumber" name="L114" href="#L114">114</a> <em class="jxr_comment">// Special case of x=0 exploiting cancellation.</em>
+<a class="jxr_linenumber" name="L115" href="#L115">115</a> <strong class="jxr_keyword">return</strong> x == 0 ? logProbabilityOfSuccess : Double.NEGATIVE_INFINITY;
+<a class="jxr_linenumber" name="L116" href="#L116">116</a> }
+<a class="jxr_linenumber" name="L117" href="#L117">117</a> <strong class="jxr_keyword">return</strong> x * log1mProbabilityOfSuccess + logProbabilityOfSuccess;
+<a class="jxr_linenumber" name="L118" href="#L118">118</a> }
+<a class="jxr_linenumber" name="L119" href="#L119">119</a>
+<a class="jxr_linenumber" name="L120" href="#L120">120</a> <em class="jxr_javadoccomment">/** {@inheritDoc} */</em>
+<a class="jxr_linenumber" name="L121" href="#L121">121</a> @Override
+<a class="jxr_linenumber" name="L122" href="#L122">122</a> <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">double</strong> cumulativeProbability(<strong class="jxr_keyword">int</strong> x) {
+<a class="jxr_linenumber" name="L123" href="#L123">123</a> <strong class="jxr_keyword">if</strong> (x <= 0) {
+<a class="jxr_linenumber" name="L124" href="#L124">124</a> <em class="jxr_comment">// Note: CDF(x=0) = PDF(x=0) = probabilityOfSuccess</em>
+<a class="jxr_linenumber" name="L125" href="#L125">125</a> <strong class="jxr_keyword">return</strong> x == 0 ? probabilityOfSuccess : 0;
+<a class="jxr_linenumber" name="L126" href="#L126">126</a> }
+<a class="jxr_linenumber" name="L127" href="#L127">127</a> <em class="jxr_comment">// Note: Double addition avoids overflow. This may compute a value less than 1.0</em>
+<a class="jxr_linenumber" name="L128" href="#L128">128</a> <em class="jxr_comment">// for the max integer value when p is very small.</em>
+<a class="jxr_linenumber" name="L129" href="#L129">129</a> <strong class="jxr_keyword">return</strong> -Math.expm1(log1mProbabilityOfSuccess * (x + 1.0));
+<a class="jxr_linenumber" name="L130" href="#L130">130</a> }
+<a class="jxr_linenumber" name="L131" href="#L131">131</a>
+<a class="jxr_linenumber" name="L132" href="#L132">132</a> <em class="jxr_javadoccomment">/** {@inheritDoc} */</em>
+<a class="jxr_linenumber" name="L133" href="#L133">133</a> @Override
+<a class="jxr_linenumber" name="L134" href="#L134">134</a> <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">double</strong> survivalProbability(<strong class="jxr_keyword">int</strong> x) {
+<a class="jxr_linenumber" name="L135" href="#L135">135</a> <strong class="jxr_keyword">if</strong> (x <= 0) {
+<a class="jxr_linenumber" name="L136" href="#L136">136</a> <em class="jxr_comment">// Note: SF(x=0) = 1 - PDF(x=0) = 1 - probabilityOfSuccess</em>
+<a class="jxr_linenumber" name="L137" href="#L137">137</a> <em class="jxr_comment">// Use a pre-computed value to avoid cancellation when probabilityOfSuccess -> 0</em>
+<a class="jxr_linenumber" name="L138" href="#L138">138</a> <strong class="jxr_keyword">return</strong> x == 0 ? sf0 : 1;
+<a class="jxr_linenumber" name="L139" href="#L139">139</a> }
+<a class="jxr_linenumber" name="L140" href="#L140">140</a> <em class="jxr_comment">// Note: Double addition avoids overflow. This may compute a value greater than 0.0</em>
+<a class="jxr_linenumber" name="L141" href="#L141">141</a> <em class="jxr_comment">// for the max integer value when p is very small.</em>
+<a class="jxr_linenumber" name="L142" href="#L142">142</a> <strong class="jxr_keyword">return</strong> Math.exp(log1mProbabilityOfSuccess * (x + 1.0));
+<a class="jxr_linenumber" name="L143" href="#L143">143</a> }
+<a class="jxr_linenumber" name="L144" href="#L144">144</a>
+<a class="jxr_linenumber" name="L145" href="#L145">145</a> <em class="jxr_javadoccomment">/** {@inheritDoc} */</em>
+<a class="jxr_linenumber" name="L146" href="#L146">146</a> @Override
+<a class="jxr_linenumber" name="L147" href="#L147">147</a> <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">int</strong> inverseCumulativeProbability(<strong class="jxr_keyword">double</strong> p) {
+<a class="jxr_linenumber" name="L148" href="#L148">148</a> ArgumentUtils.checkProbability(p);
+<a class="jxr_linenumber" name="L149" href="#L149">149</a> <strong class="jxr_keyword">if</strong> (p == 1) {
+<a class="jxr_linenumber" name="L150" href="#L150">150</a> <strong class="jxr_keyword">return</strong> getSupportUpperBound();
+<a class="jxr_linenumber" name="L151" href="#L151">151</a> }
+<a class="jxr_linenumber" name="L152" href="#L152">152</a> <strong class="jxr_keyword">if</strong> (p <= probabilityOfSuccess) {
+<a class="jxr_linenumber" name="L153" href="#L153">153</a> <strong class="jxr_keyword">return</strong> 0;
+<a class="jxr_linenumber" name="L154" href="#L154">154</a> }
+<a class="jxr_linenumber" name="L155" href="#L155">155</a> <em class="jxr_comment">// p > probabilityOfSuccess</em>
+<a class="jxr_linenumber" name="L156" href="#L156">156</a> <em class="jxr_comment">// => log(1-p) < log(1-probabilityOfSuccess);</em>
+<a class="jxr_linenumber" name="L157" href="#L157">157</a> <em class="jxr_comment">// Both terms are negative as probabilityOfSuccess > 0.</em>
+<a class="jxr_linenumber" name="L158" href="#L158">158</a> <em class="jxr_comment">// This should be lower bounded to (2 - 1) = 1</em>
+<a class="jxr_linenumber" name="L159" href="#L159">159</a> <strong class="jxr_keyword">int</strong> x = (<strong class="jxr_keyword">int</strong>) (Math.ceil(Math.log1p(-p) / log1mProbabilityOfSuccess) - 1);
+<a class="jxr_linenumber" name="L160" href="#L160">160</a>
+<a class="jxr_linenumber" name="L161" href="#L161">161</a> <em class="jxr_comment">// Correct rounding errors.</em>
+<a class="jxr_linenumber" name="L162" href="#L162">162</a> <em class="jxr_comment">// This ensures x == icdf(cdf(x))</em>
+<a class="jxr_linenumber" name="L163" href="#L163">163</a>
+<a class="jxr_linenumber" name="L164" href="#L164">164</a> <strong class="jxr_keyword">if</strong> (cumulativeProbability(x - 1) >= p) {
+<a class="jxr_linenumber" name="L165" href="#L165">165</a> <em class="jxr_comment">// No checks for x=0.</em>
+<a class="jxr_linenumber" name="L166" href="#L166">166</a> <em class="jxr_comment">// If x=0; cdf(-1) = 0 and the condition is false as p>0 at this point.</em>
+<a class="jxr_linenumber" name="L167" href="#L167">167</a> x--;
+<a class="jxr_linenumber" name="L168" href="#L168">168</a> } <strong class="jxr_keyword">else</strong> <strong class="jxr_keyword">if</strong> (cumulativeProbability(x) < p && x < Integer.MAX_VALUE) {
+<a class="jxr_linenumber" name="L169" href="#L169">169</a> <em class="jxr_comment">// The supported upper bound is max_value here as probabilityOfSuccess != 1</em>
+<a class="jxr_linenumber" name="L170" href="#L170">170</a> x++;
+<a class="jxr_linenumber" name="L171" href="#L171">171</a> }
+<a class="jxr_linenumber" name="L172" href="#L172">172</a>
+<a class="jxr_linenumber" name="L173" href="#L173">173</a> <strong class="jxr_keyword">return</strong> x;
+<a class="jxr_linenumber" name="L174" href="#L174">174</a> }
+<a class="jxr_linenumber" name="L175" href="#L175">175</a>
+<a class="jxr_linenumber" name="L176" href="#L176">176</a> <em class="jxr_javadoccomment">/** {@inheritDoc} */</em>
+<a class="jxr_linenumber" name="L177" href="#L177">177</a> @Override
+<a class="jxr_linenumber" name="L178" href="#L178">178</a> <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">int</strong> inverseSurvivalProbability(<strong class="jxr_keyword">double</strong> p) {
+<a class="jxr_linenumber" name="L179" href="#L179">179</a> ArgumentUtils.checkProbability(p);
+<a class="jxr_linenumber" name="L180" href="#L180">180</a> <strong class="jxr_keyword">if</strong> (p == 0) {
+<a class="jxr_linenumber" name="L181" href="#L181">181</a> <strong class="jxr_keyword">return</strong> getSupportUpperBound();
+<a class="jxr_linenumber" name="L182" href="#L182">182</a> }
+<a class="jxr_linenumber" name="L183" href="#L183">183</a> <strong class="jxr_keyword">if</strong> (p >= sf0) {
+<a class="jxr_linenumber" name="L184" href="#L184">184</a> <strong class="jxr_keyword">return</strong> 0;
+<a class="jxr_linenumber" name="L185" href="#L185">185</a> }
+<a class="jxr_linenumber" name="L186" href="#L186">186</a>
+<a class="jxr_linenumber" name="L187" href="#L187">187</a> <em class="jxr_comment">// p < 1 - probabilityOfSuccess</em>
+<a class="jxr_linenumber" name="L188" href="#L188">188</a> <em class="jxr_comment">// Inversion as for icdf using log(p) in place of log1p(-p)</em>
+<a class="jxr_linenumber" name="L189" href="#L189">189</a> <strong class="jxr_keyword">int</strong> x = (<strong class="jxr_keyword">int</strong>) (Math.ceil(Math.log(p) / log1mProbabilityOfSuccess) - 1);
+<a class="jxr_linenumber" name="L190" href="#L190">190</a>
+<a class="jxr_linenumber" name="L191" href="#L191">191</a> <em class="jxr_comment">// Correct rounding errors.</em>
+<a class="jxr_linenumber" name="L192" href="#L192">192</a> <em class="jxr_comment">// This ensures x == isf(sf(x))</em>
+<a class="jxr_linenumber" name="L193" href="#L193">193</a>
+<a class="jxr_linenumber" name="L194" href="#L194">194</a> <strong class="jxr_keyword">if</strong> (survivalProbability(x - 1) <= p) {
+<a class="jxr_linenumber" name="L195" href="#L195">195</a> <em class="jxr_comment">// No checks for x=0</em>
+<a class="jxr_linenumber" name="L196" href="#L196">196</a> <em class="jxr_comment">// If x=0; sf(-1) = 1 and the condition is false as p<1 at this point.</em>
+<a class="jxr_linenumber" name="L197" href="#L197">197</a> x--;
+<a class="jxr_linenumber" name="L198" href="#L198">198</a> } <strong class="jxr_keyword">else</strong> <strong class="jxr_keyword">if</strong> (survivalProbability(x) > p && x < Integer.MAX_VALUE) {
+<a class="jxr_linenumber" name="L199" href="#L199">199</a> <em class="jxr_comment">// The supported upper bound is max_value here as probabilityOfSuccess != 1</em>
+<a class="jxr_linenumber" name="L200" href="#L200">200</a> x++;
+<a class="jxr_linenumber" name="L201" href="#L201">201</a> }
+<a class="jxr_linenumber" name="L202" href="#L202">202</a>
+<a class="jxr_linenumber" name="L203" href="#L203">203</a> <strong class="jxr_keyword">return</strong> x;
+<a class="jxr_linenumber" name="L204" href="#L204">204</a> }
+<a class="jxr_linenumber" name="L205" href="#L205">205</a>
+<a class="jxr_linenumber" name="L206" href="#L206">206</a> <em class="jxr_javadoccomment">/**</em>
+<a class="jxr_linenumber" name="L207" href="#L207">207</a> <em class="jxr_javadoccomment"> * {@inheritDoc}</em>
+<a class="jxr_linenumber" name="L208" href="#L208">208</a> <em class="jxr_javadoccomment"> *</em>
+<a class="jxr_linenumber" name="L209" href="#L209">209</a> <em class="jxr_javadoccomment"> * <p>For probability parameter \( p \), the mean is:</em>
+<a class="jxr_linenumber" name="L210" href="#L210">210</a> <em class="jxr_javadoccomment"> *</em>
+<a class="jxr_linenumber" name="L211" href="#L211">211</a> <em class="jxr_javadoccomment"> * <p>\[ \frac{1 - p}{p} \]</em>
+<a class="jxr_linenumber" name="L212" href="#L212">212</a> <em class="jxr_javadoccomment"> */</em>
+<a class="jxr_linenumber" name="L213" href="#L213">213</a> @Override
+<a class="jxr_linenumber" name="L214" href="#L214">214</a> <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">double</strong> getMean() {
+<a class="jxr_linenumber" name="L215" href="#L215">215</a> <strong class="jxr_keyword">return</strong> (1 - probabilityOfSuccess) / probabilityOfSuccess;
+<a class="jxr_linenumber" name="L216" href="#L216">216</a> }
+<a class="jxr_linenumber" name="L217" href="#L217">217</a>
+<a class="jxr_linenumber" name="L218" href="#L218">218</a> <em class="jxr_javadoccomment">/**</em>
+<a class="jxr_linenumber" name="L219" href="#L219">219</a> <em class="jxr_javadoccomment"> * {@inheritDoc}</em>
+<a class="jxr_linenumber" name="L220" href="#L220">220</a> <em class="jxr_javadoccomment"> *</em>
+<a class="jxr_linenumber" name="L221" href="#L221">221</a> <em class="jxr_javadoccomment"> * <p>For probability parameter \( p \), the variance is:</em>
+<a class="jxr_linenumber" name="L222" href="#L222">222</a> <em class="jxr_javadoccomment"> *</em>
+<a class="jxr_linenumber" name="L223" href="#L223">223</a> <em class="jxr_javadoccomment"> * <p>\[ \frac{1 - p}{p^2} \]</em>
+<a class="jxr_linenumber" name="L224" href="#L224">224</a> <em class="jxr_javadoccomment"> */</em>
+<a class="jxr_linenumber" name="L225" href="#L225">225</a> @Override
+<a class="jxr_linenumber" name="L226" href="#L226">226</a> <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">double</strong> getVariance() {
+<a class="jxr_linenumber" name="L227" href="#L227">227</a> <strong class="jxr_keyword">return</strong> (1 - probabilityOfSuccess) / (probabilityOfSuccess * probabilityOfSuccess);
+<a class="jxr_linenumber" name="L228" href="#L228">228</a> }
+<a class="jxr_linenumber" name="L229" href="#L229">229</a>
+<a class="jxr_linenumber" name="L230" href="#L230">230</a> <em class="jxr_javadoccomment">/**</em>
+<a class="jxr_linenumber" name="L231" href="#L231">231</a> <em class="jxr_javadoccomment"> * {@inheritDoc}</em>
+<a class="jxr_linenumber" name="L232" href="#L232">232</a> <em class="jxr_javadoccomment"> *</em>
+<a class="jxr_linenumber" name="L233" href="#L233">233</a> <em class="jxr_javadoccomment"> * <p>The lower bound of the support is always 0.</em>
+<a class="jxr_linenumber" name="L234" href="#L234">234</a> <em class="jxr_javadoccomment"> *</em>
+<a class="jxr_linenumber" name="L235" href="#L235">235</a> <em class="jxr_javadoccomment"> * @return 0.</em>
+<a class="jxr_linenumber" name="L236" href="#L236">236</a> <em class="jxr_javadoccomment"> */</em>
+<a class="jxr_linenumber" name="L237" href="#L237">237</a> @Override
+<a class="jxr_linenumber" name="L238" href="#L238">238</a> <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">int</strong> getSupportLowerBound() {
+<a class="jxr_linenumber" name="L239" href="#L239">239</a> <strong class="jxr_keyword">return</strong> 0;
+<a class="jxr_linenumber" name="L240" href="#L240">240</a> }
+<a class="jxr_linenumber" name="L241" href="#L241">241</a>
+<a class="jxr_linenumber" name="L242" href="#L242">242</a> <em class="jxr_javadoccomment">/**</em>
+<a class="jxr_linenumber" name="L243" href="#L243">243</a> <em class="jxr_javadoccomment"> * {@inheritDoc}</em>
+<a class="jxr_linenumber" name="L244" href="#L244">244</a> <em class="jxr_javadoccomment"> *</em>
+<a class="jxr_linenumber" name="L245" href="#L245">245</a> <em class="jxr_javadoccomment"> * <p>The upper bound of the support is positive infinity except for the</em>
+<a class="jxr_linenumber" name="L246" href="#L246">246</a> <em class="jxr_javadoccomment"> * probability parameter {@code p = 1.0}.</em>
+<a class="jxr_linenumber" name="L247" href="#L247">247</a> <em class="jxr_javadoccomment"> *</em>
+<a class="jxr_linenumber" name="L248" href="#L248">248</a> <em class="jxr_javadoccomment"> * @return {@link Integer#MAX_VALUE} or 0.</em>
+<a class="jxr_linenumber" name="L249" href="#L249">249</a> <em class="jxr_javadoccomment"> */</em>
+<a class="jxr_linenumber" name="L250" href="#L250">250</a> @Override
+<a class="jxr_linenumber" name="L251" href="#L251">251</a> <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">int</strong> getSupportUpperBound() {
+<a class="jxr_linenumber" name="L252" href="#L252">252</a> <strong class="jxr_keyword">return</strong> probabilityOfSuccess < 1 ? Integer.MAX_VALUE : 0;
+<a class="jxr_linenumber" name="L253" href="#L253">253</a> }
+<a class="jxr_linenumber" name="L254" href="#L254">254</a>
+<a class="jxr_linenumber" name="L255" href="#L255">255</a> <em class="jxr_javadoccomment">/** {@inheritDoc} */</em>
+<a class="jxr_linenumber" name="L256" href="#L256">256</a> @Override
+<a class="jxr_linenumber" name="L257" href="#L257">257</a> <strong class="jxr_keyword">public</strong> Sampler createSampler(UniformRandomProvider rng) {
+<a class="jxr_linenumber" name="L258" href="#L258">258</a> <strong class="jxr_keyword">return</strong> GeometricSampler.of(rng, probabilityOfSuccess)::sample;
+<a class="jxr_linenumber" name="L259" href="#L259">259</a> }
+<a class="jxr_linenumber" name="L260" href="#L260">260</a> }
+</pre>
+<hr/>
+<div id="footer">Copyright © 2018–2022 <a href="https://www.apache.org/">The Apache Software Foundation</a>. All rights reserved.</div>
+</body>
+</html>
Added: dev/commons/statistics/1.0-RC1/site/xref/org/apache/commons/statistics/distribution/GumbelDistribution.html
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--- dev/commons/statistics/1.0-RC1/site/xref/org/apache/commons/statistics/distribution/GumbelDistribution.html (added)
+++ dev/commons/statistics/1.0-RC1/site/xref/org/apache/commons/statistics/distribution/GumbelDistribution.html Thu Dec 1 16:47:12 2022
@@ -0,0 +1,233 @@
+<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd">
+<html xmlns="http://www.w3.org/1999/xhtml" xml:lang="en" lang="en">
+<head><meta http-equiv="content-type" content="text/html; charset=UTF-8" />
+<title>GumbelDistribution xref</title>
+<link type="text/css" rel="stylesheet" href="../../../../../stylesheet.css" />
+</head>
+<body>
+<div id="overview"><a href="../../../../../../apidocs/org/apache/commons/statistics/distribution/GumbelDistribution.html">View Javadoc</a></div><pre>
+<a class="jxr_linenumber" name="L1" href="#L1">1</a> <em class="jxr_comment">/*</em>
+<a class="jxr_linenumber" name="L2" href="#L2">2</a> <em class="jxr_comment"> * Licensed to the Apache Software Foundation (ASF) under one or more</em>
+<a class="jxr_linenumber" name="L3" href="#L3">3</a> <em class="jxr_comment"> * contributor license agreements. See the NOTICE file distributed with</em>
+<a class="jxr_linenumber" name="L4" href="#L4">4</a> <em class="jxr_comment"> * this work for additional information regarding copyright ownership.</em>
+<a class="jxr_linenumber" name="L5" href="#L5">5</a> <em class="jxr_comment"> * The ASF licenses this file to You under the Apache License, Version 2.0</em>
+<a class="jxr_linenumber" name="L6" href="#L6">6</a> <em class="jxr_comment"> * (the "License"); you may not use this file except in compliance with</em>
+<a class="jxr_linenumber" name="L7" href="#L7">7</a> <em class="jxr_comment"> * the License. You may obtain a copy of the License at</em>
+<a class="jxr_linenumber" name="L8" href="#L8">8</a> <em class="jxr_comment"> *</em>
+<a class="jxr_linenumber" name="L9" href="#L9">9</a> <em class="jxr_comment"> * <a href="http://www.apache.org/licenses/LICENSE-2.0" target="alexandria_uri">http://www.apache.org/licenses/LICENSE-2.0</a></em>
+<a class="jxr_linenumber" name="L10" href="#L10">10</a> <em class="jxr_comment"> *</em>
+<a class="jxr_linenumber" name="L11" href="#L11">11</a> <em class="jxr_comment"> * Unless required by applicable law or agreed to in writing, software</em>
+<a class="jxr_linenumber" name="L12" href="#L12">12</a> <em class="jxr_comment"> * distributed under the License is distributed on an "AS IS" BASIS,</em>
+<a class="jxr_linenumber" name="L13" href="#L13">13</a> <em class="jxr_comment"> * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.</em>
+<a class="jxr_linenumber" name="L14" href="#L14">14</a> <em class="jxr_comment"> * See the License for the specific language governing permissions and</em>
+<a class="jxr_linenumber" name="L15" href="#L15">15</a> <em class="jxr_comment"> * limitations under the License.</em>
+<a class="jxr_linenumber" name="L16" href="#L16">16</a> <em class="jxr_comment"> */</em>
+<a class="jxr_linenumber" name="L17" href="#L17">17</a> <strong class="jxr_keyword">package</strong> org.apache.commons.statistics.distribution;
+<a class="jxr_linenumber" name="L18" href="#L18">18</a>
+<a class="jxr_linenumber" name="L19" href="#L19">19</a> <em class="jxr_javadoccomment">/**</em>
+<a class="jxr_linenumber" name="L20" href="#L20">20</a> <em class="jxr_javadoccomment"> * Implementation of the Gumbel distribution.</em>
+<a class="jxr_linenumber" name="L21" href="#L21">21</a> <em class="jxr_javadoccomment"> *</em>
+<a class="jxr_linenumber" name="L22" href="#L22">22</a> <em class="jxr_javadoccomment"> * <p>The probability density function of \( X \) is:</em>
+<a class="jxr_linenumber" name="L23" href="#L23">23</a> <em class="jxr_javadoccomment"> *</em>
+<a class="jxr_linenumber" name="L24" href="#L24">24</a> <em class="jxr_javadoccomment"> * <p>\[ f(x; \mu, \beta) = \frac{1}{\beta} e^{-(z+e^{-z})} \]</em>
+<a class="jxr_linenumber" name="L25" href="#L25">25</a> <em class="jxr_javadoccomment"> *</em>
+<a class="jxr_linenumber" name="L26" href="#L26">26</a> <em class="jxr_javadoccomment"> * <p>where \[ z = \frac{x - \mu}{\beta} \]</em>
+<a class="jxr_linenumber" name="L27" href="#L27">27</a> <em class="jxr_javadoccomment"> *</em>
+<a class="jxr_linenumber" name="L28" href="#L28">28</a> <em class="jxr_javadoccomment"> * <p>for \( \mu \) the location,</em>
+<a class="jxr_linenumber" name="L29" href="#L29">29</a> <em class="jxr_javadoccomment"> * \( \beta &gt; 0 \) the scale, and</em>
+<a class="jxr_linenumber" name="L30" href="#L30">30</a> <em class="jxr_javadoccomment"> * \( x \in (-\infty, \infty) \).</em>
+<a class="jxr_linenumber" name="L31" href="#L31">31</a> <em class="jxr_javadoccomment"> *</em>
+<a class="jxr_linenumber" name="L32" href="#L32">32</a> <em class="jxr_javadoccomment"> * @see <a href="<a href="https://en.wikipedia.org/wiki/Gumbel_distribution" target="alexandria_uri">https://en.wikipedia.org/wiki/Gumbel_distribution</a>">Gumbel distribution (Wikipedia)</a></em>
+<a class="jxr_linenumber" name="L33" href="#L33">33</a> <em class="jxr_javadoccomment"> * @see <a href="<a href="https://mathworld.wolfram.com/GumbelDistribution.html" target="alexandria_uri">https://mathworld.wolfram.com/GumbelDistribution.html</a>">Gumbel distribution (MathWorld)</a></em>
+<a class="jxr_linenumber" name="L34" href="#L34">34</a> <em class="jxr_javadoccomment"> */</em>
+<a class="jxr_linenumber" name="L35" href="#L35">35</a> <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">class</strong> <a name="GumbelDistribution" href="../../../../../org/apache/commons/statistics/distribution/GumbelDistribution.html#GumbelDistribution">GumbelDistribution</a> <strong class="jxr_keyword">extends</strong> <a name="AbstractContinuousDistribution" href="../../../../../org/apache/commons/statistics/distribution/AbstractContinuousDistribution.html#AbstractContinuousDistribution">AbstractContinuousDistribution</a> {
+<a class="jxr_linenumber" name="L36" href="#L36">36</a> <em class="jxr_javadoccomment">/** Support lower bound. */</em>
+<a class="jxr_linenumber" name="L37" href="#L37">37</a> <strong class="jxr_keyword">private</strong> <strong class="jxr_keyword">static</strong> <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> SUPPORT_LO = Double.NEGATIVE_INFINITY;
+<a class="jxr_linenumber" name="L38" href="#L38">38</a> <em class="jxr_javadoccomment">/** Support upper bound. */</em>
+<a class="jxr_linenumber" name="L39" href="#L39">39</a> <strong class="jxr_keyword">private</strong> <strong class="jxr_keyword">static</strong> <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> SUPPORT_HI = Double.POSITIVE_INFINITY;
+<a class="jxr_linenumber" name="L40" href="#L40">40</a> <em class="jxr_javadoccomment">/** &pi;<sup>2</sup>/6. */</em>
+<a class="jxr_linenumber" name="L41" href="#L41">41</a> <strong class="jxr_keyword">private</strong> <strong class="jxr_keyword">static</strong> <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> PI_SQUARED_OVER_SIX = Math.PI * Math.PI / 6;
+<a class="jxr_linenumber" name="L42" href="#L42">42</a> <em class="jxr_javadoccomment">/**</em>
+<a class="jxr_linenumber" name="L43" href="#L43">43</a> <em class="jxr_javadoccomment"> * <a href="<a href="https://en.wikipedia.org/wiki/Euler%27s_constant" target="alexandria_uri">https://en.wikipedia.org/wiki/Euler%27s_constant</a>"></em>
+<a class="jxr_linenumber" name="L44" href="#L44">44</a> <em class="jxr_javadoccomment"> * Approximation of Euler's constant</a>.</em>
+<a class="jxr_linenumber" name="L45" href="#L45">45</a> <em class="jxr_javadoccomment"> */</em>
+<a class="jxr_linenumber" name="L46" href="#L46">46</a> <strong class="jxr_keyword">private</strong> <strong class="jxr_keyword">static</strong> <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> EULER = 0.57721566490153286060;
+<a class="jxr_linenumber" name="L47" href="#L47">47</a> <em class="jxr_javadoccomment">/** ln(ln(2)). */</em>
+<a class="jxr_linenumber" name="L48" href="#L48">48</a> <strong class="jxr_keyword">private</strong> <strong class="jxr_keyword">static</strong> <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> LN_LN_2 = -0.3665129205816643270124;
+<a class="jxr_linenumber" name="L49" href="#L49">49</a> <em class="jxr_javadoccomment">/** Location parameter. */</em>
+<a class="jxr_linenumber" name="L50" href="#L50">50</a> <strong class="jxr_keyword">private</strong> <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> mu;
+<a class="jxr_linenumber" name="L51" href="#L51">51</a> <em class="jxr_javadoccomment">/** Scale parameter. */</em>
+<a class="jxr_linenumber" name="L52" href="#L52">52</a> <strong class="jxr_keyword">private</strong> <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> beta;
+<a class="jxr_linenumber" name="L53" href="#L53">53</a>
+<a class="jxr_linenumber" name="L54" href="#L54">54</a> <em class="jxr_javadoccomment">/**</em>
+<a class="jxr_linenumber" name="L55" href="#L55">55</a> <em class="jxr_javadoccomment"> * @param mu Location parameter.</em>
+<a class="jxr_linenumber" name="L56" href="#L56">56</a> <em class="jxr_javadoccomment"> * @param beta Scale parameter (must be positive).</em>
+<a class="jxr_linenumber" name="L57" href="#L57">57</a> <em class="jxr_javadoccomment"> */</em>
+<a class="jxr_linenumber" name="L58" href="#L58">58</a> <strong class="jxr_keyword">private</strong> <a name="GumbelDistribution" href="../../../../../org/apache/commons/statistics/distribution/GumbelDistribution.html#GumbelDistribution">GumbelDistribution</a>(<strong class="jxr_keyword">double</strong> mu,
+<a class="jxr_linenumber" name="L59" href="#L59">59</a> <strong class="jxr_keyword">double</strong> beta) {
+<a class="jxr_linenumber" name="L60" href="#L60">60</a> <strong class="jxr_keyword">this</strong>.beta = beta;
+<a class="jxr_linenumber" name="L61" href="#L61">61</a> <strong class="jxr_keyword">this</strong>.mu = mu;
+<a class="jxr_linenumber" name="L62" href="#L62">62</a> }
+<a class="jxr_linenumber" name="L63" href="#L63">63</a>
+<a class="jxr_linenumber" name="L64" href="#L64">64</a> <em class="jxr_javadoccomment">/**</em>
+<a class="jxr_linenumber" name="L65" href="#L65">65</a> <em class="jxr_javadoccomment"> * Creates a Gumbel distribution.</em>
+<a class="jxr_linenumber" name="L66" href="#L66">66</a> <em class="jxr_javadoccomment"> *</em>
+<a class="jxr_linenumber" name="L67" href="#L67">67</a> <em class="jxr_javadoccomment"> * @param mu Location parameter.</em>
+<a class="jxr_linenumber" name="L68" href="#L68">68</a> <em class="jxr_javadoccomment"> * @param beta Scale parameter (must be positive).</em>
+<a class="jxr_linenumber" name="L69" href="#L69">69</a> <em class="jxr_javadoccomment"> * @return the distribution</em>
+<a class="jxr_linenumber" name="L70" href="#L70">70</a> <em class="jxr_javadoccomment"> * @throws IllegalArgumentException if {@code beta <= 0}</em>
+<a class="jxr_linenumber" name="L71" href="#L71">71</a> <em class="jxr_javadoccomment"> */</em>
+<a class="jxr_linenumber" name="L72" href="#L72">72</a> <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">static</strong> <a name="GumbelDistribution" href="../../../../../org/apache/commons/statistics/distribution/GumbelDistribution.html#GumbelDistribution">GumbelDistribution</a> of(<strong class="jxr_keyword">double</strong> mu,
+<a class="jxr_linenumber" name="L73" href="#L73">73</a> <strong class="jxr_keyword">double</strong> beta) {
+<a class="jxr_linenumber" name="L74" href="#L74">74</a> <strong class="jxr_keyword">if</strong> (beta <= 0) {
+<a class="jxr_linenumber" name="L75" href="#L75">75</a> <strong class="jxr_keyword">throw</strong> <strong class="jxr_keyword">new</strong> <a name="DistributionException" href="../../../../../org/apache/commons/statistics/distribution/DistributionException.html#DistributionException">DistributionException</a>(DistributionException.NOT_STRICTLY_POSITIVE, beta);
+<a class="jxr_linenumber" name="L76" href="#L76">76</a> }
+<a class="jxr_linenumber" name="L77" href="#L77">77</a> <strong class="jxr_keyword">return</strong> <strong class="jxr_keyword">new</strong> <a name="GumbelDistribution" href="../../../../../org/apache/commons/statistics/distribution/GumbelDistribution.html#GumbelDistribution">GumbelDistribution</a>(mu, beta);
+<a class="jxr_linenumber" name="L78" href="#L78">78</a> }
+<a class="jxr_linenumber" name="L79" href="#L79">79</a>
+<a class="jxr_linenumber" name="L80" href="#L80">80</a> <em class="jxr_javadoccomment">/**</em>
+<a class="jxr_linenumber" name="L81" href="#L81">81</a> <em class="jxr_javadoccomment"> * Gets the location parameter of this distribution.</em>
+<a class="jxr_linenumber" name="L82" href="#L82">82</a> <em class="jxr_javadoccomment"> *</em>
+<a class="jxr_linenumber" name="L83" href="#L83">83</a> <em class="jxr_javadoccomment"> * @return the location parameter.</em>
+<a class="jxr_linenumber" name="L84" href="#L84">84</a> <em class="jxr_javadoccomment"> */</em>
+<a class="jxr_linenumber" name="L85" href="#L85">85</a> <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">double</strong> getLocation() {
+<a class="jxr_linenumber" name="L86" href="#L86">86</a> <strong class="jxr_keyword">return</strong> mu;
+<a class="jxr_linenumber" name="L87" href="#L87">87</a> }
+<a class="jxr_linenumber" name="L88" href="#L88">88</a>
+<a class="jxr_linenumber" name="L89" href="#L89">89</a> <em class="jxr_javadoccomment">/**</em>
+<a class="jxr_linenumber" name="L90" href="#L90">90</a> <em class="jxr_javadoccomment"> * Gets the scale parameter of this distribution.</em>
+<a class="jxr_linenumber" name="L91" href="#L91">91</a> <em class="jxr_javadoccomment"> *</em>
+<a class="jxr_linenumber" name="L92" href="#L92">92</a> <em class="jxr_javadoccomment"> * @return the scale parameter.</em>
+<a class="jxr_linenumber" name="L93" href="#L93">93</a> <em class="jxr_javadoccomment"> */</em>
+<a class="jxr_linenumber" name="L94" href="#L94">94</a> <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">double</strong> getScale() {
+<a class="jxr_linenumber" name="L95" href="#L95">95</a> <strong class="jxr_keyword">return</strong> beta;
+<a class="jxr_linenumber" name="L96" href="#L96">96</a> }
+<a class="jxr_linenumber" name="L97" href="#L97">97</a>
+<a class="jxr_linenumber" name="L98" href="#L98">98</a> <em class="jxr_javadoccomment">/** {@inheritDoc} */</em>
+<a class="jxr_linenumber" name="L99" href="#L99">99</a> @Override
+<a class="jxr_linenumber" name="L100" href="#L100">100</a> <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">double</strong> density(<strong class="jxr_keyword">double</strong> x) {
+<a class="jxr_linenumber" name="L101" href="#L101">101</a> <strong class="jxr_keyword">if</strong> (x <= SUPPORT_LO) {
+<a class="jxr_linenumber" name="L102" href="#L102">102</a> <strong class="jxr_keyword">return</strong> 0;
+<a class="jxr_linenumber" name="L103" href="#L103">103</a> }
+<a class="jxr_linenumber" name="L104" href="#L104">104</a>
+<a class="jxr_linenumber" name="L105" href="#L105">105</a> <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> z = (x - mu) / beta;
+<a class="jxr_linenumber" name="L106" href="#L106">106</a> <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> t = Math.exp(-z);
+<a class="jxr_linenumber" name="L107" href="#L107">107</a> <strong class="jxr_keyword">return</strong> Math.exp(-z - t) / beta;
+<a class="jxr_linenumber" name="L108" href="#L108">108</a> }
+<a class="jxr_linenumber" name="L109" href="#L109">109</a>
+<a class="jxr_linenumber" name="L110" href="#L110">110</a> <em class="jxr_javadoccomment">/** {@inheritDoc} */</em>
+<a class="jxr_linenumber" name="L111" href="#L111">111</a> @Override
+<a class="jxr_linenumber" name="L112" href="#L112">112</a> <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">double</strong> logDensity(<strong class="jxr_keyword">double</strong> x) {
+<a class="jxr_linenumber" name="L113" href="#L113">113</a> <strong class="jxr_keyword">if</strong> (x <= SUPPORT_LO) {
+<a class="jxr_linenumber" name="L114" href="#L114">114</a> <strong class="jxr_keyword">return</strong> Double.NEGATIVE_INFINITY;
+<a class="jxr_linenumber" name="L115" href="#L115">115</a> }
+<a class="jxr_linenumber" name="L116" href="#L116">116</a>
+<a class="jxr_linenumber" name="L117" href="#L117">117</a> <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> z = (x - mu) / beta;
+<a class="jxr_linenumber" name="L118" href="#L118">118</a> <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> t = Math.exp(-z);
+<a class="jxr_linenumber" name="L119" href="#L119">119</a> <strong class="jxr_keyword">return</strong> -z - t - Math.log(beta);
+<a class="jxr_linenumber" name="L120" href="#L120">120</a> }
+<a class="jxr_linenumber" name="L121" href="#L121">121</a>
+<a class="jxr_linenumber" name="L122" href="#L122">122</a> <em class="jxr_javadoccomment">/** {@inheritDoc} */</em>
+<a class="jxr_linenumber" name="L123" href="#L123">123</a> @Override
+<a class="jxr_linenumber" name="L124" href="#L124">124</a> <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">double</strong> cumulativeProbability(<strong class="jxr_keyword">double</strong> x) {
+<a class="jxr_linenumber" name="L125" href="#L125">125</a> <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> z = (x - mu) / beta;
+<a class="jxr_linenumber" name="L126" href="#L126">126</a> <strong class="jxr_keyword">return</strong> Math.exp(-Math.exp(-z));
+<a class="jxr_linenumber" name="L127" href="#L127">127</a> }
+<a class="jxr_linenumber" name="L128" href="#L128">128</a>
+<a class="jxr_linenumber" name="L129" href="#L129">129</a> <em class="jxr_javadoccomment">/** {@inheritDoc} */</em>
+<a class="jxr_linenumber" name="L130" href="#L130">130</a> @Override
+<a class="jxr_linenumber" name="L131" href="#L131">131</a> <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">double</strong> survivalProbability(<strong class="jxr_keyword">double</strong> x) {
+<a class="jxr_linenumber" name="L132" href="#L132">132</a> <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> z = (x - mu) / beta;
+<a class="jxr_linenumber" name="L133" href="#L133">133</a> <strong class="jxr_keyword">return</strong> -Math.expm1(-Math.exp(-z));
+<a class="jxr_linenumber" name="L134" href="#L134">134</a> }
+<a class="jxr_linenumber" name="L135" href="#L135">135</a>
+<a class="jxr_linenumber" name="L136" href="#L136">136</a> <em class="jxr_javadoccomment">/** {@inheritDoc} */</em>
+<a class="jxr_linenumber" name="L137" href="#L137">137</a> @Override
+<a class="jxr_linenumber" name="L138" href="#L138">138</a> <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">double</strong> inverseCumulativeProbability(<strong class="jxr_keyword">double</strong> p) {
+<a class="jxr_linenumber" name="L139" href="#L139">139</a> ArgumentUtils.checkProbability(p);
+<a class="jxr_linenumber" name="L140" href="#L140">140</a> <strong class="jxr_keyword">if</strong> (p == 0) {
+<a class="jxr_linenumber" name="L141" href="#L141">141</a> <strong class="jxr_keyword">return</strong> Double.NEGATIVE_INFINITY;
+<a class="jxr_linenumber" name="L142" href="#L142">142</a> } <strong class="jxr_keyword">else</strong> <strong class="jxr_keyword">if</strong> (p == 1) {
+<a class="jxr_linenumber" name="L143" href="#L143">143</a> <strong class="jxr_keyword">return</strong> Double.POSITIVE_INFINITY;
+<a class="jxr_linenumber" name="L144" href="#L144">144</a> }
+<a class="jxr_linenumber" name="L145" href="#L145">145</a> <strong class="jxr_keyword">return</strong> mu - Math.log(-Math.log(p)) * beta;
+<a class="jxr_linenumber" name="L146" href="#L146">146</a> }
+<a class="jxr_linenumber" name="L147" href="#L147">147</a>
+<a class="jxr_linenumber" name="L148" href="#L148">148</a> <em class="jxr_javadoccomment">/** {@inheritDoc} */</em>
+<a class="jxr_linenumber" name="L149" href="#L149">149</a> @Override
+<a class="jxr_linenumber" name="L150" href="#L150">150</a> <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">double</strong> inverseSurvivalProbability(<strong class="jxr_keyword">double</strong> p) {
+<a class="jxr_linenumber" name="L151" href="#L151">151</a> ArgumentUtils.checkProbability(p);
+<a class="jxr_linenumber" name="L152" href="#L152">152</a> <strong class="jxr_keyword">if</strong> (p == 1) {
+<a class="jxr_linenumber" name="L153" href="#L153">153</a> <strong class="jxr_keyword">return</strong> Double.NEGATIVE_INFINITY;
+<a class="jxr_linenumber" name="L154" href="#L154">154</a> } <strong class="jxr_keyword">else</strong> <strong class="jxr_keyword">if</strong> (p == 0) {
+<a class="jxr_linenumber" name="L155" href="#L155">155</a> <strong class="jxr_keyword">return</strong> Double.POSITIVE_INFINITY;
+<a class="jxr_linenumber" name="L156" href="#L156">156</a> }
+<a class="jxr_linenumber" name="L157" href="#L157">157</a> <strong class="jxr_keyword">return</strong> mu - Math.log(-Math.log1p(-p)) * beta;
+<a class="jxr_linenumber" name="L158" href="#L158">158</a> }
+<a class="jxr_linenumber" name="L159" href="#L159">159</a>
+<a class="jxr_linenumber" name="L160" href="#L160">160</a> <em class="jxr_javadoccomment">/**</em>
+<a class="jxr_linenumber" name="L161" href="#L161">161</a> <em class="jxr_javadoccomment"> * {@inheritDoc}</em>
+<a class="jxr_linenumber" name="L162" href="#L162">162</a> <em class="jxr_javadoccomment"> *</em>
+<a class="jxr_linenumber" name="L163" href="#L163">163</a> <em class="jxr_javadoccomment"> * <p>For location parameter \( \mu \) and scale parameter \( \beta \), the mean is:</em>
+<a class="jxr_linenumber" name="L164" href="#L164">164</a> <em class="jxr_javadoccomment"> *</em>
+<a class="jxr_linenumber" name="L165" href="#L165">165</a> <em class="jxr_javadoccomment"> * <p>\[ \mu + \beta \gamma \]</em>
+<a class="jxr_linenumber" name="L166" href="#L166">166</a> <em class="jxr_javadoccomment"> *</em>
+<a class="jxr_linenumber" name="L167" href="#L167">167</a> <em class="jxr_javadoccomment"> * <p>where \( \gamma \) is the</em>
+<a class="jxr_linenumber" name="L168" href="#L168">168</a> <em class="jxr_javadoccomment"> * <a href="<a href="https://mathworld.wolfram.com/Euler-MascheroniConstantApproximations.html" target="alexandria_uri">https://mathworld.wolfram.com/Euler-MascheroniConstantApproximations.html</a>"></em>
+<a class="jxr_linenumber" name="L169" href="#L169">169</a> <em class="jxr_javadoccomment"> * Euler-Mascheroni constant</a>.</em>
+<a class="jxr_linenumber" name="L170" href="#L170">170</a> <em class="jxr_javadoccomment"> */</em>
+<a class="jxr_linenumber" name="L171" href="#L171">171</a> @Override
+<a class="jxr_linenumber" name="L172" href="#L172">172</a> <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">double</strong> getMean() {
+<a class="jxr_linenumber" name="L173" href="#L173">173</a> <strong class="jxr_keyword">return</strong> mu + EULER * beta;
+<a class="jxr_linenumber" name="L174" href="#L174">174</a> }
+<a class="jxr_linenumber" name="L175" href="#L175">175</a>
+<a class="jxr_linenumber" name="L176" href="#L176">176</a> <em class="jxr_javadoccomment">/**</em>
+<a class="jxr_linenumber" name="L177" href="#L177">177</a> <em class="jxr_javadoccomment"> * {@inheritDoc}</em>
+<a class="jxr_linenumber" name="L178" href="#L178">178</a> <em class="jxr_javadoccomment"> *</em>
+<a class="jxr_linenumber" name="L179" href="#L179">179</a> <em class="jxr_javadoccomment"> * <p>For scale parameter \( \beta \), the variance is:</em>
+<a class="jxr_linenumber" name="L180" href="#L180">180</a> <em class="jxr_javadoccomment"> *</em>
+<a class="jxr_linenumber" name="L181" href="#L181">181</a> <em class="jxr_javadoccomment"> * <p>\[ \frac{\pi^2}{6} \beta^2 \]</em>
+<a class="jxr_linenumber" name="L182" href="#L182">182</a> <em class="jxr_javadoccomment"> */</em>
+<a class="jxr_linenumber" name="L183" href="#L183">183</a> @Override
+<a class="jxr_linenumber" name="L184" href="#L184">184</a> <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">double</strong> getVariance() {
+<a class="jxr_linenumber" name="L185" href="#L185">185</a> <strong class="jxr_keyword">return</strong> PI_SQUARED_OVER_SIX * beta * beta;
+<a class="jxr_linenumber" name="L186" href="#L186">186</a> }
+<a class="jxr_linenumber" name="L187" href="#L187">187</a>
+<a class="jxr_linenumber" name="L188" href="#L188">188</a> <em class="jxr_javadoccomment">/**</em>
+<a class="jxr_linenumber" name="L189" href="#L189">189</a> <em class="jxr_javadoccomment"> * {@inheritDoc}</em>
+<a class="jxr_linenumber" name="L190" href="#L190">190</a> <em class="jxr_javadoccomment"> *</em>
+<a class="jxr_linenumber" name="L191" href="#L191">191</a> <em class="jxr_javadoccomment"> * <p>The lower bound of the support is always negative infinity.</em>
+<a class="jxr_linenumber" name="L192" href="#L192">192</a> <em class="jxr_javadoccomment"> *</em>
+<a class="jxr_linenumber" name="L193" href="#L193">193</a> <em class="jxr_javadoccomment"> * @return {@link Double#NEGATIVE_INFINITY negative infinity}.</em>
+<a class="jxr_linenumber" name="L194" href="#L194">194</a> <em class="jxr_javadoccomment"> */</em>
+<a class="jxr_linenumber" name="L195" href="#L195">195</a> @Override
+<a class="jxr_linenumber" name="L196" href="#L196">196</a> <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">double</strong> getSupportLowerBound() {
+<a class="jxr_linenumber" name="L197" href="#L197">197</a> <strong class="jxr_keyword">return</strong> SUPPORT_LO;
+<a class="jxr_linenumber" name="L198" href="#L198">198</a> }
+<a class="jxr_linenumber" name="L199" href="#L199">199</a>
+<a class="jxr_linenumber" name="L200" href="#L200">200</a> <em class="jxr_javadoccomment">/**</em>
+<a class="jxr_linenumber" name="L201" href="#L201">201</a> <em class="jxr_javadoccomment"> * {@inheritDoc}</em>
+<a class="jxr_linenumber" name="L202" href="#L202">202</a> <em class="jxr_javadoccomment"> *</em>
+<a class="jxr_linenumber" name="L203" href="#L203">203</a> <em class="jxr_javadoccomment"> * <p>The upper bound of the support is always positive infinity.</em>
+<a class="jxr_linenumber" name="L204" href="#L204">204</a> <em class="jxr_javadoccomment"> *</em>
+<a class="jxr_linenumber" name="L205" href="#L205">205</a> <em class="jxr_javadoccomment"> * @return {@link Double#POSITIVE_INFINITY positive infinity}.</em>
+<a class="jxr_linenumber" name="L206" href="#L206">206</a> <em class="jxr_javadoccomment"> */</em>
+<a class="jxr_linenumber" name="L207" href="#L207">207</a> @Override
+<a class="jxr_linenumber" name="L208" href="#L208">208</a> <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">double</strong> getSupportUpperBound() {
+<a class="jxr_linenumber" name="L209" href="#L209">209</a> <strong class="jxr_keyword">return</strong> SUPPORT_HI;
+<a class="jxr_linenumber" name="L210" href="#L210">210</a> }
+<a class="jxr_linenumber" name="L211" href="#L211">211</a>
+<a class="jxr_linenumber" name="L212" href="#L212">212</a> <em class="jxr_javadoccomment">/** {@inheritDoc} */</em>
+<a class="jxr_linenumber" name="L213" href="#L213">213</a> @Override
+<a class="jxr_linenumber" name="L214" href="#L214">214</a> <strong class="jxr_keyword">double</strong> getMedian() {
+<a class="jxr_linenumber" name="L215" href="#L215">215</a> <em class="jxr_comment">// Overridden for the probability(double, double) method.</em>
+<a class="jxr_linenumber" name="L216" href="#L216">216</a> <em class="jxr_comment">// This is intentionally not a public method.</em>
+<a class="jxr_linenumber" name="L217" href="#L217">217</a> <em class="jxr_comment">// u - beta * ln(ln(2))</em>
+<a class="jxr_linenumber" name="L218" href="#L218">218</a> <strong class="jxr_keyword">return</strong> mu - beta * LN_LN_2;
+<a class="jxr_linenumber" name="L219" href="#L219">219</a> }
+<a class="jxr_linenumber" name="L220" href="#L220">220</a> }
+</pre>
+<hr/>
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