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Added: dev/commons/statistics/1.0-RC1/site/xref/org/apache/commons/statistics/distribution/WeibullDistribution.html
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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>WeibullDistribution xref</title>
+<link type="text/css" rel="stylesheet" href="../../../../../stylesheet.css" />
+</head>
+<body>
+<div id="overview"><a href="../../../../../../apidocs/org/apache/commons/statistics/distribution/WeibullDistribution.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>
+<a class="jxr_linenumber" name="L18" href="#L18">18</a> <strong class="jxr_keyword">package</strong> org.apache.commons.statistics.distribution;
+<a class="jxr_linenumber" name="L19" href="#L19">19</a>
+<a class="jxr_linenumber" name="L20" href="#L20">20</a> <strong class="jxr_keyword">import</strong> org.apache.commons.numbers.gamma.LogGamma;
+<a class="jxr_linenumber" name="L21" href="#L21">21</a> <strong class="jxr_keyword">import</strong> org.apache.commons.rng.UniformRandomProvider;
+<a class="jxr_linenumber" name="L22" href="#L22">22</a> <strong class="jxr_keyword">import</strong> org.apache.commons.rng.sampling.distribution.ZigguratSampler;
+<a class="jxr_linenumber" name="L23" href="#L23">23</a>
+<a class="jxr_linenumber" name="L24" href="#L24">24</a> <em class="jxr_javadoccomment">/**</em>
+<a class="jxr_linenumber" name="L25" href="#L25">25</a> <em class="jxr_javadoccomment"> * Implementation of the Weibull distribution.</em>
+<a class="jxr_linenumber" name="L26" href="#L26">26</a> <em class="jxr_javadoccomment"> *</em>
+<a class="jxr_linenumber" name="L27" href="#L27">27</a> <em class="jxr_javadoccomment"> * <p>The probability density function of \( X \) is:</em>
+<a class="jxr_linenumber" name="L28" href="#L28">28</a> <em class="jxr_javadoccomment"> *</em>
+<a class="jxr_linenumber" name="L29" href="#L29">29</a> <em class="jxr_javadoccomment"> * <p>\[ f(x;k,\lambda) = \frac{k}{\lambda}\left(\frac{x}{\lambda}\right)^{k-1}e^{-(x/\lambda)^{k}} \]</em>
+<a class="jxr_linenumber" name="L30" href="#L30">30</a> <em class="jxr_javadoccomment"> *</em>
+<a class="jxr_linenumber" name="L31" href="#L31">31</a> <em class="jxr_javadoccomment"> * <p>for \( k &gt; 0 \) the shape,</em>
+<a class="jxr_linenumber" name="L32" href="#L32">32</a> <em class="jxr_javadoccomment"> * \( \lambda &gt; 0 \) the scale, and</em>
+<a class="jxr_linenumber" name="L33" href="#L33">33</a> <em class="jxr_javadoccomment"> * \( x \in (0, \infty) \).</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> <em class="jxr_javadoccomment"> * <p>Note the special cases:</em>
+<a class="jxr_linenumber" name="L36" href="#L36">36</a> <em class="jxr_javadoccomment"> * <ul></em>
+<a class="jxr_linenumber" name="L37" href="#L37">37</a> <em class="jxr_javadoccomment"> * <li>\( k = 1 \) is the exponential distribution</em>
+<a class="jxr_linenumber" name="L38" href="#L38">38</a> <em class="jxr_javadoccomment"> * <li>\( k = 2 \) is the Rayleigh distribution with scale \( \sigma = \frac {\lambda}{\sqrt{2}} \)</em>
+<a class="jxr_linenumber" name="L39" href="#L39">39</a> <em class="jxr_javadoccomment"> * </ul></em>
+<a class="jxr_linenumber" name="L40" href="#L40">40</a> <em class="jxr_javadoccomment"> *</em>
+<a class="jxr_linenumber" name="L41" href="#L41">41</a> <em class="jxr_javadoccomment"> * @see <a href="<a href="https://en.wikipedia.org/wiki/Weibull_distribution" target="alexandria_uri">https://en.wikipedia.org/wiki/Weibull_distribution</a>">Weibull distribution (Wikipedia)</a></em>
+<a class="jxr_linenumber" name="L42" href="#L42">42</a> <em class="jxr_javadoccomment"> * @see <a href="<a href="https://mathworld.wolfram.com/WeibullDistribution.html" target="alexandria_uri">https://mathworld.wolfram.com/WeibullDistribution.html</a>">Weibull distribution (MathWorld)</a></em>
+<a class="jxr_linenumber" name="L43" href="#L43">43</a> <em class="jxr_javadoccomment"> */</em>
+<a class="jxr_linenumber" name="L44" href="#L44">44</a> <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">class</strong> <a name="WeibullDistribution" href="../../../../../org/apache/commons/statistics/distribution/WeibullDistribution.html#WeibullDistribution">WeibullDistribution</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="L45" href="#L45">45</a> <em class="jxr_javadoccomment">/** Support lower bound. */</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> SUPPORT_LO = 0;
+<a class="jxr_linenumber" name="L47" href="#L47">47</a> <em class="jxr_javadoccomment">/** Support upper bound. */</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> SUPPORT_HI = Double.POSITIVE_INFINITY;
+<a class="jxr_linenumber" name="L49" href="#L49">49</a> <em class="jxr_javadoccomment">/** The shape 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> shape;
+<a class="jxr_linenumber" name="L51" href="#L51">51</a> <em class="jxr_javadoccomment">/** The 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> scale;
+<a class="jxr_linenumber" name="L53" href="#L53">53</a> <em class="jxr_javadoccomment">/** shape / scale. */</em>
+<a class="jxr_linenumber" name="L54" href="#L54">54</a> <strong class="jxr_keyword">private</strong> <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> shapeOverScale;
+<a class="jxr_linenumber" name="L55" href="#L55">55</a> <em class="jxr_javadoccomment">/** log(shape / scale). */</em>
+<a class="jxr_linenumber" name="L56" href="#L56">56</a> <strong class="jxr_keyword">private</strong> <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> logShapeOverScale;
+<a class="jxr_linenumber" name="L57" href="#L57">57</a>
+<a class="jxr_linenumber" name="L58" href="#L58">58</a> <em class="jxr_javadoccomment">/**</em>
+<a class="jxr_linenumber" name="L59" href="#L59">59</a> <em class="jxr_javadoccomment"> * @param shape Shape parameter.</em>
+<a class="jxr_linenumber" name="L60" href="#L60">60</a> <em class="jxr_javadoccomment"> * @param scale Scale parameter.</em>
+<a class="jxr_linenumber" name="L61" href="#L61">61</a> <em class="jxr_javadoccomment"> */</em>
+<a class="jxr_linenumber" name="L62" href="#L62">62</a> <strong class="jxr_keyword">private</strong> <a name="WeibullDistribution" href="../../../../../org/apache/commons/statistics/distribution/WeibullDistribution.html#WeibullDistribution">WeibullDistribution</a>(<strong class="jxr_keyword">double</strong> shape,
+<a class="jxr_linenumber" name="L63" href="#L63">63</a> <strong class="jxr_keyword">double</strong> scale) {
+<a class="jxr_linenumber" name="L64" href="#L64">64</a> <strong class="jxr_keyword">this</strong>.scale = scale;
+<a class="jxr_linenumber" name="L65" href="#L65">65</a> <strong class="jxr_keyword">this</strong>.shape = shape;
+<a class="jxr_linenumber" name="L66" href="#L66">66</a> shapeOverScale = shape / scale;
+<a class="jxr_linenumber" name="L67" href="#L67">67</a> logShapeOverScale = Math.log(shapeOverScale);
+<a class="jxr_linenumber" name="L68" href="#L68">68</a> }
+<a class="jxr_linenumber" name="L69" href="#L69">69</a>
+<a class="jxr_linenumber" name="L70" href="#L70">70</a> <em class="jxr_javadoccomment">/**</em>
+<a class="jxr_linenumber" name="L71" href="#L71">71</a> <em class="jxr_javadoccomment"> * Creates a Weibull distribution.</em>
+<a class="jxr_linenumber" name="L72" href="#L72">72</a> <em class="jxr_javadoccomment"> *</em>
+<a class="jxr_linenumber" name="L73" href="#L73">73</a> <em class="jxr_javadoccomment"> * @param shape Shape parameter.</em>
+<a class="jxr_linenumber" name="L74" href="#L74">74</a> <em class="jxr_javadoccomment"> * @param scale Scale parameter.</em>
+<a class="jxr_linenumber" name="L75" href="#L75">75</a> <em class="jxr_javadoccomment"> * @return the distribution</em>
+<a class="jxr_linenumber" name="L76" href="#L76">76</a> <em class="jxr_javadoccomment"> * @throws IllegalArgumentException if {@code shape <= 0} or {@code scale <= 0}.</em>
+<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> <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">static</strong> <a name="WeibullDistribution" href="../../../../../org/apache/commons/statistics/distribution/WeibullDistribution.html#WeibullDistribution">WeibullDistribution</a> of(<strong class="jxr_keyword">double</strong> shape,
+<a class="jxr_linenumber" name="L79" href="#L79">79</a> <strong class="jxr_keyword">double</strong> scale) {
+<a class="jxr_linenumber" name="L80" href="#L80">80</a> <strong class="jxr_keyword">if</strong> (shape <= 0) {
+<a class="jxr_linenumber" name="L81" href="#L81">81</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,
+<a class="jxr_linenumber" name="L82" href="#L82">82</a> shape);
+<a class="jxr_linenumber" name="L83" href="#L83">83</a> }
+<a class="jxr_linenumber" name="L84" href="#L84">84</a> <strong class="jxr_keyword">if</strong> (scale <= 0) {
+<a class="jxr_linenumber" name="L85" href="#L85">85</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,
+<a class="jxr_linenumber" name="L86" href="#L86">86</a> scale);
+<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="WeibullDistribution" href="../../../../../org/apache/commons/statistics/distribution/WeibullDistribution.html#WeibullDistribution">WeibullDistribution</a>(shape, scale);
+<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 shape 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 shape parameter.</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> getShape() {
+<a class="jxr_linenumber" name="L97" href="#L97">97</a> <strong class="jxr_keyword">return</strong> shape;
+<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">/**</em>
+<a class="jxr_linenumber" name="L101" href="#L101">101</a> <em class="jxr_javadoccomment"> * Gets the scale parameter of this distribution.</em>
+<a class="jxr_linenumber" name="L102" href="#L102">102</a> <em class="jxr_javadoccomment"> *</em>
+<a class="jxr_linenumber" name="L103" href="#L103">103</a> <em class="jxr_javadoccomment"> * @return the scale parameter.</em>
+<a class="jxr_linenumber" name="L104" href="#L104">104</a> <em class="jxr_javadoccomment"> */</em>
+<a class="jxr_linenumber" name="L105" href="#L105">105</a> <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">double</strong> getScale() {
+<a class="jxr_linenumber" name="L106" href="#L106">106</a> <strong class="jxr_keyword">return</strong> scale;
+<a class="jxr_linenumber" name="L107" href="#L107">107</a> }
+<a class="jxr_linenumber" name="L108" href="#L108">108</a>
+<a class="jxr_linenumber" name="L109" href="#L109">109</a> <em class="jxr_javadoccomment">/** {@inheritDoc}</em>
+<a class="jxr_linenumber" name="L110" href="#L110">110</a> <em class="jxr_javadoccomment"> *</em>
+<a class="jxr_linenumber" name="L111" href="#L111">111</a> <em class="jxr_javadoccomment"> * <p>Returns the limit when {@code x = 0}:</em>
+<a class="jxr_linenumber" name="L112" href="#L112">112</a> <em class="jxr_javadoccomment"> * <ul></em>
+<a class="jxr_linenumber" name="L113" href="#L113">113</a> <em class="jxr_javadoccomment"> * <li>{@code shape < 1}: Infinity</em>
+<a class="jxr_linenumber" name="L114" href="#L114">114</a> <em class="jxr_javadoccomment"> * <li>{@code shape == 1}: 1 / scale</em>
+<a class="jxr_linenumber" name="L115" href="#L115">115</a> <em class="jxr_javadoccomment"> * <li>{@code shape > 1}: 0</em>
+<a class="jxr_linenumber" name="L116" href="#L116">116</a> <em class="jxr_javadoccomment"> * </ul></em>
+<a class="jxr_linenumber" name="L117" href="#L117">117</a> <em class="jxr_javadoccomment"> */</em>
+<a class="jxr_linenumber" name="L118" href="#L118">118</a> @Override
+<a class="jxr_linenumber" name="L119" href="#L119">119</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="L120" href="#L120">120</a> <strong class="jxr_keyword">if</strong> (x <= SUPPORT_LO || x >= SUPPORT_HI) {
+<a class="jxr_linenumber" name="L121" href="#L121">121</a> <em class="jxr_comment">// Special case x=0</em>
+<a class="jxr_linenumber" name="L122" href="#L122">122</a> <strong class="jxr_keyword">if</strong> (x == SUPPORT_LO && shape <= 1) {
+<a class="jxr_linenumber" name="L123" href="#L123">123</a> <strong class="jxr_keyword">return</strong> shape == 1 ?
+<a class="jxr_linenumber" name="L124" href="#L124">124</a> <em class="jxr_comment">// Exponential distribution</em>
+<a class="jxr_linenumber" name="L125" href="#L125">125</a> shapeOverScale :
+<a class="jxr_linenumber" name="L126" href="#L126">126</a> Double.POSITIVE_INFINITY;
+<a class="jxr_linenumber" name="L127" href="#L127">127</a> }
+<a class="jxr_linenumber" name="L128" href="#L128">128</a> <strong class="jxr_keyword">return</strong> 0;
+<a class="jxr_linenumber" name="L129" href="#L129">129</a> }
+<a class="jxr_linenumber" name="L130" href="#L130">130</a>
+<a class="jxr_linenumber" name="L131" href="#L131">131</a> <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> xscale = x / scale;
+<a class="jxr_linenumber" name="L132" href="#L132">132</a> <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> xscalepow = Math.pow(xscale, shape - 1);
+<a class="jxr_linenumber" name="L133" href="#L133">133</a>
+<a class="jxr_linenumber" name="L134" href="#L134">134</a> <em class="jxr_comment">/*</em>
+<a class="jxr_linenumber" name="L135" href="#L135">135</a> <em class="jxr_comment"> * Math.pow(x / scale, shape) =</em>
+<a class="jxr_linenumber" name="L136" href="#L136">136</a> <em class="jxr_comment"> * Math.pow(xscale, shape) =</em>
+<a class="jxr_linenumber" name="L137" href="#L137">137</a> <em class="jxr_comment"> * Math.pow(xscale, shape - 1) * xscale</em>
+<a class="jxr_linenumber" name="L138" href="#L138">138</a> <em class="jxr_comment"> */</em>
+<a class="jxr_linenumber" name="L139" href="#L139">139</a> <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> xscalepowshape = xscalepow * xscale;
+<a class="jxr_linenumber" name="L140" href="#L140">140</a>
+<a class="jxr_linenumber" name="L141" href="#L141">141</a> <strong class="jxr_keyword">return</strong> shapeOverScale * xscalepow * Math.exp(-xscalepowshape);
+<a class="jxr_linenumber" name="L142" href="#L142">142</a> }
+<a class="jxr_linenumber" name="L143" href="#L143">143</a>
+<a class="jxr_linenumber" name="L144" href="#L144">144</a> <em class="jxr_javadoccomment">/** {@inheritDoc}</em>
+<a class="jxr_linenumber" name="L145" href="#L145">145</a> <em class="jxr_javadoccomment"> *</em>
+<a class="jxr_linenumber" name="L146" href="#L146">146</a> <em class="jxr_javadoccomment"> * <p>Returns the limit when {@code x = 0}:</em>
+<a class="jxr_linenumber" name="L147" href="#L147">147</a> <em class="jxr_javadoccomment"> * <ul></em>
+<a class="jxr_linenumber" name="L148" href="#L148">148</a> <em class="jxr_javadoccomment"> * <li>{@code shape < 1}: Infinity</em>
+<a class="jxr_linenumber" name="L149" href="#L149">149</a> <em class="jxr_javadoccomment"> * <li>{@code shape == 1}: log(1 / scale)</em>
+<a class="jxr_linenumber" name="L150" href="#L150">150</a> <em class="jxr_javadoccomment"> * <li>{@code shape > 1}: -Infinity</em>
+<a class="jxr_linenumber" name="L151" href="#L151">151</a> <em class="jxr_javadoccomment"> * </ul></em>
+<a class="jxr_linenumber" name="L152" href="#L152">152</a> <em class="jxr_javadoccomment"> */</em>
+<a class="jxr_linenumber" name="L153" href="#L153">153</a> @Override
+<a class="jxr_linenumber" name="L154" href="#L154">154</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="L155" href="#L155">155</a> <strong class="jxr_keyword">if</strong> (x <= SUPPORT_LO || x >= SUPPORT_HI) {
+<a class="jxr_linenumber" name="L156" href="#L156">156</a> <em class="jxr_comment">// Special case x=0</em>
+<a class="jxr_linenumber" name="L157" href="#L157">157</a> <strong class="jxr_keyword">if</strong> (x == SUPPORT_LO && shape <= 1) {
+<a class="jxr_linenumber" name="L158" href="#L158">158</a> <strong class="jxr_keyword">return</strong> shape == 1 ?
+<a class="jxr_linenumber" name="L159" href="#L159">159</a> <em class="jxr_comment">// Exponential distribution</em>
+<a class="jxr_linenumber" name="L160" href="#L160">160</a> logShapeOverScale :
+<a class="jxr_linenumber" name="L161" href="#L161">161</a> Double.POSITIVE_INFINITY;
+<a class="jxr_linenumber" name="L162" href="#L162">162</a> }
+<a class="jxr_linenumber" name="L163" href="#L163">163</a> <strong class="jxr_keyword">return</strong> Double.NEGATIVE_INFINITY;
+<a class="jxr_linenumber" name="L164" href="#L164">164</a> }
+<a class="jxr_linenumber" name="L165" href="#L165">165</a>
+<a class="jxr_linenumber" name="L166" href="#L166">166</a> <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> xscale = x / scale;
+<a class="jxr_linenumber" name="L167" href="#L167">167</a> <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> logxscalepow = Math.log(xscale) * (shape - 1);
+<a class="jxr_linenumber" name="L168" href="#L168">168</a>
+<a class="jxr_linenumber" name="L169" href="#L169">169</a> <em class="jxr_comment">/*</em>
+<a class="jxr_linenumber" name="L170" href="#L170">170</a> <em class="jxr_comment"> * Math.pow(x / scale, shape) =</em>
+<a class="jxr_linenumber" name="L171" href="#L171">171</a> <em class="jxr_comment"> * Math.pow(xscale, shape) =</em>
+<a class="jxr_linenumber" name="L172" href="#L172">172</a> <em class="jxr_comment"> * Math.pow(xscale, shape - 1) * xscale</em>
+<a class="jxr_linenumber" name="L173" href="#L173">173</a> <em class="jxr_comment"> * Math.exp(log(xscale) * (shape - 1)) * xscale</em>
+<a class="jxr_linenumber" name="L174" href="#L174">174</a> <em class="jxr_comment"> */</em>
+<a class="jxr_linenumber" name="L175" href="#L175">175</a> <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> xscalepowshape = Math.exp(logxscalepow) * xscale;
+<a class="jxr_linenumber" name="L176" href="#L176">176</a>
+<a class="jxr_linenumber" name="L177" href="#L177">177</a> <strong class="jxr_keyword">return</strong> logShapeOverScale + logxscalepow - xscalepowshape;
+<a class="jxr_linenumber" name="L178" href="#L178">178</a> }
+<a class="jxr_linenumber" name="L179" href="#L179">179</a>
+<a class="jxr_linenumber" name="L180" href="#L180">180</a> <em class="jxr_javadoccomment">/** {@inheritDoc} */</em>
+<a class="jxr_linenumber" name="L181" href="#L181">181</a> @Override
+<a class="jxr_linenumber" name="L182" href="#L182">182</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="L183" href="#L183">183</a> <strong class="jxr_keyword">if</strong> (x <= SUPPORT_LO) {
+<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> <strong class="jxr_keyword">return</strong> -Math.expm1(-Math.pow(x / scale, shape));
+<a class="jxr_linenumber" name="L188" href="#L188">188</a> }
+<a class="jxr_linenumber" name="L189" href="#L189">189</a>
+<a class="jxr_linenumber" name="L190" href="#L190">190</a> <em class="jxr_javadoccomment">/** {@inheritDoc} */</em>
+<a class="jxr_linenumber" name="L191" href="#L191">191</a> @Override
+<a class="jxr_linenumber" name="L192" href="#L192">192</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="L193" href="#L193">193</a> <strong class="jxr_keyword">if</strong> (x <= SUPPORT_LO) {
+<a class="jxr_linenumber" name="L194" href="#L194">194</a> <strong class="jxr_keyword">return</strong> 1;
+<a class="jxr_linenumber" name="L195" href="#L195">195</a> }
+<a class="jxr_linenumber" name="L196" href="#L196">196</a>
+<a class="jxr_linenumber" name="L197" href="#L197">197</a> <strong class="jxr_keyword">return</strong> Math.exp(-Math.pow(x / scale, shape));
+<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>Returns {@code 0} when {@code p == 0} and</em>
+<a class="jxr_linenumber" name="L204" href="#L204">204</a> <em class="jxr_javadoccomment"> * {@link Double#POSITIVE_INFINITY} when {@code p == 1}.</em>
+<a class="jxr_linenumber" name="L205" href="#L205">205</a> <em class="jxr_javadoccomment"> */</em>
+<a class="jxr_linenumber" name="L206" href="#L206">206</a> @Override
+<a class="jxr_linenumber" name="L207" href="#L207">207</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="L208" href="#L208">208</a> ArgumentUtils.checkProbability(p);
+<a class="jxr_linenumber" name="L209" href="#L209">209</a> <strong class="jxr_keyword">if</strong> (p == 0) {
+<a class="jxr_linenumber" name="L210" href="#L210">210</a> <strong class="jxr_keyword">return</strong> 0.0;
+<a class="jxr_linenumber" name="L211" href="#L211">211</a> } <strong class="jxr_keyword">else</strong> <strong class="jxr_keyword">if</strong> (p == 1) {
+<a class="jxr_linenumber" name="L212" href="#L212">212</a> <strong class="jxr_keyword">return</strong> Double.POSITIVE_INFINITY;
+<a class="jxr_linenumber" name="L213" href="#L213">213</a> }
+<a class="jxr_linenumber" name="L214" href="#L214">214</a> <strong class="jxr_keyword">return</strong> scale * Math.pow(-Math.log1p(-p), 1.0 / shape);
+<a class="jxr_linenumber" name="L215" href="#L215">215</a> }
+<a class="jxr_linenumber" name="L216" href="#L216">216</a>
+<a class="jxr_linenumber" name="L217" href="#L217">217</a> <em class="jxr_javadoccomment">/**</em>
+<a class="jxr_linenumber" name="L218" href="#L218">218</a> <em class="jxr_javadoccomment"> * {@inheritDoc}</em>
+<a class="jxr_linenumber" name="L219" href="#L219">219</a> <em class="jxr_javadoccomment"> *</em>
+<a class="jxr_linenumber" name="L220" href="#L220">220</a> <em class="jxr_javadoccomment"> * <p>Returns {@code 0} when {@code p == 1} and</em>
+<a class="jxr_linenumber" name="L221" href="#L221">221</a> <em class="jxr_javadoccomment"> * {@link Double#POSITIVE_INFINITY} when {@code p == 0}.</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> @Override
+<a class="jxr_linenumber" name="L224" href="#L224">224</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="L225" href="#L225">225</a> ArgumentUtils.checkProbability(p);
+<a class="jxr_linenumber" name="L226" href="#L226">226</a> <strong class="jxr_keyword">if</strong> (p == 1) {
+<a class="jxr_linenumber" name="L227" href="#L227">227</a> <strong class="jxr_keyword">return</strong> 0.0;
+<a class="jxr_linenumber" name="L228" href="#L228">228</a> } <strong class="jxr_keyword">else</strong> <strong class="jxr_keyword">if</strong> (p == 0) {
+<a class="jxr_linenumber" name="L229" href="#L229">229</a> <strong class="jxr_keyword">return</strong> Double.POSITIVE_INFINITY;
+<a class="jxr_linenumber" name="L230" href="#L230">230</a> }
+<a class="jxr_linenumber" name="L231" href="#L231">231</a> <strong class="jxr_keyword">return</strong> scale * Math.pow(-Math.log(p), 1.0 / shape);
+<a class="jxr_linenumber" name="L232" href="#L232">232</a> }
+<a class="jxr_linenumber" name="L233" href="#L233">233</a>
+<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"> * {@inheritDoc}</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> <em class="jxr_javadoccomment"> * <p>For shape parameter \( k \) and scale parameter \( \lambda \), the mean is:</em>
+<a class="jxr_linenumber" name="L238" href="#L238">238</a> <em class="jxr_javadoccomment"> *</em>
+<a class="jxr_linenumber" name="L239" href="#L239">239</a> <em class="jxr_javadoccomment"> * <p>\[ \lambda \, \Gamma(1+\frac{1}{k}) \]</em>
+<a class="jxr_linenumber" name="L240" href="#L240">240</a> <em class="jxr_javadoccomment"> *</em>
+<a class="jxr_linenumber" name="L241" href="#L241">241</a> <em class="jxr_javadoccomment"> * <p>where \( \Gamma \) is the Gamma-function.</em>
+<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> @Override
+<a class="jxr_linenumber" name="L244" href="#L244">244</a> <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">double</strong> getMean() {
+<a class="jxr_linenumber" name="L245" href="#L245">245</a> <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> sh = getShape();
+<a class="jxr_linenumber" name="L246" href="#L246">246</a> <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> sc = getScale();
+<a class="jxr_linenumber" name="L247" href="#L247">247</a>
+<a class="jxr_linenumber" name="L248" href="#L248">248</a> <em class="jxr_comment">// Special case of exponential when shape is 1</em>
+<a class="jxr_linenumber" name="L249" href="#L249">249</a> <strong class="jxr_keyword">return</strong> sh == 1 ? sc : sc * Math.exp(LogGamma.value(1 + (1 / sh)));
+<a class="jxr_linenumber" name="L250" href="#L250">250</a> }
+<a class="jxr_linenumber" name="L251" href="#L251">251</a>
+<a class="jxr_linenumber" name="L252" href="#L252">252</a> <em class="jxr_javadoccomment">/**</em>
+<a class="jxr_linenumber" name="L253" href="#L253">253</a> <em class="jxr_javadoccomment"> * {@inheritDoc}</em>
+<a class="jxr_linenumber" name="L254" href="#L254">254</a> <em class="jxr_javadoccomment"> *</em>
+<a class="jxr_linenumber" name="L255" href="#L255">255</a> <em class="jxr_javadoccomment"> * <p>For shape parameter \( k \) and scale parameter \( \lambda \), the variance is:</em>
+<a class="jxr_linenumber" name="L256" href="#L256">256</a> <em class="jxr_javadoccomment"> *</em>
+<a class="jxr_linenumber" name="L257" href="#L257">257</a> <em class="jxr_javadoccomment"> * <p>\[ \lambda^2 \left[ \Gamma\left(1+\frac{2}{k}\right) -</em>
+<a class="jxr_linenumber" name="L258" href="#L258">258</a> <em class="jxr_javadoccomment"> * \left(\Gamma\left(1+\frac{1}{k}\right)\right)^2 \right] \]</em>
+<a class="jxr_linenumber" name="L259" href="#L259">259</a> <em class="jxr_javadoccomment"> *</em>
+<a class="jxr_linenumber" name="L260" href="#L260">260</a> <em class="jxr_javadoccomment"> * <p>where \( \Gamma \) is the Gamma-function.</em>
+<a class="jxr_linenumber" name="L261" href="#L261">261</a> <em class="jxr_javadoccomment"> */</em>
+<a class="jxr_linenumber" name="L262" href="#L262">262</a> @Override
+<a class="jxr_linenumber" name="L263" href="#L263">263</a> <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">double</strong> getVariance() {
+<a class="jxr_linenumber" name="L264" href="#L264">264</a> <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> sh = getShape();
+<a class="jxr_linenumber" name="L265" href="#L265">265</a> <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> sc = getScale();
+<a class="jxr_linenumber" name="L266" href="#L266">266</a> <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> mn = getMean();
+<a class="jxr_linenumber" name="L267" href="#L267">267</a>
+<a class="jxr_linenumber" name="L268" href="#L268">268</a> <em class="jxr_comment">// Special case of exponential when shape is 1</em>
+<a class="jxr_linenumber" name="L269" href="#L269">269</a> <strong class="jxr_keyword">return</strong> sh == 1 ?
+<a class="jxr_linenumber" name="L270" href="#L270">270</a> sc * sc :
+<a class="jxr_linenumber" name="L271" href="#L271">271</a> (sc * sc) * Math.exp(LogGamma.value(1 + (2 / sh))) -
+<a class="jxr_linenumber" name="L272" href="#L272">272</a> (mn * mn);
+<a class="jxr_linenumber" name="L273" href="#L273">273</a> }
+<a class="jxr_linenumber" name="L274" href="#L274">274</a>
+<a class="jxr_linenumber" name="L275" href="#L275">275</a> <em class="jxr_javadoccomment">/**</em>
+<a class="jxr_linenumber" name="L276" href="#L276">276</a> <em class="jxr_javadoccomment"> * {@inheritDoc}</em>
+<a class="jxr_linenumber" name="L277" href="#L277">277</a> <em class="jxr_javadoccomment"> *</em>
+<a class="jxr_linenumber" name="L278" href="#L278">278</a> <em class="jxr_javadoccomment"> * <p>The lower bound of the support is always 0.</em>
+<a class="jxr_linenumber" name="L279" href="#L279">279</a> <em class="jxr_javadoccomment"> *</em>
+<a class="jxr_linenumber" name="L280" href="#L280">280</a> <em class="jxr_javadoccomment"> * @return 0.</em>
+<a class="jxr_linenumber" name="L281" href="#L281">281</a> <em class="jxr_javadoccomment"> */</em>
+<a class="jxr_linenumber" name="L282" href="#L282">282</a> @Override
+<a class="jxr_linenumber" name="L283" href="#L283">283</a> <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">double</strong> getSupportLowerBound() {
+<a class="jxr_linenumber" name="L284" href="#L284">284</a> <strong class="jxr_keyword">return</strong> SUPPORT_LO;
+<a class="jxr_linenumber" name="L285" href="#L285">285</a> }
+<a class="jxr_linenumber" name="L286" href="#L286">286</a>
+<a class="jxr_linenumber" name="L287" href="#L287">287</a> <em class="jxr_javadoccomment">/**</em>
+<a class="jxr_linenumber" name="L288" href="#L288">288</a> <em class="jxr_javadoccomment"> * {@inheritDoc}</em>
+<a class="jxr_linenumber" name="L289" href="#L289">289</a> <em class="jxr_javadoccomment"> *</em>
+<a class="jxr_linenumber" name="L290" href="#L290">290</a> <em class="jxr_javadoccomment"> * <p>The upper bound of the support is always positive infinity.</em>
+<a class="jxr_linenumber" name="L291" href="#L291">291</a> <em class="jxr_javadoccomment"> *</em>
+<a class="jxr_linenumber" name="L292" href="#L292">292</a> <em class="jxr_javadoccomment"> * @return {@link Double#POSITIVE_INFINITY positive infinity}.</em>
+<a class="jxr_linenumber" name="L293" href="#L293">293</a> <em class="jxr_javadoccomment"> */</em>
+<a class="jxr_linenumber" name="L294" href="#L294">294</a> @Override
+<a class="jxr_linenumber" name="L295" href="#L295">295</a> <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">double</strong> getSupportUpperBound() {
+<a class="jxr_linenumber" name="L296" href="#L296">296</a> <strong class="jxr_keyword">return</strong> SUPPORT_HI;
+<a class="jxr_linenumber" name="L297" href="#L297">297</a> }
+<a class="jxr_linenumber" name="L298" href="#L298">298</a>
+<a class="jxr_linenumber" name="L299" href="#L299">299</a> <em class="jxr_javadoccomment">/** {@inheritDoc} */</em>
+<a class="jxr_linenumber" name="L300" href="#L300">300</a> @Override
+<a class="jxr_linenumber" name="L301" href="#L301">301</a> <strong class="jxr_keyword">public</strong> ContinuousDistribution.Sampler createSampler(<strong class="jxr_keyword">final</strong> UniformRandomProvider rng) {
+<a class="jxr_linenumber" name="L302" href="#L302">302</a> <em class="jxr_comment">// Special case: shape=1 is the exponential distribution</em>
+<a class="jxr_linenumber" name="L303" href="#L303">303</a> <strong class="jxr_keyword">if</strong> (shape == 1) {
+<a class="jxr_linenumber" name="L304" href="#L304">304</a> <em class="jxr_comment">// Exponential distribution sampler.</em>
+<a class="jxr_linenumber" name="L305" href="#L305">305</a> <strong class="jxr_keyword">return</strong> ZigguratSampler.Exponential.of(rng, scale)::sample;
+<a class="jxr_linenumber" name="L306" href="#L306">306</a> }
+<a class="jxr_linenumber" name="L307" href="#L307">307</a> <strong class="jxr_keyword">return</strong> <strong class="jxr_keyword">super</strong>.createSampler(rng);
+<a class="jxr_linenumber" name="L308" href="#L308">308</a> }
+<a class="jxr_linenumber" name="L309" href="#L309">309</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>
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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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+<div id="overview"><a href="../../../../../../apidocs/org/apache/commons/statistics/distribution/ZipfDistribution.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>
+<a class="jxr_linenumber" name="L18" href="#L18">18</a> <strong class="jxr_keyword">package</strong> org.apache.commons.statistics.distribution;
+<a class="jxr_linenumber" name="L19" href="#L19">19</a>
+<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.RejectionInversionZipfSampler;
+<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 Zipf 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>\[ f(k; N, s) = \frac{1/k^s}{H_{N,s}} \]</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 \( N \in \{1, 2, 3, \dots\} \) the number of elements,</em>
+<a class="jxr_linenumber" name="L31" href="#L31">31</a> <em class="jxr_javadoccomment"> * \( s \gt 0 \) the exponent characterizing the distribution,</em>
+<a class="jxr_linenumber" name="L32" href="#L32">32</a> <em class="jxr_javadoccomment"> * \( k \in \{1, 2, \dots, N\} \) the element rank, and</em>
+<a class="jxr_linenumber" name="L33" href="#L33">33</a> <em class="jxr_javadoccomment"> * \( H_{N,s} \) is the normalizing constant which corresponds to the</em>
+<a class="jxr_linenumber" name="L34" href="#L34">34</a> <em class="jxr_javadoccomment"> * <a href="<a href="https://en.wikipedia.org/wiki/Harmonic_number" target="alexandria_uri">https://en.wikipedia.org/wiki/Harmonic_number</a>#Generalized_harmonic_numbers"></em>
+<a class="jxr_linenumber" name="L35" href="#L35">35</a> <em class="jxr_javadoccomment"> * generalized harmonic number</a> of order N of s.</em>
+<a class="jxr_linenumber" name="L36" href="#L36">36</a> <em class="jxr_javadoccomment"> *</em>
+<a class="jxr_linenumber" name="L37" href="#L37">37</a> <em class="jxr_javadoccomment"> * @see <a href="<a href="https://en.wikipedia.org/wiki/Zipf's_law" target="alexandria_uri">https://en.wikipedia.org/wiki/Zipf's_law</a>">Zipf distribution (Wikipedia)</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="ZipfDistribution" href="../../../../../org/apache/commons/statistics/distribution/ZipfDistribution.html#ZipfDistribution">ZipfDistribution</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">/** Number of elements. */</em>
+<a class="jxr_linenumber" name="L41" href="#L41">41</a> <strong class="jxr_keyword">private</strong> <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">int</strong> numberOfElements;
+<a class="jxr_linenumber" name="L42" href="#L42">42</a> <em class="jxr_javadoccomment">/** Exponent parameter of the distribution. */</em>
+<a class="jxr_linenumber" name="L43" href="#L43">43</a> <strong class="jxr_keyword">private</strong> <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> exponent;
+<a class="jxr_linenumber" name="L44" href="#L44">44</a> <em class="jxr_javadoccomment">/** Cached value of the nth generalized harmonic. */</em>
+<a class="jxr_linenumber" name="L45" href="#L45">45</a> <strong class="jxr_keyword">private</strong> <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> nthHarmonic;
+<a class="jxr_linenumber" name="L46" href="#L46">46</a> <em class="jxr_javadoccomment">/** Cached value of the log of the nth generalized harmonic. */</em>
+<a class="jxr_linenumber" name="L47" href="#L47">47</a> <strong class="jxr_keyword">private</strong> <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> logNthHarmonic;
+<a class="jxr_linenumber" name="L48" href="#L48">48</a>
+<a class="jxr_linenumber" name="L49" href="#L49">49</a> <em class="jxr_javadoccomment">/**</em>
+<a class="jxr_linenumber" name="L50" href="#L50">50</a> <em class="jxr_javadoccomment"> * @param numberOfElements Number of elements.</em>
+<a class="jxr_linenumber" name="L51" href="#L51">51</a> <em class="jxr_javadoccomment"> * @param exponent Exponent.</em>
+<a class="jxr_linenumber" name="L52" href="#L52">52</a> <em class="jxr_javadoccomment"> */</em>
+<a class="jxr_linenumber" name="L53" href="#L53">53</a> <strong class="jxr_keyword">private</strong> <a name="ZipfDistribution" href="../../../../../org/apache/commons/statistics/distribution/ZipfDistribution.html#ZipfDistribution">ZipfDistribution</a>(<strong class="jxr_keyword">int</strong> numberOfElements,
+<a class="jxr_linenumber" name="L54" href="#L54">54</a> <strong class="jxr_keyword">double</strong> exponent) {
+<a class="jxr_linenumber" name="L55" href="#L55">55</a> <strong class="jxr_keyword">this</strong>.numberOfElements = numberOfElements;
+<a class="jxr_linenumber" name="L56" href="#L56">56</a> <strong class="jxr_keyword">this</strong>.exponent = exponent;
+<a class="jxr_linenumber" name="L57" href="#L57">57</a> <strong class="jxr_keyword">this</strong>.nthHarmonic = generalizedHarmonic(numberOfElements, exponent);
+<a class="jxr_linenumber" name="L58" href="#L58">58</a> logNthHarmonic = Math.log(nthHarmonic);
+<a class="jxr_linenumber" name="L59" href="#L59">59</a> }
+<a class="jxr_linenumber" name="L60" href="#L60">60</a>
+<a class="jxr_linenumber" name="L61" href="#L61">61</a> <em class="jxr_javadoccomment">/**</em>
+<a class="jxr_linenumber" name="L62" href="#L62">62</a> <em class="jxr_javadoccomment"> * Creates a Zipf distribution.</em>
+<a class="jxr_linenumber" name="L63" href="#L63">63</a> <em class="jxr_javadoccomment"> *</em>
+<a class="jxr_linenumber" name="L64" href="#L64">64</a> <em class="jxr_javadoccomment"> * @param numberOfElements Number of elements.</em>
+<a class="jxr_linenumber" name="L65" href="#L65">65</a> <em class="jxr_javadoccomment"> * @param exponent Exponent.</em>
+<a class="jxr_linenumber" name="L66" href="#L66">66</a> <em class="jxr_javadoccomment"> * @return the distribution</em>
+<a class="jxr_linenumber" name="L67" href="#L67">67</a> <em class="jxr_javadoccomment"> * @exception IllegalArgumentException if {@code numberOfElements <= 0}</em>
+<a class="jxr_linenumber" name="L68" href="#L68">68</a> <em class="jxr_javadoccomment"> * or {@code exponent <= 0}.</em>
+<a class="jxr_linenumber" name="L69" href="#L69">69</a> <em class="jxr_javadoccomment"> */</em>
+<a class="jxr_linenumber" name="L70" href="#L70">70</a> <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">static</strong> <a name="ZipfDistribution" href="../../../../../org/apache/commons/statistics/distribution/ZipfDistribution.html#ZipfDistribution">ZipfDistribution</a> of(<strong class="jxr_keyword">int</strong> numberOfElements,
+<a class="jxr_linenumber" name="L71" href="#L71">71</a> <strong class="jxr_keyword">double</strong> exponent) {
+<a class="jxr_linenumber" name="L72" href="#L72">72</a> <strong class="jxr_keyword">if</strong> (numberOfElements <= 0) {
+<a class="jxr_linenumber" name="L73" href="#L73">73</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,
+<a class="jxr_linenumber" name="L74" href="#L74">74</a> numberOfElements);
+<a class="jxr_linenumber" name="L75" href="#L75">75</a> }
+<a class="jxr_linenumber" name="L76" href="#L76">76</a> <strong class="jxr_keyword">if</strong> (exponent < 0) {
+<a class="jxr_linenumber" name="L77" href="#L77">77</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.NEGATIVE,
+<a class="jxr_linenumber" name="L78" href="#L78">78</a> exponent);
+<a class="jxr_linenumber" name="L79" href="#L79">79</a> }
+<a class="jxr_linenumber" name="L80" href="#L80">80</a> <strong class="jxr_keyword">return</strong> <strong class="jxr_keyword">new</strong> <a name="ZipfDistribution" href="../../../../../org/apache/commons/statistics/distribution/ZipfDistribution.html#ZipfDistribution">ZipfDistribution</a>(numberOfElements, exponent);
+<a class="jxr_linenumber" name="L81" href="#L81">81</a> }
+<a class="jxr_linenumber" name="L82" href="#L82">82</a>
+<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> <em class="jxr_javadoccomment"> * Gets the number of elements parameter of this distribution.</em>
+<a class="jxr_linenumber" name="L85" href="#L85">85</a> <em class="jxr_javadoccomment"> *</em>
+<a class="jxr_linenumber" name="L86" href="#L86">86</a> <em class="jxr_javadoccomment"> * @return the number of elements.</em>
+<a class="jxr_linenumber" name="L87" href="#L87">87</a> <em class="jxr_javadoccomment"> */</em>
+<a class="jxr_linenumber" name="L88" href="#L88">88</a> <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">int</strong> getNumberOfElements() {
+<a class="jxr_linenumber" name="L89" href="#L89">89</a> <strong class="jxr_keyword">return</strong> numberOfElements;
+<a class="jxr_linenumber" name="L90" href="#L90">90</a> }
+<a class="jxr_linenumber" name="L91" href="#L91">91</a>
+<a class="jxr_linenumber" name="L92" href="#L92">92</a> <em class="jxr_javadoccomment">/**</em>
+<a class="jxr_linenumber" name="L93" href="#L93">93</a> <em class="jxr_javadoccomment"> * Gets the exponent parameter of this distribution.</em>
+<a class="jxr_linenumber" name="L94" href="#L94">94</a> <em class="jxr_javadoccomment"> *</em>
+<a class="jxr_linenumber" name="L95" href="#L95">95</a> <em class="jxr_javadoccomment"> * @return the exponent.</em>
+<a class="jxr_linenumber" name="L96" href="#L96">96</a> <em class="jxr_javadoccomment"> */</em>
+<a class="jxr_linenumber" name="L97" href="#L97">97</a> <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">double</strong> getExponent() {
+<a class="jxr_linenumber" name="L98" href="#L98">98</a> <strong class="jxr_keyword">return</strong> exponent;
+<a class="jxr_linenumber" name="L99" href="#L99">99</a> }
+<a class="jxr_linenumber" name="L100" href="#L100">100</a>
+<a class="jxr_linenumber" name="L101" href="#L101">101</a> <em class="jxr_javadoccomment">/** {@inheritDoc} */</em>
+<a class="jxr_linenumber" name="L102" href="#L102">102</a> @Override
+<a class="jxr_linenumber" name="L103" href="#L103">103</a> <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">double</strong> probability(<strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">int</strong> x) {
+<a class="jxr_linenumber" name="L104" href="#L104">104</a> <strong class="jxr_keyword">if</strong> (x <= 0 || x > numberOfElements) {
+<a class="jxr_linenumber" name="L105" href="#L105">105</a> <strong class="jxr_keyword">return</strong> 0;
+<a class="jxr_linenumber" name="L106" href="#L106">106</a> }
+<a class="jxr_linenumber" name="L107" href="#L107">107</a>
+<a class="jxr_linenumber" name="L108" href="#L108">108</a> <strong class="jxr_keyword">return</strong> Math.pow(x, -exponent) / nthHarmonic;
+<a class="jxr_linenumber" name="L109" href="#L109">109</a> }
+<a class="jxr_linenumber" name="L110" href="#L110">110</a>
+<a class="jxr_linenumber" name="L111" href="#L111">111</a> <em class="jxr_javadoccomment">/** {@inheritDoc} */</em>
+<a class="jxr_linenumber" name="L112" href="#L112">112</a> @Override
+<a class="jxr_linenumber" name="L113" href="#L113">113</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="L114" href="#L114">114</a> <strong class="jxr_keyword">if</strong> (x <= 0 || x > numberOfElements) {
+<a class="jxr_linenumber" name="L115" href="#L115">115</a> <strong class="jxr_keyword">return</strong> Double.NEGATIVE_INFINITY;
+<a class="jxr_linenumber" name="L116" href="#L116">116</a> }
+<a class="jxr_linenumber" name="L117" href="#L117">117</a>
+<a class="jxr_linenumber" name="L118" href="#L118">118</a> <strong class="jxr_keyword">return</strong> -Math.log(x) * exponent - logNthHarmonic;
+<a class="jxr_linenumber" name="L119" href="#L119">119</a> }
+<a class="jxr_linenumber" name="L120" href="#L120">120</a>
+<a class="jxr_linenumber" name="L121" href="#L121">121</a> <em class="jxr_javadoccomment">/** {@inheritDoc} */</em>
+<a class="jxr_linenumber" name="L122" href="#L122">122</a> @Override
+<a class="jxr_linenumber" name="L123" href="#L123">123</a> <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">double</strong> cumulativeProbability(<strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">int</strong> x) {
+<a class="jxr_linenumber" name="L124" href="#L124">124</a> <strong class="jxr_keyword">if</strong> (x <= 0) {
+<a class="jxr_linenumber" name="L125" href="#L125">125</a> <strong class="jxr_keyword">return</strong> 0;
+<a class="jxr_linenumber" name="L126" href="#L126">126</a> } <strong class="jxr_keyword">else</strong> <strong class="jxr_keyword">if</strong> (x >= numberOfElements) {
+<a class="jxr_linenumber" name="L127" href="#L127">127</a> <strong class="jxr_keyword">return</strong> 1;
+<a class="jxr_linenumber" name="L128" href="#L128">128</a> }
+<a class="jxr_linenumber" name="L129" href="#L129">129</a>
+<a class="jxr_linenumber" name="L130" href="#L130">130</a> <strong class="jxr_keyword">return</strong> generalizedHarmonic(x, exponent) / nthHarmonic;
+<a class="jxr_linenumber" name="L131" href="#L131">131</a> }
+<a class="jxr_linenumber" name="L132" href="#L132">132</a>
+<a class="jxr_linenumber" name="L133" href="#L133">133</a> <em class="jxr_javadoccomment">/** {@inheritDoc} */</em>
+<a class="jxr_linenumber" name="L134" href="#L134">134</a> @Override
+<a class="jxr_linenumber" name="L135" href="#L135">135</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="L136" href="#L136">136</a> <strong class="jxr_keyword">if</strong> (x <= 0) {
+<a class="jxr_linenumber" name="L137" href="#L137">137</a> <strong class="jxr_keyword">return</strong> 1;
+<a class="jxr_linenumber" name="L138" href="#L138">138</a> } <strong class="jxr_keyword">else</strong> <strong class="jxr_keyword">if</strong> (x >= numberOfElements) {
+<a class="jxr_linenumber" name="L139" href="#L139">139</a> <strong class="jxr_keyword">return</strong> 0;
+<a class="jxr_linenumber" name="L140" href="#L140">140</a> }
+<a class="jxr_linenumber" name="L141" href="#L141">141</a>
+<a class="jxr_linenumber" name="L142" href="#L142">142</a> <em class="jxr_comment">// See http://www.math.wm.edu/~leemis/chart/UDR/PDFs/Zipf.pdf</em>
+<a class="jxr_linenumber" name="L143" href="#L143">143</a> <em class="jxr_comment">// S(x) = P(X > x) = ((x+1)^a Hn,a - (x+1)^a Hx+1,a + 1) / ((x+1)^a Hn,a)</em>
+<a class="jxr_linenumber" name="L144" href="#L144">144</a> <em class="jxr_comment">// where a = exponent and Hx,a is the generalized harmonic for x with exponent a.</em>
+<a class="jxr_linenumber" name="L145" href="#L145">145</a> <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> z = Math.pow(x + 1.0, exponent);
+<a class="jxr_linenumber" name="L146" href="#L146">146</a> <em class="jxr_comment">// Compute generalizedHarmonic(x, exponent) and generalizedHarmonic(x+1, exponent)</em>
+<a class="jxr_linenumber" name="L147" href="#L147">147</a> <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> hx = generalizedHarmonic(x, exponent);
+<a class="jxr_linenumber" name="L148" href="#L148">148</a> <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> hx1 = hx + Math.pow(x + 1.0, -exponent);
+<a class="jxr_linenumber" name="L149" href="#L149">149</a> <em class="jxr_comment">// Compute the survival function</em>
+<a class="jxr_linenumber" name="L150" href="#L150">150</a> <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> p = (z * (nthHarmonic - hx1) + 1) / (z * nthHarmonic);
+<a class="jxr_linenumber" name="L151" href="#L151">151</a> <em class="jxr_comment">// May overflow for large exponent so validate the probability.</em>
+<a class="jxr_linenumber" name="L152" href="#L152">152</a> <em class="jxr_comment">// If this occurs revert to 1 - CDF(x), reusing the generalized harmonic for x</em>
+<a class="jxr_linenumber" name="L153" href="#L153">153</a> <strong class="jxr_keyword">return</strong> p <= 1.0 ? p : 1.0 - hx / nthHarmonic;
+<a class="jxr_linenumber" name="L154" href="#L154">154</a> }
+<a class="jxr_linenumber" name="L155" href="#L155">155</a>
+<a class="jxr_linenumber" name="L156" href="#L156">156</a> <em class="jxr_javadoccomment">/**</em>
+<a class="jxr_linenumber" name="L157" href="#L157">157</a> <em class="jxr_javadoccomment"> * {@inheritDoc}</em>
+<a class="jxr_linenumber" name="L158" href="#L158">158</a> <em class="jxr_javadoccomment"> *</em>
+<a class="jxr_linenumber" name="L159" href="#L159">159</a> <em class="jxr_javadoccomment"> * <p>For number of elements \( N \) and exponent \( s \), the mean is:</em>
+<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"> * <p>\[ \frac{H_{N,s-1}}{H_{N,s}} \]</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>where \( H_{N,k} \) is the</em>
+<a class="jxr_linenumber" name="L164" href="#L164">164</a> <em class="jxr_javadoccomment"> * <a href="<a href="https://en.wikipedia.org/wiki/Harmonic_number" target="alexandria_uri">https://en.wikipedia.org/wiki/Harmonic_number</a>#Generalized_harmonic_numbers"></em>
+<a class="jxr_linenumber" name="L165" href="#L165">165</a> <em class="jxr_javadoccomment"> * generalized harmonic number</a> of order \( N \) of \( k \).</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> @Override
+<a class="jxr_linenumber" name="L168" href="#L168">168</a> <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">double</strong> getMean() {
+<a class="jxr_linenumber" name="L169" href="#L169">169</a> <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">int</strong> N = getNumberOfElements();
+<a class="jxr_linenumber" name="L170" href="#L170">170</a> <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> s = getExponent();
+<a class="jxr_linenumber" name="L171" href="#L171">171</a>
+<a class="jxr_linenumber" name="L172" href="#L172">172</a> <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> Hs1 = generalizedHarmonicAscendingSum(N, s - 1);
+<a class="jxr_linenumber" name="L173" href="#L173">173</a>
+<a class="jxr_linenumber" name="L174" href="#L174">174</a> <strong class="jxr_keyword">return</strong> Hs1 / nthHarmonic;
+<a class="jxr_linenumber" name="L175" href="#L175">175</a> }
+<a class="jxr_linenumber" name="L176" href="#L176">176</a>
+<a class="jxr_linenumber" name="L177" href="#L177">177</a> <em class="jxr_javadoccomment">/**</em>
+<a class="jxr_linenumber" name="L178" href="#L178">178</a> <em class="jxr_javadoccomment"> * {@inheritDoc}</em>
+<a class="jxr_linenumber" name="L179" href="#L179">179</a> <em class="jxr_javadoccomment"> *</em>
+<a class="jxr_linenumber" name="L180" href="#L180">180</a> <em class="jxr_javadoccomment"> * <p>For number of elements \( N \) and exponent \( s \), the variance is:</em>
+<a class="jxr_linenumber" name="L181" href="#L181">181</a> <em class="jxr_javadoccomment"> *</em>
+<a class="jxr_linenumber" name="L182" href="#L182">182</a> <em class="jxr_javadoccomment"> * <p>\[ \frac{H_{N,s-2}}{H_{N,s}} - \frac{H_{N,s-1}^2}{H_{N,s}^2} \]</em>
+<a class="jxr_linenumber" name="L183" href="#L183">183</a> <em class="jxr_javadoccomment"> *</em>
+<a class="jxr_linenumber" name="L184" href="#L184">184</a> <em class="jxr_javadoccomment"> * <p>where \( H_{N,k} \) is the</em>
+<a class="jxr_linenumber" name="L185" href="#L185">185</a> <em class="jxr_javadoccomment"> * <a href="<a href="https://en.wikipedia.org/wiki/Harmonic_number" target="alexandria_uri">https://en.wikipedia.org/wiki/Harmonic_number</a>#Generalized_harmonic_numbers"></em>
+<a class="jxr_linenumber" name="L186" href="#L186">186</a> <em class="jxr_javadoccomment"> * generalized harmonic number</a> of order \( N \) of \( k \).</em>
+<a class="jxr_linenumber" name="L187" href="#L187">187</a> <em class="jxr_javadoccomment"> */</em>
+<a class="jxr_linenumber" name="L188" href="#L188">188</a> @Override
+<a class="jxr_linenumber" name="L189" href="#L189">189</a> <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">double</strong> getVariance() {
+<a class="jxr_linenumber" name="L190" href="#L190">190</a> <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">int</strong> N = getNumberOfElements();
+<a class="jxr_linenumber" name="L191" href="#L191">191</a> <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> s = getExponent();
+<a class="jxr_linenumber" name="L192" href="#L192">192</a>
+<a class="jxr_linenumber" name="L193" href="#L193">193</a> <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> Hs2 = generalizedHarmonicAscendingSum(N, s - 2);
+<a class="jxr_linenumber" name="L194" href="#L194">194</a> <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> Hs1 = generalizedHarmonicAscendingSum(N, s - 1);
+<a class="jxr_linenumber" name="L195" href="#L195">195</a> <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> Hs = nthHarmonic;
+<a class="jxr_linenumber" name="L196" href="#L196">196</a>
+<a class="jxr_linenumber" name="L197" href="#L197">197</a> <strong class="jxr_keyword">return</strong> (Hs2 / Hs) - ((Hs1 * Hs1) / (Hs * Hs));
+<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"> * Calculates the Nth generalized harmonic number. See</em>
+<a class="jxr_linenumber" name="L202" href="#L202">202</a> <em class="jxr_javadoccomment"> * <a href="<a href="https://mathworld.wolfram.com/HarmonicSeries.html" target="alexandria_uri">https://mathworld.wolfram.com/HarmonicSeries.html</a>">Harmonic</em>
+<a class="jxr_linenumber" name="L203" href="#L203">203</a> <em class="jxr_javadoccomment"> * Series</a>.</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"> * <p>Assumes {@code exponent > 0} to arrange the terms to sum from small to large.</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> <em class="jxr_javadoccomment"> * @param n Term in the series to calculate (must be larger than 1)</em>
+<a class="jxr_linenumber" name="L208" href="#L208">208</a> <em class="jxr_javadoccomment"> * @param m Exponent (special case {@code m = 1} is the harmonic series).</em>
+<a class="jxr_linenumber" name="L209" href="#L209">209</a> <em class="jxr_javadoccomment"> * @return the n<sup>th</sup> generalized harmonic number.</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> <strong class="jxr_keyword">private</strong> <strong class="jxr_keyword">static</strong> <strong class="jxr_keyword">double</strong> generalizedHarmonic(<strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">int</strong> n, <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> m) {
+<a class="jxr_linenumber" name="L212" href="#L212">212</a> <strong class="jxr_keyword">double</strong> value = 0;
+<a class="jxr_linenumber" name="L213" href="#L213">213</a> <em class="jxr_comment">// Sum small to large</em>
+<a class="jxr_linenumber" name="L214" href="#L214">214</a> <strong class="jxr_keyword">for</strong> (<strong class="jxr_keyword">int</strong> k = n; k >= 1; k--) {
+<a class="jxr_linenumber" name="L215" href="#L215">215</a> value += Math.pow(k, -m);
+<a class="jxr_linenumber" name="L216" href="#L216">216</a> }
+<a class="jxr_linenumber" name="L217" href="#L217">217</a> <strong class="jxr_keyword">return</strong> value;
+<a class="jxr_linenumber" name="L218" href="#L218">218</a> }
+<a class="jxr_linenumber" name="L219" href="#L219">219</a>
+<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"> * Calculates the Nth generalized harmonic number.</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>Checks the value of the {@code exponent} to arrange the terms to sum from from small to large.</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> <em class="jxr_javadoccomment"> * @param n Term in the series to calculate (must be larger than 1)</em>
+<a class="jxr_linenumber" name="L226" href="#L226">226</a> <em class="jxr_javadoccomment"> * @param m Exponent (special case {@code m = 1} is the harmonic series).</em>
+<a class="jxr_linenumber" name="L227" href="#L227">227</a> <em class="jxr_javadoccomment"> * @return the n<sup>th</sup> generalized harmonic number.</em>
+<a class="jxr_linenumber" name="L228" href="#L228">228</a> <em class="jxr_javadoccomment"> */</em>
+<a class="jxr_linenumber" name="L229" href="#L229">229</a> <strong class="jxr_keyword">private</strong> <strong class="jxr_keyword">static</strong> <strong class="jxr_keyword">double</strong> generalizedHarmonicAscendingSum(<strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">int</strong> n, <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> m) {
+<a class="jxr_linenumber" name="L230" href="#L230">230</a> <strong class="jxr_keyword">double</strong> value = 0;
+<a class="jxr_linenumber" name="L231" href="#L231">231</a> <em class="jxr_comment">// Sum small to large</em>
+<a class="jxr_linenumber" name="L232" href="#L232">232</a> <em class="jxr_comment">// If m < 0 then sum ascending, otherwise descending</em>
+<a class="jxr_linenumber" name="L233" href="#L233">233</a> <strong class="jxr_keyword">if</strong> (m < 0) {
+<a class="jxr_linenumber" name="L234" href="#L234">234</a> <strong class="jxr_keyword">for</strong> (<strong class="jxr_keyword">int</strong> k = 1; k <= n; k++) {
+<a class="jxr_linenumber" name="L235" href="#L235">235</a> value += Math.pow(k, -m);
+<a class="jxr_linenumber" name="L236" href="#L236">236</a> }
+<a class="jxr_linenumber" name="L237" href="#L237">237</a> } <strong class="jxr_keyword">else</strong> {
+<a class="jxr_linenumber" name="L238" href="#L238">238</a> <strong class="jxr_keyword">for</strong> (<strong class="jxr_keyword">int</strong> k = n; k >= 1; k--) {
+<a class="jxr_linenumber" name="L239" href="#L239">239</a> value += Math.pow(k, -m);
+<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> <strong class="jxr_keyword">return</strong> value;
+<a class="jxr_linenumber" name="L243" href="#L243">243</a> }
+<a class="jxr_linenumber" name="L244" href="#L244">244</a>
+<a class="jxr_linenumber" name="L245" href="#L245">245</a> <em class="jxr_javadoccomment">/**</em>
+<a class="jxr_linenumber" name="L246" href="#L246">246</a> <em class="jxr_javadoccomment"> * {@inheritDoc}</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"> * <p>The lower bound of the support is always 1.</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> <em class="jxr_javadoccomment"> * @return 1.</em>
+<a class="jxr_linenumber" name="L251" href="#L251">251</a> <em class="jxr_javadoccomment"> */</em>
+<a class="jxr_linenumber" name="L252" href="#L252">252</a> @Override
+<a class="jxr_linenumber" name="L253" href="#L253">253</a> <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">int</strong> getSupportLowerBound() {
+<a class="jxr_linenumber" name="L254" href="#L254">254</a> <strong class="jxr_keyword">return</strong> 1;
+<a class="jxr_linenumber" name="L255" href="#L255">255</a> }
+<a class="jxr_linenumber" name="L256" href="#L256">256</a>
+<a class="jxr_linenumber" name="L257" href="#L257">257</a> <em class="jxr_javadoccomment">/**</em>
+<a class="jxr_linenumber" name="L258" href="#L258">258</a> <em class="jxr_javadoccomment"> * {@inheritDoc}</em>
+<a class="jxr_linenumber" name="L259" href="#L259">259</a> <em class="jxr_javadoccomment"> *</em>
+<a class="jxr_linenumber" name="L260" href="#L260">260</a> <em class="jxr_javadoccomment"> * <p>The upper bound of the support is the number of elements.</em>
+<a class="jxr_linenumber" name="L261" href="#L261">261</a> <em class="jxr_javadoccomment"> *</em>
+<a class="jxr_linenumber" name="L262" href="#L262">262</a> <em class="jxr_javadoccomment"> * @return number of elements.</em>
+<a class="jxr_linenumber" name="L263" href="#L263">263</a> <em class="jxr_javadoccomment"> */</em>
+<a class="jxr_linenumber" name="L264" href="#L264">264</a> @Override
+<a class="jxr_linenumber" name="L265" href="#L265">265</a> <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">int</strong> getSupportUpperBound() {
+<a class="jxr_linenumber" name="L266" href="#L266">266</a> <strong class="jxr_keyword">return</strong> getNumberOfElements();
+<a class="jxr_linenumber" name="L267" href="#L267">267</a> }
+<a class="jxr_linenumber" name="L268" href="#L268">268</a>
+<a class="jxr_linenumber" name="L269" href="#L269">269</a> <em class="jxr_javadoccomment">/** {@inheritDoc} */</em>
+<a class="jxr_linenumber" name="L270" href="#L270">270</a> @Override
+<a class="jxr_linenumber" name="L271" href="#L271">271</a> <strong class="jxr_keyword">public</strong> DiscreteDistribution.Sampler createSampler(<strong class="jxr_keyword">final</strong> UniformRandomProvider rng) {
+<a class="jxr_linenumber" name="L272" href="#L272">272</a> <em class="jxr_comment">// Zipf distribution sampler.</em>
+<a class="jxr_linenumber" name="L273" href="#L273">273</a> <strong class="jxr_keyword">return</strong> RejectionInversionZipfSampler.of(rng, numberOfElements, exponent)::sample;
+<a class="jxr_linenumber" name="L274" href="#L274">274</a> }
+<a class="jxr_linenumber" name="L275" href="#L275">275</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>
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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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+ <a href="AbstractDiscreteDistribution.html#AbstractDiscreteDistribution" target="classFrame">AbstractDiscreteDistribution</a>
+ </li>
+ <li>
+ <a href="ArgumentUtils.html#ArgumentUtils" target="classFrame">ArgumentUtils</a>
+ </li>
+ <li>
+ <a href="BetaDistribution.html#BetaDistribution" target="classFrame">BetaDistribution</a>
+ </li>
+ <li>
+ <a href="BinomialDistribution.html#BinomialDistribution" target="classFrame">BinomialDistribution</a>
+ </li>
+ <li>
+ <a href="CauchyDistribution.html#CauchyDistribution" target="classFrame">CauchyDistribution</a>
+ </li>
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+ <a href="ChiSquaredDistribution.html#ChiSquaredDistribution" target="classFrame">ChiSquaredDistribution</a>
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+ </li>
+ <li>
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+ <a href="TDistribution.html#TDistribution.NormalTDistribution" target="classFrame">TDistribution.NormalTDistribution</a>
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+ <a href="TDistribution.html#TDistribution.StudentsTDistribution" target="classFrame">TDistribution.StudentsTDistribution</a>
+ </li>
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+ <a href="TrapezoidalDistribution.html#TrapezoidalDistribution" target="classFrame">TrapezoidalDistribution</a>
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+ <li>
+ <a href="TrapezoidalDistribution.html#TrapezoidalDistribution.DelegatedTrapezoidalDistribution" target="classFrame">TrapezoidalDistribution.DelegatedTrapezoidalDistribution</a>
+ </li>
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+ <a href="TrapezoidalDistribution.html#TrapezoidalDistribution.RegularTrapezoidalDistribution" target="classFrame">TrapezoidalDistribution.RegularTrapezoidalDistribution</a>
+ </li>
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+ <a href="TrapezoidalDistribution.html#TrapezoidalDistribution.TriangularTrapezoidalDistribution" target="classFrame">TrapezoidalDistribution.TriangularTrapezoidalDistribution</a>
+ </li>
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+ <a href="TrapezoidalDistribution.html#TrapezoidalDistribution.UniformTrapezoidalDistribution" target="classFrame">TrapezoidalDistribution.UniformTrapezoidalDistribution</a>
+ </li>
+ <li>
+ <a href="TriangularDistribution.html#TriangularDistribution" target="classFrame">TriangularDistribution</a>
+ </li>
+ <li>
+ <a href="TruncatedNormalDistribution.html#TruncatedNormalDistribution" target="classFrame">TruncatedNormalDistribution</a>
+ </li>
+ <li>
+ <a href="UniformContinuousDistribution.html#UniformContinuousDistribution" target="classFrame">UniformContinuousDistribution</a>
+ </li>
+ <li>
+ <a href="UniformDiscreteDistribution.html#UniformDiscreteDistribution" target="classFrame">UniformDiscreteDistribution</a>
+ </li>
+ <li>
+ <a href="WeibullDistribution.html#WeibullDistribution" target="classFrame">WeibullDistribution</a>
+ </li>
+ <li>
+ <a href="ZipfDistribution.html#ZipfDistribution" target="classFrame">ZipfDistribution</a>
+ </li>
+ </ul>
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