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+<div id="overview"><a href="../../../../../../testapidocs/org/apache/commons/statistics/distribution/ParetoDistributionTest.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.simple.RandomSource;
+<a class="jxr_linenumber" name="L22" href="#L22">22</a> <strong class="jxr_keyword">import</strong> org.junit.jupiter.api.Assertions;
+<a class="jxr_linenumber" name="L23" href="#L23">23</a> <strong class="jxr_keyword">import</strong> org.junit.jupiter.api.Test;
+<a class="jxr_linenumber" name="L24" href="#L24">24</a> <strong class="jxr_keyword">import</strong> org.junit.jupiter.params.ParameterizedTest;
+<a class="jxr_linenumber" name="L25" href="#L25">25</a> <strong class="jxr_keyword">import</strong> org.junit.jupiter.params.provider.CsvSource;
+<a class="jxr_linenumber" name="L26" href="#L26">26</a>
+<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"> * Test cases for {@link ParetoDistribution}.</em>
+<a class="jxr_linenumber" name="L29" href="#L29">29</a> <em class="jxr_javadoccomment"> * Extends {@link BaseContinuousDistributionTest}. See javadoc of that class for details.</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> <strong class="jxr_keyword">class</strong> <a name="ParetoDistributionTest" href="../../../../../org/apache/commons/statistics/distribution/ParetoDistributionTest.html#ParetoDistributionTest">ParetoDistributionTest</a> <strong class="jxr_keyword">extends</strong> <a name="BaseContinuousDistributionTest" href="../../../../../org/apache/commons/statistics/distribution/BaseContinuousDistributionTest.html#BaseContinuousDistributionTest">BaseContinuousDistributionTest</a> {
+<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"> * The difference each of the 2^53 dyadic rationals in [0, 1).</em>
+<a class="jxr_linenumber" name="L34" href="#L34">34</a> <em class="jxr_javadoccomment"> * This is the smallest non-zero value for p to use when inverse transform sampling.</em>
+<a class="jxr_linenumber" name="L35" href="#L35">35</a> <em class="jxr_javadoccomment"> * Equal to 2^-53.</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> <strong class="jxr_keyword">private</strong> <strong class="jxr_keyword">static</strong> <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> U = 0x1.0p-53;
+<a class="jxr_linenumber" name="L38" href="#L38">38</a>
+<a class="jxr_linenumber" name="L39" href="#L39">39</a> @Override
+<a class="jxr_linenumber" name="L40" href="#L40">40</a> ContinuousDistribution makeDistribution(Object... parameters) {
+<a class="jxr_linenumber" name="L41" href="#L41">41</a> <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> scale = (Double) parameters[0];
+<a class="jxr_linenumber" name="L42" href="#L42">42</a> <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> shape = (Double) parameters[1];
+<a class="jxr_linenumber" name="L43" href="#L43">43</a> <strong class="jxr_keyword">return</strong> ParetoDistribution.of(scale, shape);
+<a class="jxr_linenumber" name="L44" href="#L44">44</a> }
+<a class="jxr_linenumber" name="L45" href="#L45">45</a>
+<a class="jxr_linenumber" name="L46" href="#L46">46</a> @Override
+<a class="jxr_linenumber" name="L47" href="#L47">47</a> Object[][] makeInvalidParameters() {
+<a class="jxr_linenumber" name="L48" href="#L48">48</a> <strong class="jxr_keyword">return</strong> <strong class="jxr_keyword">new</strong> Object[][] {
+<a class="jxr_linenumber" name="L49" href="#L49">49</a> {0.0, 1.0},
+<a class="jxr_linenumber" name="L50" href="#L50">50</a> {-0.1, 1.0},
+<a class="jxr_linenumber" name="L51" href="#L51">51</a> {1.0, 0.0},
+<a class="jxr_linenumber" name="L52" href="#L52">52</a> {1.0, -0.1},
+<a class="jxr_linenumber" name="L53" href="#L53">53</a> {Double.POSITIVE_INFINITY, 1.0},
+<a class="jxr_linenumber" name="L54" href="#L54">54</a> };
+<a class="jxr_linenumber" name="L55" href="#L55">55</a> }
+<a class="jxr_linenumber" name="L56" href="#L56">56</a>
+<a class="jxr_linenumber" name="L57" href="#L57">57</a> @Override
+<a class="jxr_linenumber" name="L58" href="#L58">58</a> String[] getParameterNames() {
+<a class="jxr_linenumber" name="L59" href="#L59">59</a> <strong class="jxr_keyword">return</strong> <strong class="jxr_keyword">new</strong> String[] {<span class="jxr_string">"Scale"</span>, <span class="jxr_string">"Shape"</span>};
+<a class="jxr_linenumber" name="L60" href="#L60">60</a> }
+<a class="jxr_linenumber" name="L61" href="#L61">61</a>
+<a class="jxr_linenumber" name="L62" href="#L62">62</a> @Override
+<a class="jxr_linenumber" name="L63" href="#L63">63</a> <strong class="jxr_keyword">protected</strong> <strong class="jxr_keyword">double</strong> getRelativeTolerance() {
+<a class="jxr_linenumber" name="L64" href="#L64">64</a> <strong class="jxr_keyword">return</strong> 5e-15;
+<a class="jxr_linenumber" name="L65" href="#L65">65</a> }
+<a class="jxr_linenumber" name="L66" href="#L66">66</a>
+<a class="jxr_linenumber" name="L67" href="#L67">67</a> <em class="jxr_comment">//-------------------- Additional test cases -------------------------------</em>
+<a class="jxr_linenumber" name="L68" href="#L68">68</a>
+<a class="jxr_linenumber" name="L69" href="#L69">69</a> @ParameterizedTest
+<a class="jxr_linenumber" name="L70" href="#L70">70</a> @CsvSource({
+<a class="jxr_linenumber" name="L71" href="#L71">71</a> <span class="jxr_string">"1, 1, Infinity, Infinity"</span>,
+<a class="jxr_linenumber" name="L72" href="#L72">72</a> <span class="jxr_string">"2.2, 2.4, 3.771428571428, 14.816326530"</span>,
+<a class="jxr_linenumber" name="L73" href="#L73">73</a> })
+<a class="jxr_linenumber" name="L74" href="#L74">74</a> <strong class="jxr_keyword">void</strong> testAdditionalMoments(<strong class="jxr_keyword">double</strong> scale, <strong class="jxr_keyword">double</strong> shape, <strong class="jxr_keyword">double</strong> mean, <strong class="jxr_keyword">double</strong> variance) {
+<a class="jxr_linenumber" name="L75" href="#L75">75</a> <strong class="jxr_keyword">final</strong> ParetoDistribution dist = ParetoDistribution.of(scale, shape);
+<a class="jxr_linenumber" name="L76" href="#L76">76</a> testMoments(dist, mean, variance, createRelTolerance(1e-9));
+<a class="jxr_linenumber" name="L77" href="#L77">77</a> }
+<a class="jxr_linenumber" name="L78" href="#L78">78</a>
+<a class="jxr_linenumber" name="L79" href="#L79">79</a> @Test
+<a class="jxr_linenumber" name="L80" href="#L80">80</a> <strong class="jxr_keyword">void</strong> testAdditionalCumulativeProbabilityHighPrecision() {
+<a class="jxr_linenumber" name="L81" href="#L81">81</a> <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> scale = 2.1;
+<a class="jxr_linenumber" name="L82" href="#L82">82</a> <em class="jxr_comment">// 2.1000000000000005, 2.100000000000001</em>
+<a class="jxr_linenumber" name="L83" href="#L83">83</a> <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong>[] x = {Math.nextUp(scale), Math.nextUp(Math.nextUp(scale))};
+<a class="jxr_linenumber" name="L84" href="#L84">84</a>
+<a class="jxr_linenumber" name="L85" href="#L85">85</a> <em class="jxr_comment">// R and Wolfram alpha do not match for high precision CDF at small x.</em>
+<a class="jxr_linenumber" name="L86" href="#L86">86</a> <em class="jxr_comment">// The answers were computed using BigDecimal with a math context precision of 100.</em>
+<a class="jxr_linenumber" name="L87" href="#L87">87</a> <em class="jxr_comment">// Note that the results using double are limited by intermediate rounding and the</em>
+<a class="jxr_linenumber" name="L88" href="#L88">88</a> <em class="jxr_comment">// CDF is not high precision as the number of bits of accuracy is low:</em>
+<a class="jxr_linenumber" name="L89" href="#L89">89</a> <em class="jxr_comment">//</em>
+<a class="jxr_linenumber" name="L90" href="#L90">90</a> <em class="jxr_comment">// x = Math.nextUp(scale)</em>
+<a class="jxr_linenumber" name="L91" href="#L91">91</a> <em class="jxr_comment">// 1.0 - pow(scale/x, 0.75) ==> 1.1102230246251565E-16</em>
+<a class="jxr_linenumber" name="L92" href="#L92">92</a> <em class="jxr_comment">// -expm1(shape * log(scale/x)) ==> 1.665334536937735E-16</em>
+<a class="jxr_linenumber" name="L93" href="#L93">93</a> <em class="jxr_comment">// -expm1(shape * log(scale) - shape * log(x)) ==> 2.2204460492503128E-16</em>
+<a class="jxr_linenumber" name="L94" href="#L94">94</a> <em class="jxr_comment">//</em>
+<a class="jxr_linenumber" name="L95" href="#L95">95</a> <em class="jxr_comment">// x = Math.nextUp(Math.nextUp(scale))</em>
+<a class="jxr_linenumber" name="L96" href="#L96">96</a> <em class="jxr_comment">// 1.0 - pow(scale/x, 0.75) ==> 3.3306690738754696E-16</em>
+<a class="jxr_linenumber" name="L97" href="#L97">97</a> <em class="jxr_comment">// -expm1(shape * log(scale/x)) ==> 3.33066907387547E-16</em>
+<a class="jxr_linenumber" name="L98" href="#L98">98</a> <em class="jxr_comment">// -expm1(shape * log(scale) - shape * log(x)) ==> 4.440892098500625E-16</em>
+<a class="jxr_linenumber" name="L99" href="#L99">99</a>
+<a class="jxr_linenumber" name="L100" href="#L100">100</a> <strong class="jxr_keyword">final</strong> ParetoDistribution dist = ParetoDistribution.of(scale, 0.75);
+<a class="jxr_linenumber" name="L101" href="#L101">101</a> <em class="jxr_comment">// BigDecimal: 1 - (scale/x).pow(3).sqrt().sqrt()</em>
+<a class="jxr_linenumber" name="L102" href="#L102">102</a> <em class="jxr_comment">// MathContext mc = new MathContext(100)</em>
+<a class="jxr_linenumber" name="L103" href="#L103">103</a> <em class="jxr_comment">// BigDecimal.ONE.subtract(</em>
+<a class="jxr_linenumber" name="L104" href="#L104">104</a> <em class="jxr_comment">// new BigDecimal(2.1).divide(new BigDecimal(Math.nextUp(Math.nextUp(2.1))), mc)</em>
+<a class="jxr_linenumber" name="L105" href="#L105">105</a> <em class="jxr_comment">// .pow(3).sqrt(mc).sqrt(mc)).doubleValue()</em>
+<a class="jxr_linenumber" name="L106" href="#L106">106</a> <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong>[] values = {1.5860328923216517E-16, 3.172065784643303E-16};
+<a class="jxr_linenumber" name="L107" href="#L107">107</a> testCumulativeProbabilityHighPrecision(dist, x, values, createRelTolerance(0.05));
+<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> @Test
+<a class="jxr_linenumber" name="L111" href="#L111">111</a> <strong class="jxr_keyword">void</strong> testAdditionalCumulativeProbabilityHighPrecision2() {
+<a class="jxr_linenumber" name="L112" href="#L112">112</a> <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> scale = 3;
+<a class="jxr_linenumber" name="L113" href="#L113">113</a> <em class="jxr_comment">// 3.0000000000000004, 3.000000000000001</em>
+<a class="jxr_linenumber" name="L114" href="#L114">114</a> <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong>[] x = {Math.nextUp(scale), Math.nextUp(Math.nextUp(scale))};
+<a class="jxr_linenumber" name="L115" href="#L115">115</a>
+<a class="jxr_linenumber" name="L116" href="#L116">116</a> <em class="jxr_comment">// The current implementation is closer to the answer than either R or Wolfram but</em>
+<a class="jxr_linenumber" name="L117" href="#L117">117</a> <em class="jxr_comment">// the relative error is typically 0.25 (error in the first or second digit).</em>
+<a class="jxr_linenumber" name="L118" href="#L118">118</a> <em class="jxr_comment">// The absolute tolerance checks the result to a closer tolerance than</em>
+<a class="jxr_linenumber" name="L119" href="#L119">119</a> <em class="jxr_comment">// the answer computed using 1 - Math.pow(scale/x, shape), which is zero.</em>
+<a class="jxr_linenumber" name="L120" href="#L120">120</a>
+<a class="jxr_linenumber" name="L121" href="#L121">121</a> <strong class="jxr_keyword">final</strong> ParetoDistribution dist = ParetoDistribution.of(3, 0.25);
+<a class="jxr_linenumber" name="L122" href="#L122">122</a> <em class="jxr_comment">// BigDecimal: 1 - (scale/x).sqrt().sqrt()</em>
+<a class="jxr_linenumber" name="L123" href="#L123">123</a> <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong>[] values = {3.700743415417188E-17, 7.401486830834375E-17};
+<a class="jxr_linenumber" name="L124" href="#L124">124</a> testCumulativeProbabilityHighPrecision(dist, x, values, createAbsTolerance(1e-17));
+<a class="jxr_linenumber" name="L125" href="#L125">125</a>
+<a class="jxr_linenumber" name="L126" href="#L126">126</a> <strong class="jxr_keyword">final</strong> ParetoDistribution dist2 = ParetoDistribution.of(3, 1.5);
+<a class="jxr_linenumber" name="L127" href="#L127">127</a> <em class="jxr_comment">// BigDecimal: 1 - (scale/x).pow(3).sqrt()</em>
+<a class="jxr_linenumber" name="L128" href="#L128">128</a> <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong>[] values2 = {2.2204460492503126E-16, 4.4408920985006247E-16};
+<a class="jxr_linenumber" name="L129" href="#L129">129</a> testCumulativeProbabilityHighPrecision(dist2, x, values2, createAbsTolerance(6e-17));
+<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> @Test
+<a class="jxr_linenumber" name="L133" href="#L133">133</a> <strong class="jxr_keyword">void</strong> testAdditionalSurvivalProbabilityHighPrecision() {
+<a class="jxr_linenumber" name="L134" href="#L134">134</a> <strong class="jxr_keyword">final</strong> ParetoDistribution dist = ParetoDistribution.of(2.1, 1.4);
+<a class="jxr_linenumber" name="L135" href="#L135">135</a> testSurvivalProbabilityHighPrecision(
+<a class="jxr_linenumber" name="L136" href="#L136">136</a> dist,
+<a class="jxr_linenumber" name="L137" href="#L137">137</a> <strong class="jxr_keyword">new</strong> <strong class="jxr_keyword">double</strong>[] {42e11, 64e11},
+<a class="jxr_linenumber" name="L138" href="#L138">138</a> <strong class="jxr_keyword">new</strong> <strong class="jxr_keyword">double</strong>[] {6.005622169907148e-18, 3.330082930386111e-18},
+<a class="jxr_linenumber" name="L139" href="#L139">139</a> DoubleTolerances.relative(5e-14));
+<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_javadoccomment">/**</em>
+<a class="jxr_linenumber" name="L143" href="#L143">143</a> <em class="jxr_javadoccomment"> * Check to make sure top-coding of extreme values works correctly.</em>
+<a class="jxr_linenumber" name="L144" href="#L144">144</a> <em class="jxr_javadoccomment"> */</em>
+<a class="jxr_linenumber" name="L145" href="#L145">145</a> @Test
+<a class="jxr_linenumber" name="L146" href="#L146">146</a> <strong class="jxr_keyword">void</strong> testExtremeValues() {
+<a class="jxr_linenumber" name="L147" href="#L147">147</a> <strong class="jxr_keyword">final</strong> ParetoDistribution dist = ParetoDistribution.of(1, 1);
+<a class="jxr_linenumber" name="L148" href="#L148">148</a> <strong class="jxr_keyword">for</strong> (<strong class="jxr_keyword">int</strong> i = 0; i < 10000; i++) { <em class="jxr_comment">// make sure no convergence exception</em>
+<a class="jxr_linenumber" name="L149" href="#L149">149</a> <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> upperTail = dist.cumulativeProbability(i);
+<a class="jxr_linenumber" name="L150" href="#L150">150</a> <strong class="jxr_keyword">if</strong> (i <= 1000) { <em class="jxr_comment">// make sure not top-coded</em>
+<a class="jxr_linenumber" name="L151" href="#L151">151</a> Assertions.assertTrue(upperTail < 1.0d);
+<a class="jxr_linenumber" name="L152" href="#L152">152</a> } <strong class="jxr_keyword">else</strong> { <em class="jxr_comment">// make sure top coding not reversed</em>
+<a class="jxr_linenumber" name="L153" href="#L153">153</a> Assertions.assertTrue(upperTail > 0.999);
+<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>
+<a class="jxr_linenumber" name="L157" href="#L157">157</a> Assertions.assertEquals(1, dist.cumulativeProbability(Double.MAX_VALUE));
+<a class="jxr_linenumber" name="L158" href="#L158">158</a> Assertions.assertEquals(0, dist.cumulativeProbability(-Double.MAX_VALUE));
+<a class="jxr_linenumber" name="L159" href="#L159">159</a> Assertions.assertEquals(1, dist.cumulativeProbability(Double.POSITIVE_INFINITY));
+<a class="jxr_linenumber" name="L160" href="#L160">160</a> Assertions.assertEquals(0, dist.cumulativeProbability(Double.NEGATIVE_INFINITY));
+<a class="jxr_linenumber" name="L161" href="#L161">161</a> }
+<a class="jxr_linenumber" name="L162" href="#L162">162</a>
+<a class="jxr_linenumber" name="L163" href="#L163">163</a> <em class="jxr_javadoccomment">/**</em>
+<a class="jxr_linenumber" name="L164" href="#L164">164</a> <em class="jxr_javadoccomment"> * Test extreme parameters to the distribution. This uses the same computation to precompute</em>
+<a class="jxr_linenumber" name="L165" href="#L165">165</a> <em class="jxr_javadoccomment"> * factors for the PMF and log PMF as performed by the distribution. When the factors are</em>
+<a class="jxr_linenumber" name="L166" href="#L166">166</a> <em class="jxr_javadoccomment"> * not finite then the edges cases must be appropriately handled.</em>
+<a class="jxr_linenumber" name="L167" href="#L167">167</a> <em class="jxr_javadoccomment"> */</em>
+<a class="jxr_linenumber" name="L168" href="#L168">168</a> @Test
+<a class="jxr_linenumber" name="L169" href="#L169">169</a> <strong class="jxr_keyword">void</strong> testExtremeParameters() {
+<a class="jxr_linenumber" name="L170" href="#L170">170</a> <strong class="jxr_keyword">double</strong> scale;
+<a class="jxr_linenumber" name="L171" href="#L171">171</a> <strong class="jxr_keyword">double</strong> shape;
+<a class="jxr_linenumber" name="L172" href="#L172">172</a>
+<a class="jxr_linenumber" name="L173" href="#L173">173</a> <em class="jxr_comment">// Overflow of standard computation. Log computation OK.</em>
+<a class="jxr_linenumber" name="L174" href="#L174">174</a> scale = 10;
+<a class="jxr_linenumber" name="L175" href="#L175">175</a> shape = 306;
+<a class="jxr_linenumber" name="L176" href="#L176">176</a> Assertions.assertEquals(Double.POSITIVE_INFINITY, shape * Math.pow(scale, shape));
+<a class="jxr_linenumber" name="L177" href="#L177">177</a> Assertions.assertTrue(Double.isFinite(Math.log(shape) + Math.log(scale) * shape));
+<a class="jxr_linenumber" name="L178" href="#L178">178</a>
+<a class="jxr_linenumber" name="L179" href="#L179">179</a> <em class="jxr_comment">// ---</em>
+<a class="jxr_linenumber" name="L180" href="#L180">180</a>
+<a class="jxr_linenumber" name="L181" href="#L181">181</a> <em class="jxr_comment">// Overflow of standard computation. Overflow of Log computation.</em>
+<a class="jxr_linenumber" name="L182" href="#L182">182</a> scale = 10;
+<a class="jxr_linenumber" name="L183" href="#L183">183</a> shape = Double.POSITIVE_INFINITY;
+<a class="jxr_linenumber" name="L184" href="#L184">184</a> Assertions.assertEquals(Double.POSITIVE_INFINITY, shape * Math.pow(scale, shape));
+<a class="jxr_linenumber" name="L185" href="#L185">185</a> Assertions.assertEquals(Double.POSITIVE_INFINITY, Math.log(shape) + Math.log(scale) * shape);
+<a class="jxr_linenumber" name="L186" href="#L186">186</a>
+<a class="jxr_linenumber" name="L187" href="#L187">187</a> <em class="jxr_comment">// This case can compute as if shape is big (Dirac delta function)</em>
+<a class="jxr_linenumber" name="L188" href="#L188">188</a> shape = 1e300;
+<a class="jxr_linenumber" name="L189" href="#L189">189</a> Assertions.assertEquals(Double.POSITIVE_INFINITY, shape * Math.pow(scale, shape));
+<a class="jxr_linenumber" name="L190" href="#L190">190</a> Assertions.assertTrue(Double.isFinite(Math.log(shape) + Math.log(scale) * shape));
+<a class="jxr_linenumber" name="L191" href="#L191">191</a>
+<a class="jxr_linenumber" name="L192" href="#L192">192</a> <em class="jxr_comment">// ---</em>
+<a class="jxr_linenumber" name="L193" href="#L193">193</a>
+<a class="jxr_linenumber" name="L194" href="#L194">194</a> <em class="jxr_comment">// NaN of standard computation. NaN of Log computation.</em>
+<a class="jxr_linenumber" name="L195" href="#L195">195</a> scale = 1;
+<a class="jxr_linenumber" name="L196" href="#L196">196</a> shape = Double.POSITIVE_INFINITY;
+<a class="jxr_linenumber" name="L197" href="#L197">197</a> <em class="jxr_comment">// 1^inf == NaN</em>
+<a class="jxr_linenumber" name="L198" href="#L198">198</a> Assertions.assertEquals(Double.NaN, shape * Math.pow(scale, shape));
+<a class="jxr_linenumber" name="L199" href="#L199">199</a> <em class="jxr_comment">// 0 * inf == NaN</em>
+<a class="jxr_linenumber" name="L200" href="#L200">200</a> Assertions.assertEquals(Double.NaN, Math.log(shape) + Math.log(scale) * shape);
+<a class="jxr_linenumber" name="L201" href="#L201">201</a>
+<a class="jxr_linenumber" name="L202" href="#L202">202</a> <em class="jxr_comment">// This case can compute as if shape is big (Dirac delta function)</em>
+<a class="jxr_linenumber" name="L203" href="#L203">203</a> shape = 1e300;
+<a class="jxr_linenumber" name="L204" href="#L204">204</a> Assertions.assertEquals(shape, shape * Math.pow(scale, shape));
+<a class="jxr_linenumber" name="L205" href="#L205">205</a> Assertions.assertTrue(Double.isFinite(Math.log(shape) + Math.log(scale) * shape));
+<a class="jxr_linenumber" name="L206" href="#L206">206</a>
+<a class="jxr_linenumber" name="L207" href="#L207">207</a> <em class="jxr_comment">// ---</em>
+<a class="jxr_linenumber" name="L208" href="#L208">208</a>
+<a class="jxr_linenumber" name="L209" href="#L209">209</a> <em class="jxr_comment">// Underflow of standard computation. Log computation OK.</em>
+<a class="jxr_linenumber" name="L210" href="#L210">210</a> scale = 0.1;
+<a class="jxr_linenumber" name="L211" href="#L211">211</a> shape = 324;
+<a class="jxr_linenumber" name="L212" href="#L212">212</a> Assertions.assertEquals(0.0, shape * Math.pow(scale, shape));
+<a class="jxr_linenumber" name="L213" href="#L213">213</a> Assertions.assertTrue(Double.isFinite(Math.log(shape) + Math.log(scale) * shape));
+<a class="jxr_linenumber" name="L214" href="#L214">214</a>
+<a class="jxr_linenumber" name="L215" href="#L215">215</a> <em class="jxr_comment">// ---</em>
+<a class="jxr_linenumber" name="L216" href="#L216">216</a>
+<a class="jxr_linenumber" name="L217" href="#L217">217</a> <em class="jxr_comment">// Underflow of standard computation. Underflow of Log computation.</em>
+<a class="jxr_linenumber" name="L218" href="#L218">218</a> scale = 0.1;
+<a class="jxr_linenumber" name="L219" href="#L219">219</a> shape = Double.MAX_VALUE;
+<a class="jxr_linenumber" name="L220" href="#L220">220</a> Assertions.assertEquals(0.0, shape * Math.pow(scale, shape));
+<a class="jxr_linenumber" name="L221" href="#L221">221</a> Assertions.assertEquals(Double.NEGATIVE_INFINITY, Math.log(shape) + Math.log(scale) * shape);
+<a class="jxr_linenumber" name="L222" href="#L222">222</a>
+<a class="jxr_linenumber" name="L223" href="#L223">223</a> <em class="jxr_comment">// This case can compute as if shape is big (Dirac delta function)</em>
+<a class="jxr_linenumber" name="L224" href="#L224">224</a>
+<a class="jxr_linenumber" name="L225" href="#L225">225</a> <em class="jxr_comment">// ---</em>
+<a class="jxr_linenumber" name="L226" href="#L226">226</a>
+<a class="jxr_linenumber" name="L227" href="#L227">227</a> <em class="jxr_comment">// Underflow of standard computation to NaN. NaN of Log computation.</em>
+<a class="jxr_linenumber" name="L228" href="#L228">228</a> scale = 0.1;
+<a class="jxr_linenumber" name="L229" href="#L229">229</a> shape = Double.POSITIVE_INFINITY;
+<a class="jxr_linenumber" name="L230" href="#L230">230</a> Assertions.assertEquals(Double.NaN, shape * Math.pow(scale, shape));
+<a class="jxr_linenumber" name="L231" href="#L231">231</a> Assertions.assertEquals(Double.NaN, Math.log(shape) + Math.log(scale) * shape);
+<a class="jxr_linenumber" name="L232" href="#L232">232</a>
+<a class="jxr_linenumber" name="L233" href="#L233">233</a> <em class="jxr_comment">// This case can compute as if shape is big (Dirac delta function)</em>
+<a class="jxr_linenumber" name="L234" href="#L234">234</a>
+<a class="jxr_linenumber" name="L235" href="#L235">235</a> <em class="jxr_comment">// ---</em>
+<a class="jxr_linenumber" name="L236" href="#L236">236</a>
+<a class="jxr_linenumber" name="L237" href="#L237">237</a> <em class="jxr_comment">// Smallest possible value of shape is OK.</em>
+<a class="jxr_linenumber" name="L238" href="#L238">238</a> <em class="jxr_comment">// The Math.pow function -> 1 as the exponent -> 0.</em>
+<a class="jxr_linenumber" name="L239" href="#L239">239</a> shape = Double.MIN_VALUE;
+<a class="jxr_linenumber" name="L240" href="#L240">240</a> <strong class="jxr_keyword">for</strong> (<strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> scale2 : <strong class="jxr_keyword">new</strong> <strong class="jxr_keyword">double</strong>[] {Double.MIN_VALUE, 0.1, 1, 10, 100}) {
+<a class="jxr_linenumber" name="L241" href="#L241">241</a> Assertions.assertEquals(shape, shape * Math.pow(scale2, shape));
+<a class="jxr_linenumber" name="L242" href="#L242">242</a> Assertions.assertTrue(Double.isFinite(Math.log(shape) + Math.log(scale2) * shape));
+<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>
+<a class="jxr_linenumber" name="L246" href="#L246">246</a> <em class="jxr_javadoccomment">/**</em>
+<a class="jxr_linenumber" name="L247" href="#L247">247</a> <em class="jxr_javadoccomment"> * Test sampling with a large shape. As {@code shape -> inf} then the distribution</em>
+<a class="jxr_linenumber" name="L248" href="#L248">248</a> <em class="jxr_javadoccomment"> * approaches a delta function with {@code CDF(x=scale)} = 0 and {@code CDF(x>scale) = 1}.</em>
+<a class="jxr_linenumber" name="L249" href="#L249">249</a> <em class="jxr_javadoccomment"> * This test verifies that a large shape is effectively sampled from p in [0, 1) to avoid</em>
+<a class="jxr_linenumber" name="L250" href="#L250">250</a> <em class="jxr_javadoccomment"> * spurious infinite samples when p=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> <em class="jxr_javadoccomment"> * <p>Sampling Details</em>
+<a class="jxr_linenumber" name="L253" href="#L253">253</a> <em class="jxr_javadoccomment"> *</em>
+<a class="jxr_linenumber" name="L254" href="#L254">254</a> <em class="jxr_javadoccomment"> * <p>Note that sampling is using inverse transform sampling by inverting the CDF:</em>
+<a class="jxr_linenumber" name="L255" href="#L255">255</a> <em class="jxr_javadoccomment"> * <pre></em>
+<a class="jxr_linenumber" name="L256" href="#L256">256</a> <em class="jxr_javadoccomment"> * CDF(x) = 1 - (scale / x)^shape</em>
+<a class="jxr_linenumber" name="L257" href="#L257">257</a> <em class="jxr_javadoccomment"> * x = scale / (1 - p)^(1 / shape)</em>
+<a class="jxr_linenumber" name="L258" href="#L258">258</a> <em class="jxr_javadoccomment"> * = scale / exp(log(1 - p) / shape)</em>
+<a class="jxr_linenumber" name="L259" href="#L259">259</a> <em class="jxr_javadoccomment"> * </pre></em>
+<a class="jxr_linenumber" name="L260" href="#L260">260</a> <em class="jxr_javadoccomment"> *</em>
+<a class="jxr_linenumber" name="L261" href="#L261">261</a> <em class="jxr_javadoccomment"> * <p>The sampler in Commons RNG is inverting the CDF function using Math.pow:</em>
+<a class="jxr_linenumber" name="L262" href="#L262">262</a> <em class="jxr_javadoccomment"> * <pre></em>
+<a class="jxr_linenumber" name="L263" href="#L263">263</a> <em class="jxr_javadoccomment"> * x = scale / Math.pow(1 - p, 1 / shape)</em>
+<a class="jxr_linenumber" name="L264" href="#L264">264</a> <em class="jxr_javadoccomment"> * </pre></em>
+<a class="jxr_linenumber" name="L265" href="#L265">265</a> <em class="jxr_javadoccomment"> *</em>
+<a class="jxr_linenumber" name="L266" href="#L266">266</a> <em class="jxr_javadoccomment"> * <p>The Pareto distribution uses log functions to achieve the same result:</em>
+<a class="jxr_linenumber" name="L267" href="#L267">267</a> <em class="jxr_javadoccomment"> * <pre></em>
+<a class="jxr_linenumber" name="L268" href="#L268">268</a> <em class="jxr_javadoccomment"> * x = scale / Math.exp(Math.log1p(-p) / shape);</em>
+<a class="jxr_linenumber" name="L269" href="#L269">269</a> <em class="jxr_javadoccomment"> * </pre></em>
+<a class="jxr_linenumber" name="L270" href="#L270">270</a> <em class="jxr_javadoccomment"> *</em>
+<a class="jxr_linenumber" name="L271" href="#L271">271</a> <em class="jxr_javadoccomment"> * <p>Inversion will return the scale when Math.exp(X) == 1 where X (in [-inf, 0]) is:</em>
+<a class="jxr_linenumber" name="L272" href="#L272">272</a> <em class="jxr_javadoccomment"> * <pre></em>
+<a class="jxr_linenumber" name="L273" href="#L273">273</a> <em class="jxr_javadoccomment"> * X = log(1 - p) / shape</em>
+<a class="jxr_linenumber" name="L274" href="#L274">274</a> <em class="jxr_javadoccomment"> * </pre></em>
+<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"> * <p>This occurs when {@code X > log(1.0 - epsilon)}, or larger (closer to zero) than</em>
+<a class="jxr_linenumber" name="L277" href="#L277">277</a> <em class="jxr_javadoccomment"> * {@code Math.log(Math.nextDown(1.0))}; X is approximately -1.11e-16.</em>
+<a class="jxr_linenumber" name="L278" href="#L278">278</a> <em class="jxr_javadoccomment"> * During sampling p is bounded to the 2^53 dyadic rationals in [0, 1). The largest</em>
+<a class="jxr_linenumber" name="L279" href="#L279">279</a> <em class="jxr_javadoccomment"> * finite value for the logarithm is log(2^-53) thus the critical size for shape is around:</em>
+<a class="jxr_linenumber" name="L280" href="#L280">280</a> <em class="jxr_javadoccomment"> * <pre></em>
+<a class="jxr_linenumber" name="L281" href="#L281">281</a> <em class="jxr_javadoccomment"> * shape = log(2^-53) / -1.1102230246251565e-16 = 3.3089568271276403e17</em>
+<a class="jxr_linenumber" name="L282" href="#L282">282</a> <em class="jxr_javadoccomment"> * </pre></em>
+<a class="jxr_linenumber" name="L283" href="#L283">283</a> <em class="jxr_javadoccomment"> *</em>
+<a class="jxr_linenumber" name="L284" href="#L284">284</a> <em class="jxr_javadoccomment"> * <p>Note that if the p-value is 1 then inverseCumulativeProbability(1.0) == inf.</em>
+<a class="jxr_linenumber" name="L285" href="#L285">285</a> <em class="jxr_javadoccomment"> * However using the power function to invert this ignores this possibility when the shape</em>
+<a class="jxr_linenumber" name="L286" href="#L286">286</a> <em class="jxr_javadoccomment"> * is infinite and will always return scale / x^0 = scale / 1 = scale. If the inversion</em>
+<a class="jxr_linenumber" name="L287" href="#L287">287</a> <em class="jxr_javadoccomment"> * using logarithms is directly used then a log(0) / inf == -inf / inf == NaN occurs.</em>
+<a class="jxr_linenumber" name="L288" href="#L288">288</a> <em class="jxr_javadoccomment"> */</em>
+<a class="jxr_linenumber" name="L289" href="#L289">289</a> @ParameterizedTest
+<a class="jxr_linenumber" name="L290" href="#L290">290</a> @CsvSource({
+<a class="jxr_linenumber" name="L291" href="#L291">291</a> <em class="jxr_comment">// Scale values match those from the test resource files where the sampling test is disabled</em>
+<a class="jxr_linenumber" name="L292" href="#L292">292</a> <span class="jxr_string">"10, Infinity"</span>,
+<a class="jxr_linenumber" name="L293" href="#L293">293</a> <span class="jxr_string">"1, Infinity"</span>,
+<a class="jxr_linenumber" name="L294" href="#L294">294</a> <span class="jxr_string">"0.1, Infinity"</span>,
+<a class="jxr_linenumber" name="L295" href="#L295">295</a> <em class="jxr_comment">// This behaviour occurs even when the shape is not infinite due to limited precision</em>
+<a class="jxr_linenumber" name="L296" href="#L296">296</a> <em class="jxr_comment">// of double values. Shape is set to twice the limit derived above to account for rounding:</em>
+<a class="jxr_linenumber" name="L297" href="#L297">297</a> <em class="jxr_comment">// double p = 0x1.0p-53</em>
+<a class="jxr_linenumber" name="L298" href="#L298">298</a> <em class="jxr_comment">// Math.pow(p, 1 / (Math.log(p) / -p)) ==> 0.9999999999999999</em>
+<a class="jxr_linenumber" name="L299" href="#L299">299</a> <em class="jxr_comment">// Math.pow(p, 1 / (2 * Math.log(p) / -p)) ==> 1.0</em>
+<a class="jxr_linenumber" name="L300" href="#L300">300</a> <em class="jxr_comment">// shape = (2 * Math.log(p) / -p)</em>
+<a class="jxr_linenumber" name="L301" href="#L301">301</a> <span class="jxr_string">"10, 6.6179136542552806e17"</span>,
+<a class="jxr_linenumber" name="L302" href="#L302">302</a> <span class="jxr_string">"1, 6.6179136542552806e17"</span>,
+<a class="jxr_linenumber" name="L303" href="#L303">303</a> <span class="jxr_string">"0.1, 6.6179136542552806e17"</span>,
+<a class="jxr_linenumber" name="L304" href="#L304">304</a> })
+<a class="jxr_linenumber" name="L305" href="#L305">305</a> <strong class="jxr_keyword">void</strong> testSamplingWithLargeShape(<strong class="jxr_keyword">double</strong> scale, <strong class="jxr_keyword">double</strong> shape) {
+<a class="jxr_linenumber" name="L306" href="#L306">306</a> <strong class="jxr_keyword">final</strong> ParetoDistribution dist = ParetoDistribution.of(scale, shape);
+<a class="jxr_linenumber" name="L307" href="#L307">307</a>
+<a class="jxr_linenumber" name="L308" href="#L308">308</a> <em class="jxr_comment">// Sampling should act as if inverting p in [0, 1)</em>
+<a class="jxr_linenumber" name="L309" href="#L309">309</a> <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> x0 = dist.inverseCumulativeProbability(0);
+<a class="jxr_linenumber" name="L310" href="#L310">310</a> <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> x1 = dist.inverseCumulativeProbability(1 - U);
+<a class="jxr_linenumber" name="L311" href="#L311">311</a> Assertions.assertEquals(scale, x0);
+<a class="jxr_linenumber" name="L312" href="#L312">312</a> Assertions.assertEquals(x0, x1, <span class="jxr_string">"Test parameters did not create an extreme distribution"</span>);
+<a class="jxr_linenumber" name="L313" href="#L313">313</a>
+<a class="jxr_linenumber" name="L314" href="#L314">314</a> <em class="jxr_comment">// Sampling for p in [0, 1): returns scale when shape is large</em>
+<a class="jxr_linenumber" name="L315" href="#L315">315</a> assertSampler(dist, scale);
+<a class="jxr_linenumber" name="L316" href="#L316">316</a> }
+<a class="jxr_linenumber" name="L317" href="#L317">317</a>
+<a class="jxr_linenumber" name="L318" href="#L318">318</a> <em class="jxr_javadoccomment">/**</em>
+<a class="jxr_linenumber" name="L319" href="#L319">319</a> <em class="jxr_javadoccomment"> * Test sampling with a tiny shape. As {@code shape -> 0} then the distribution</em>
+<a class="jxr_linenumber" name="L320" href="#L320">320</a> <em class="jxr_javadoccomment"> * approaches a function with {@code CDF(x=inf) = 1} and {@code CDF(x>=scale) = 0}.</em>
+<a class="jxr_linenumber" name="L321" href="#L321">321</a> <em class="jxr_javadoccomment"> * This test verifies that a tiny shape is effectively sampled from p in (0, 1] to avoid</em>
+<a class="jxr_linenumber" name="L322" href="#L322">322</a> <em class="jxr_javadoccomment"> * spurious NaN samples when p=0.</em>
+<a class="jxr_linenumber" name="L323" href="#L323">323</a> <em class="jxr_javadoccomment"> *</em>
+<a class="jxr_linenumber" name="L324" href="#L324">324</a> <em class="jxr_javadoccomment"> * <p>Sampling Details</em>
+<a class="jxr_linenumber" name="L325" href="#L325">325</a> <em class="jxr_javadoccomment"> *</em>
+<a class="jxr_linenumber" name="L326" href="#L326">326</a> <em class="jxr_javadoccomment"> * <p>The sampler in Commons RNG is inverting the CDF function using Math.pow:</em>
+<a class="jxr_linenumber" name="L327" href="#L327">327</a> <em class="jxr_javadoccomment"> * <pre></em>
+<a class="jxr_linenumber" name="L328" href="#L328">328</a> <em class="jxr_javadoccomment"> * x = scale / Math.pow(1 - p, 1 / shape)</em>
+<a class="jxr_linenumber" name="L329" href="#L329">329</a> <em class="jxr_javadoccomment"> * </pre></em>
+<a class="jxr_linenumber" name="L330" href="#L330">330</a> <em class="jxr_javadoccomment"> *</em>
+<a class="jxr_linenumber" name="L331" href="#L331">331</a> <em class="jxr_javadoccomment"> * <p>However Math.pow(1, infinity) == NaN. This can be avoided if p=0 is not used.</em>
+<a class="jxr_linenumber" name="L332" href="#L332">332</a> <em class="jxr_javadoccomment"> * For all other values Math.pow(1 - p, infinity) == 0 and the sample is infinite.</em>
+<a class="jxr_linenumber" name="L333" href="#L333">333</a> <em class="jxr_javadoccomment"> */</em>
+<a class="jxr_linenumber" name="L334" href="#L334">334</a> @ParameterizedTest
+<a class="jxr_linenumber" name="L335" href="#L335">335</a> @CsvSource({
+<a class="jxr_linenumber" name="L336" href="#L336">336</a> <em class="jxr_comment">// 1 / shape is infinite</em>
+<a class="jxr_linenumber" name="L337" href="#L337">337</a> <em class="jxr_comment">// Scale values match those from the test resource files where the sampling test is disabled</em>
+<a class="jxr_linenumber" name="L338" href="#L338">338</a> <span class="jxr_string">"10, 4.9e-324"</span>,
+<a class="jxr_linenumber" name="L339" href="#L339">339</a> <span class="jxr_string">"1, 4.9e-324"</span>,
+<a class="jxr_linenumber" name="L340" href="#L340">340</a> <span class="jxr_string">"0.1, 4.9e-324"</span>,
+<a class="jxr_linenumber" name="L341" href="#L341">341</a> <em class="jxr_comment">// This behaviour occurs even when 1 / shape is not infinite due to limited precision</em>
+<a class="jxr_linenumber" name="L342" href="#L342">342</a> <em class="jxr_comment">// of double values. Shape provides the largest possible finite value from 1 / shape:</em>
+<a class="jxr_linenumber" name="L343" href="#L343">343</a> <em class="jxr_comment">// shape = (1.0 + Math.ulp(1.0)*2) / Double.MAX_VALUE</em>
+<a class="jxr_linenumber" name="L344" href="#L344">344</a> <em class="jxr_comment">// 1 / shape = 1.7976931348623143e308</em>
+<a class="jxr_linenumber" name="L345" href="#L345">345</a> <em class="jxr_comment">// 1 / Math.nextDown(shape) = Infinity</em>
+<a class="jxr_linenumber" name="L346" href="#L346">346</a> <span class="jxr_string">"10, 5.56268464626801E-309"</span>,
+<a class="jxr_linenumber" name="L347" href="#L347">347</a> <span class="jxr_string">"1, 5.56268464626801E-309"</span>,
+<a class="jxr_linenumber" name="L348" href="#L348">348</a> <span class="jxr_string">"0.1, 5.56268464626801E-309"</span>,
+<a class="jxr_linenumber" name="L349" href="#L349">349</a> <em class="jxr_comment">// Lower limit is where pow(1 - p, 1 / shape) < Double.MIN_VALUE:</em>
+<a class="jxr_linenumber" name="L350" href="#L350">350</a> <em class="jxr_comment">// shape < log(1 - p) / log(MIN_VALUE)</em>
+<a class="jxr_linenumber" name="L351" href="#L351">351</a> <em class="jxr_comment">// Shape is set to half this limit to account for rounding:</em>
+<a class="jxr_linenumber" name="L352" href="#L352">352</a> <em class="jxr_comment">// double p = 0x1.0p-53</em>
+<a class="jxr_linenumber" name="L353" href="#L353">353</a> <em class="jxr_comment">// Math.pow(1 - p, 1 / (Math.log(1 - p) / Math.log(Double.MIN_VALUE))) ==> 4.9e-324</em>
+<a class="jxr_linenumber" name="L354" href="#L354">354</a> <em class="jxr_comment">// Math.pow(1 - p, 2 / (Math.log(1 - p) / Math.log(Double.MIN_VALUE))) ==> 0.0</em>
+<a class="jxr_linenumber" name="L355" href="#L355">355</a> <em class="jxr_comment">// shape = 0.5 * Math.log(1 - p) / Math.log(Double.MIN_VALUE)</em>
+<a class="jxr_linenumber" name="L356" href="#L356">356</a> <span class="jxr_string">"10, 7.456765604783329e-20"</span>,
+<a class="jxr_linenumber" name="L357" href="#L357">357</a> <span class="jxr_string">"1, 7.456765604783329e-20"</span>,
+<a class="jxr_linenumber" name="L358" href="#L358">358</a> <em class="jxr_comment">// Use smallest possible scale: test will fail if shape is not half the limit</em>
+<a class="jxr_linenumber" name="L359" href="#L359">359</a> <span class="jxr_string">"4.9e-324, 7.456765604783329e-20"</span>,
+<a class="jxr_linenumber" name="L360" href="#L360">360</a> })
+<a class="jxr_linenumber" name="L361" href="#L361">361</a> <strong class="jxr_keyword">void</strong> testSamplingWithTinyShape(<strong class="jxr_keyword">double</strong> scale, <strong class="jxr_keyword">double</strong> shape) {
+<a class="jxr_linenumber" name="L362" href="#L362">362</a> <strong class="jxr_keyword">final</strong> ParetoDistribution dist = ParetoDistribution.of(scale, shape);
+<a class="jxr_linenumber" name="L363" href="#L363">363</a>
+<a class="jxr_linenumber" name="L364" href="#L364">364</a> <em class="jxr_comment">// Sampling should act as if inverting p in (0, 1]</em>
+<a class="jxr_linenumber" name="L365" href="#L365">365</a> <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> x0 = dist.inverseCumulativeProbability(U);
+<a class="jxr_linenumber" name="L366" href="#L366">366</a> <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> x1 = dist.inverseCumulativeProbability(1);
+<a class="jxr_linenumber" name="L367" href="#L367">367</a> Assertions.assertEquals(Double.POSITIVE_INFINITY, x1);
+<a class="jxr_linenumber" name="L368" href="#L368">368</a> Assertions.assertEquals(x1, x0, <span class="jxr_string">"Test parameters did not create an extreme distribution"</span>);
+<a class="jxr_linenumber" name="L369" href="#L369">369</a>
+<a class="jxr_linenumber" name="L370" href="#L370">370</a> <em class="jxr_comment">// Sampling for p in [0, 1): returns infinity when shape is tiny</em>
+<a class="jxr_linenumber" name="L371" href="#L371">371</a> assertSampler(dist, Double.POSITIVE_INFINITY);
+<a class="jxr_linenumber" name="L372" href="#L372">372</a> }
+<a class="jxr_linenumber" name="L373" href="#L373">373</a>
+<a class="jxr_linenumber" name="L374" href="#L374">374</a> <em class="jxr_javadoccomment">/**</em>
+<a class="jxr_linenumber" name="L375" href="#L375">375</a> <em class="jxr_javadoccomment"> * Assert the sampler produces the expected sample value irrespective of the values from the RNG.</em>
+<a class="jxr_linenumber" name="L376" href="#L376">376</a> <em class="jxr_javadoccomment"> *</em>
+<a class="jxr_linenumber" name="L377" href="#L377">377</a> <em class="jxr_javadoccomment"> * @param dist Distribution</em>
+<a class="jxr_linenumber" name="L378" href="#L378">378</a> <em class="jxr_javadoccomment"> * @param expected Expected sample value</em>
+<a class="jxr_linenumber" name="L379" href="#L379">379</a> <em class="jxr_javadoccomment"> */</em>
+<a class="jxr_linenumber" name="L380" href="#L380">380</a> <strong class="jxr_keyword">private</strong> <strong class="jxr_keyword">static</strong> <strong class="jxr_keyword">void</strong> assertSampler(ParetoDistribution dist, <strong class="jxr_keyword">double</strong> expected) {
+<a class="jxr_linenumber" name="L381" href="#L381">381</a> <em class="jxr_comment">// Extreme random numbers using no bits or all bits, then combinations</em>
+<a class="jxr_linenumber" name="L382" href="#L382">382</a> <em class="jxr_comment">// that may be used to generate a double from the lower or upper 53-bits</em>
+<a class="jxr_linenumber" name="L383" href="#L383">383</a> <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">long</strong>[] values = {0, -1, 1, 1L << 11, -2, -2L << 11};
+<a class="jxr_linenumber" name="L384" href="#L384">384</a> <strong class="jxr_keyword">final</strong> UniformRandomProvider rng = createRNG(values);
+<a class="jxr_linenumber" name="L385" href="#L385">385</a> ContinuousDistribution.Sampler s = dist.createSampler(rng);
+<a class="jxr_linenumber" name="L386" href="#L386">386</a> <strong class="jxr_keyword">for</strong> (<strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">long</strong> l : values) {
+<a class="jxr_linenumber" name="L387" href="#L387">387</a> Assertions.assertEquals(expected, s.sample(), () -> <span class="jxr_string">"long bits = "</span> + l);
+<a class="jxr_linenumber" name="L388" href="#L388">388</a> }
+<a class="jxr_linenumber" name="L389" href="#L389">389</a> <em class="jxr_comment">// Any random number</em>
+<a class="jxr_linenumber" name="L390" href="#L390">390</a> <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">long</strong> seed = RandomSource.createLong();
+<a class="jxr_linenumber" name="L391" href="#L391">391</a> s = dist.createSampler(RandomSource.SPLIT_MIX_64.create(seed));
+<a class="jxr_linenumber" name="L392" href="#L392">392</a> <strong class="jxr_keyword">for</strong> (<strong class="jxr_keyword">int</strong> i = 0; i < 100; i++) {
+<a class="jxr_linenumber" name="L393" href="#L393">393</a> Assertions.assertEquals(expected, s.sample(), () -> <span class="jxr_string">"seed = "</span> + seed);
+<a class="jxr_linenumber" name="L394" href="#L394">394</a> }
+<a class="jxr_linenumber" name="L395" href="#L395">395</a> }
+<a class="jxr_linenumber" name="L396" href="#L396">396</a>
+<a class="jxr_linenumber" name="L397" href="#L397">397</a> <em class="jxr_javadoccomment">/**</em>
+<a class="jxr_linenumber" name="L398" href="#L398">398</a> <em class="jxr_javadoccomment"> * Creates the RNG to return the given values from the nextLong() method.</em>
+<a class="jxr_linenumber" name="L399" href="#L399">399</a> <em class="jxr_javadoccomment"> *</em>
+<a class="jxr_linenumber" name="L400" href="#L400">400</a> <em class="jxr_javadoccomment"> * @param values Long values</em>
+<a class="jxr_linenumber" name="L401" href="#L401">401</a> <em class="jxr_javadoccomment"> * @return the RNG</em>
+<a class="jxr_linenumber" name="L402" href="#L402">402</a> <em class="jxr_javadoccomment"> */</em>
+<a class="jxr_linenumber" name="L403" href="#L403">403</a> <strong class="jxr_keyword">private</strong> <strong class="jxr_keyword">static</strong> UniformRandomProvider createRNG(<strong class="jxr_keyword">long</strong>... values) {
+<a class="jxr_linenumber" name="L404" href="#L404">404</a> <strong class="jxr_keyword">return</strong> <strong class="jxr_keyword">new</strong> UniformRandomProvider() {
+<a class="jxr_linenumber" name="L405" href="#L405">405</a> <strong class="jxr_keyword">private</strong> <strong class="jxr_keyword">int</strong> i;
+<a class="jxr_linenumber" name="L406" href="#L406">406</a>
+<a class="jxr_linenumber" name="L407" href="#L407">407</a> @Override
+<a class="jxr_linenumber" name="L408" href="#L408">408</a> <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">long</strong> nextLong() {
+<a class="jxr_linenumber" name="L409" href="#L409">409</a> <strong class="jxr_keyword">return</strong> values[i++];
+<a class="jxr_linenumber" name="L410" href="#L410">410</a> }
+<a class="jxr_linenumber" name="L411" href="#L411">411</a>
+<a class="jxr_linenumber" name="L412" href="#L412">412</a> @Override
+<a class="jxr_linenumber" name="L413" href="#L413">413</a> <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">double</strong> nextDouble() {
+<a class="jxr_linenumber" name="L414" href="#L414">414</a> <strong class="jxr_keyword">throw</strong> <strong class="jxr_keyword">new</strong> IllegalStateException(<span class="jxr_string">"nextDouble cannot be trusted to be in [0, 1) and should be ignored"</span>);
+<a class="jxr_linenumber" name="L415" href="#L415">415</a> }
+<a class="jxr_linenumber" name="L416" href="#L416">416</a> };
+<a class="jxr_linenumber" name="L417" href="#L417">417</a> }
+<a class="jxr_linenumber" name="L418" href="#L418">418</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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@@ -0,0 +1,86 @@
+<!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>PascalDistributionTest xref</title>
+<link type="text/css" rel="stylesheet" href="../../../../../stylesheet.css" />
+</head>
+<body>
+<div id="overview"><a href="../../../../../../testapidocs/org/apache/commons/statistics/distribution/PascalDistributionTest.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.stream.Stream;
+<a class="jxr_linenumber" name="L20" href="#L20">20</a> <strong class="jxr_keyword">import</strong> org.junit.jupiter.params.ParameterizedTest;
+<a class="jxr_linenumber" name="L21" href="#L21">21</a> <strong class="jxr_keyword">import</strong> org.junit.jupiter.params.provider.Arguments;
+<a class="jxr_linenumber" name="L22" href="#L22">22</a> <strong class="jxr_keyword">import</strong> org.junit.jupiter.params.provider.MethodSource;
+<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"> * Test cases for {@link PascalDistribution}.</em>
+<a class="jxr_linenumber" name="L26" href="#L26">26</a> <em class="jxr_javadoccomment"> * Extends {@link BaseDiscreteDistributionTest}. See javadoc of that class for details.</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> <strong class="jxr_keyword">class</strong> <a name="PascalDistributionTest" href="../../../../../org/apache/commons/statistics/distribution/PascalDistributionTest.html#PascalDistributionTest">PascalDistributionTest</a> <strong class="jxr_keyword">extends</strong> <a name="BaseDiscreteDistributionTest" href="../../../../../org/apache/commons/statistics/distribution/BaseDiscreteDistributionTest.html#BaseDiscreteDistributionTest">BaseDiscreteDistributionTest</a> {
+<a class="jxr_linenumber" name="L29" href="#L29">29</a> @Override
+<a class="jxr_linenumber" name="L30" href="#L30">30</a> DiscreteDistribution makeDistribution(Object... parameters) {
+<a class="jxr_linenumber" name="L31" href="#L31">31</a> <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">int</strong> r = (Integer) parameters[0];
+<a class="jxr_linenumber" name="L32" href="#L32">32</a> <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> p = (Double) parameters[1];
+<a class="jxr_linenumber" name="L33" href="#L33">33</a> <strong class="jxr_keyword">return</strong> PascalDistribution.of(r, p);
+<a class="jxr_linenumber" name="L34" href="#L34">34</a> }
+<a class="jxr_linenumber" name="L35" href="#L35">35</a>
+<a class="jxr_linenumber" name="L36" href="#L36">36</a>
+<a class="jxr_linenumber" name="L37" href="#L37">37</a> @Override
+<a class="jxr_linenumber" name="L38" href="#L38">38</a> Object[][] makeInvalidParameters() {
+<a class="jxr_linenumber" name="L39" href="#L39">39</a> <strong class="jxr_keyword">return</strong> <strong class="jxr_keyword">new</strong> Object[][] {
+<a class="jxr_linenumber" name="L40" href="#L40">40</a> {0, 0.5},
+<a class="jxr_linenumber" name="L41" href="#L41">41</a> {-1, 0.5},
+<a class="jxr_linenumber" name="L42" href="#L42">42</a> {3, -0.1},
+<a class="jxr_linenumber" name="L43" href="#L43">43</a> {3, 0.0},
+<a class="jxr_linenumber" name="L44" href="#L44">44</a> {3, 1.1},
+<a class="jxr_linenumber" name="L45" href="#L45">45</a> };
+<a class="jxr_linenumber" name="L46" href="#L46">46</a> }
+<a class="jxr_linenumber" name="L47" href="#L47">47</a>
+<a class="jxr_linenumber" name="L48" href="#L48">48</a> @Override
+<a class="jxr_linenumber" name="L49" href="#L49">49</a> String[] getParameterNames() {
+<a class="jxr_linenumber" name="L50" href="#L50">50</a> <strong class="jxr_keyword">return</strong> <strong class="jxr_keyword">new</strong> String[] {<span class="jxr_string">"NumberOfSuccesses"</span>, <span class="jxr_string">"ProbabilityOfSuccess"</span>};
+<a class="jxr_linenumber" name="L51" href="#L51">51</a> }
+<a class="jxr_linenumber" name="L52" href="#L52">52</a>
+<a class="jxr_linenumber" name="L53" href="#L53">53</a> @Override
+<a class="jxr_linenumber" name="L54" href="#L54">54</a> <strong class="jxr_keyword">protected</strong> <strong class="jxr_keyword">double</strong> getRelativeTolerance() {
+<a class="jxr_linenumber" name="L55" href="#L55">55</a> <strong class="jxr_keyword">return</strong> 5e-15;
+<a class="jxr_linenumber" name="L56" href="#L56">56</a> }
+<a class="jxr_linenumber" name="L57" href="#L57">57</a>
+<a class="jxr_linenumber" name="L58" href="#L58">58</a> <em class="jxr_comment">//-------------------- Additional test cases -------------------------------</em>
+<a class="jxr_linenumber" name="L59" href="#L59">59</a>
+<a class="jxr_linenumber" name="L60" href="#L60">60</a> @ParameterizedTest
+<a class="jxr_linenumber" name="L61" href="#L61">61</a> @MethodSource
+<a class="jxr_linenumber" name="L62" href="#L62">62</a> <strong class="jxr_keyword">void</strong> testAdditionalMoments(<strong class="jxr_keyword">int</strong> r, <strong class="jxr_keyword">double</strong> p, <strong class="jxr_keyword">double</strong> mean, <strong class="jxr_keyword">double</strong> variance) {
+<a class="jxr_linenumber" name="L63" href="#L63">63</a> <strong class="jxr_keyword">final</strong> PascalDistribution dist = PascalDistribution.of(r, p);
+<a class="jxr_linenumber" name="L64" href="#L64">64</a> testMoments(dist, mean, variance, DoubleTolerances.ulps(1));
+<a class="jxr_linenumber" name="L65" href="#L65">65</a> }
+<a class="jxr_linenumber" name="L66" href="#L66">66</a>
+<a class="jxr_linenumber" name="L67" href="#L67">67</a> <strong class="jxr_keyword">static</strong> Stream<Arguments> testAdditionalMoments() {
+<a class="jxr_linenumber" name="L68" href="#L68">68</a> <strong class="jxr_keyword">return</strong> Stream.of(
+<a class="jxr_linenumber" name="L69" href="#L69">69</a> Arguments.of(10, 0.5, (10d * 0.5d) / 0.5, (10d * 0.5d) / (0.5d * 0.5d)),
+<a class="jxr_linenumber" name="L70" href="#L70">70</a> Arguments.of(25, 0.7, (25d * 0.3d) / 0.7, (25d * 0.3d) / (0.7d * 0.7d))
+<a class="jxr_linenumber" name="L71" href="#L71">71</a> );
+<a class="jxr_linenumber" name="L72" href="#L72">72</a> }
+<a class="jxr_linenumber" name="L73" href="#L73">73</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-test/org/apache/commons/statistics/distribution/PoissonDistributionTest.html
==============================================================================
--- dev/commons/statistics/1.0-RC1/site/xref-test/org/apache/commons/statistics/distribution/PoissonDistributionTest.html (added)
+++ dev/commons/statistics/1.0-RC1/site/xref-test/org/apache/commons/statistics/distribution/PoissonDistributionTest.html Thu Dec 1 16:47:12 2022
@@ -0,0 +1,163 @@
+<!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>PoissonDistributionTest xref</title>
+<link type="text/css" rel="stylesheet" href="../../../../../stylesheet.css" />
+</head>
+<body>
+<div id="overview"><a href="../../../../../../testapidocs/org/apache/commons/statistics/distribution/PoissonDistributionTest.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> org.apache.commons.rng.UniformRandomProvider;
+<a class="jxr_linenumber" name="L20" href="#L20">20</a> <strong class="jxr_keyword">import</strong> org.apache.commons.rng.simple.RandomSource;
+<a class="jxr_linenumber" name="L21" href="#L21">21</a> <strong class="jxr_keyword">import</strong> org.junit.jupiter.api.Assertions;
+<a class="jxr_linenumber" name="L22" href="#L22">22</a> <strong class="jxr_keyword">import</strong> org.junit.jupiter.api.Test;
+<a class="jxr_linenumber" name="L23" href="#L23">23</a> <strong class="jxr_keyword">import</strong> org.junit.jupiter.params.ParameterizedTest;
+<a class="jxr_linenumber" name="L24" href="#L24">24</a> <strong class="jxr_keyword">import</strong> org.junit.jupiter.params.provider.CsvSource;
+<a class="jxr_linenumber" name="L25" href="#L25">25</a>
+<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"> * Test cases for {@link PoissonDistribution}.</em>
+<a class="jxr_linenumber" name="L28" href="#L28">28</a> <em class="jxr_javadoccomment"> * Extends {@link BaseDiscreteDistributionTest}. See javadoc of that class for details.</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> <strong class="jxr_keyword">class</strong> <a name="PoissonDistributionTest" href="../../../../../org/apache/commons/statistics/distribution/PoissonDistributionTest.html#PoissonDistributionTest">PoissonDistributionTest</a> <strong class="jxr_keyword">extends</strong> <a name="BaseDiscreteDistributionTest" href="../../../../../org/apache/commons/statistics/distribution/BaseDiscreteDistributionTest.html#BaseDiscreteDistributionTest">BaseDiscreteDistributionTest</a> {
+<a class="jxr_linenumber" name="L31" href="#L31">31</a> @Override
+<a class="jxr_linenumber" name="L32" href="#L32">32</a> DiscreteDistribution makeDistribution(Object... parameters) {
+<a class="jxr_linenumber" name="L33" href="#L33">33</a> <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> mean = (Double) parameters[0];
+<a class="jxr_linenumber" name="L34" href="#L34">34</a> <strong class="jxr_keyword">return</strong> PoissonDistribution.of(mean);
+<a class="jxr_linenumber" name="L35" href="#L35">35</a> }
+<a class="jxr_linenumber" name="L36" href="#L36">36</a>
+<a class="jxr_linenumber" name="L37" href="#L37">37</a>
+<a class="jxr_linenumber" name="L38" href="#L38">38</a> @Override
+<a class="jxr_linenumber" name="L39" href="#L39">39</a> Object[][] makeInvalidParameters() {
+<a class="jxr_linenumber" name="L40" href="#L40">40</a> <strong class="jxr_keyword">return</strong> <strong class="jxr_keyword">new</strong> Object[][] {
+<a class="jxr_linenumber" name="L41" href="#L41">41</a> {0.0},
+<a class="jxr_linenumber" name="L42" href="#L42">42</a> {-0.1},
+<a class="jxr_linenumber" name="L43" href="#L43">43</a> };
+<a class="jxr_linenumber" name="L44" href="#L44">44</a> }
+<a class="jxr_linenumber" name="L45" href="#L45">45</a>
+<a class="jxr_linenumber" name="L46" href="#L46">46</a> @Override
+<a class="jxr_linenumber" name="L47" href="#L47">47</a> String[] getParameterNames() {
+<a class="jxr_linenumber" name="L48" href="#L48">48</a> <strong class="jxr_keyword">return</strong> <strong class="jxr_keyword">new</strong> String[] {<span class="jxr_string">"Mean"</span>};
+<a class="jxr_linenumber" name="L49" href="#L49">49</a> }
+<a class="jxr_linenumber" name="L50" href="#L50">50</a>
+<a class="jxr_linenumber" name="L51" href="#L51">51</a> @Override
+<a class="jxr_linenumber" name="L52" href="#L52">52</a> <strong class="jxr_keyword">protected</strong> <strong class="jxr_keyword">double</strong> getRelativeTolerance() {
+<a class="jxr_linenumber" name="L53" href="#L53">53</a> <strong class="jxr_keyword">return</strong> 1e-14;
+<a class="jxr_linenumber" name="L54" href="#L54">54</a> }
+<a class="jxr_linenumber" name="L55" href="#L55">55</a>
+<a class="jxr_linenumber" name="L56" href="#L56">56</a> <em class="jxr_comment">//-------------------- Additional test cases -------------------------------</em>
+<a class="jxr_linenumber" name="L57" href="#L57">57</a>
+<a class="jxr_linenumber" name="L58" href="#L58">58</a> @Test
+<a class="jxr_linenumber" name="L59" href="#L59">59</a> <strong class="jxr_keyword">void</strong> testLargeMeanCumulativeProbability() {
+<a class="jxr_linenumber" name="L60" href="#L60">60</a> <strong class="jxr_keyword">double</strong> mean = 1.0;
+<a class="jxr_linenumber" name="L61" href="#L61">61</a> <strong class="jxr_keyword">while</strong> (mean <= 10000000.0) {
+<a class="jxr_linenumber" name="L62" href="#L62">62</a> <strong class="jxr_keyword">final</strong> PoissonDistribution dist = PoissonDistribution.of(mean);
+<a class="jxr_linenumber" name="L63" href="#L63">63</a>
+<a class="jxr_linenumber" name="L64" href="#L64">64</a> <strong class="jxr_keyword">double</strong> x = mean * 2.0;
+<a class="jxr_linenumber" name="L65" href="#L65">65</a> <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> dx = x / 10.0;
+<a class="jxr_linenumber" name="L66" href="#L66">66</a> <strong class="jxr_keyword">double</strong> p = Double.NaN;
+<a class="jxr_linenumber" name="L67" href="#L67">67</a> <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> sigma = Math.sqrt(mean);
+<a class="jxr_linenumber" name="L68" href="#L68">68</a> <strong class="jxr_keyword">while</strong> (x >= 0) {
+<a class="jxr_linenumber" name="L69" href="#L69">69</a> <strong class="jxr_keyword">try</strong> {
+<a class="jxr_linenumber" name="L70" href="#L70">70</a> p = dist.cumulativeProbability((<strong class="jxr_keyword">int</strong>) x);
+<a class="jxr_linenumber" name="L71" href="#L71">71</a> Assertions.assertFalse(Double.isNaN(p), <span class="jxr_string">"NaN cumulative probability"</span>);
+<a class="jxr_linenumber" name="L72" href="#L72">72</a> <strong class="jxr_keyword">if</strong> (x > mean - 2 * sigma) {
+<a class="jxr_linenumber" name="L73" href="#L73">73</a> Assertions.assertTrue(p > 0, <span class="jxr_string">"Zero cumulative probaility"</span>);
+<a class="jxr_linenumber" name="L74" href="#L74">74</a> }
+<a class="jxr_linenumber" name="L75" href="#L75">75</a> } <strong class="jxr_keyword">catch</strong> (<strong class="jxr_keyword">final</strong> AssertionError ex) {
+<a class="jxr_linenumber" name="L76" href="#L76">76</a> Assertions.fail(<span class="jxr_string">"mean of "</span> + mean + <span class="jxr_string">" and x of "</span> + x + <span class="jxr_string">" caused "</span> + ex.getMessage());
+<a class="jxr_linenumber" name="L77" href="#L77">77</a> }
+<a class="jxr_linenumber" name="L78" href="#L78">78</a> x -= dx;
+<a class="jxr_linenumber" name="L79" href="#L79">79</a> }
+<a class="jxr_linenumber" name="L80" href="#L80">80</a>
+<a class="jxr_linenumber" name="L81" href="#L81">81</a> mean *= 10.0;
+<a class="jxr_linenumber" name="L82" href="#L82">82</a> }
+<a class="jxr_linenumber" name="L83" href="#L83">83</a> }
+<a class="jxr_linenumber" name="L84" href="#L84">84</a>
+<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"> * JIRA: MATH-282</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> @ParameterizedTest
+<a class="jxr_linenumber" name="L89" href="#L89">89</a> @CsvSource({
+<a class="jxr_linenumber" name="L90" href="#L90">90</a> <span class="jxr_string">"9120, 9075"</span>,
+<a class="jxr_linenumber" name="L91" href="#L91">91</a> <span class="jxr_string">"9120, 9102"</span>,
+<a class="jxr_linenumber" name="L92" href="#L92">92</a> <span class="jxr_string">"5058, 5044"</span>,
+<a class="jxr_linenumber" name="L93" href="#L93">93</a> <span class="jxr_string">"6986, 6950"</span>,
+<a class="jxr_linenumber" name="L94" href="#L94">94</a> })
+<a class="jxr_linenumber" name="L95" href="#L95">95</a> <strong class="jxr_keyword">void</strong> testCumulativeProbabilitySpecial(<strong class="jxr_keyword">double</strong> mean, <strong class="jxr_keyword">int</strong> x) {
+<a class="jxr_linenumber" name="L96" href="#L96">96</a> <strong class="jxr_keyword">final</strong> PoissonDistribution dist = PoissonDistribution.of(mean);
+<a class="jxr_linenumber" name="L97" href="#L97">97</a> <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> p = dist.cumulativeProbability(x);
+<a class="jxr_linenumber" name="L98" href="#L98">98</a> Assertions.assertFalse(Double.isNaN(p), () -> <span class="jxr_string">"NaN cumulative probability returned for mean = "</span> +
+<a class="jxr_linenumber" name="L99" href="#L99">99</a> dist.getMean() + <span class="jxr_string">" x = "</span> + x);
+<a class="jxr_linenumber" name="L100" href="#L100">100</a> Assertions.assertTrue(p > 0, () -> <span class="jxr_string">"Zero cum probability returned for mean = "</span> +
+<a class="jxr_linenumber" name="L101" href="#L101">101</a> dist.getMean() + <span class="jxr_string">" x = "</span> + x);
+<a class="jxr_linenumber" name="L102" href="#L102">102</a> }
+<a class="jxr_linenumber" name="L103" href="#L103">103</a>
+<a class="jxr_linenumber" name="L104" href="#L104">104</a> @Test
+<a class="jxr_linenumber" name="L105" href="#L105">105</a> <strong class="jxr_keyword">void</strong> testLargeMeanInverseCumulativeProbability() {
+<a class="jxr_linenumber" name="L106" href="#L106">106</a> <strong class="jxr_keyword">double</strong> mean = 1.0;
+<a class="jxr_linenumber" name="L107" href="#L107">107</a> <strong class="jxr_keyword">while</strong> (mean <= 100000.0) { <em class="jxr_comment">// Extended test value: 1E7. Reduced to limit run time.</em>
+<a class="jxr_linenumber" name="L108" href="#L108">108</a> <strong class="jxr_keyword">final</strong> PoissonDistribution dist = PoissonDistribution.of(mean);
+<a class="jxr_linenumber" name="L109" href="#L109">109</a> <strong class="jxr_keyword">double</strong> p = 0.1;
+<a class="jxr_linenumber" name="L110" href="#L110">110</a> <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> dp = p;
+<a class="jxr_linenumber" name="L111" href="#L111">111</a> <strong class="jxr_keyword">while</strong> (p < .99) {
+<a class="jxr_linenumber" name="L112" href="#L112">112</a> <strong class="jxr_keyword">try</strong> {
+<a class="jxr_linenumber" name="L113" href="#L113">113</a> <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">int</strong> ret = dist.inverseCumulativeProbability(p);
+<a class="jxr_linenumber" name="L114" href="#L114">114</a> <em class="jxr_comment">// Verify that returned value satisfies definition</em>
+<a class="jxr_linenumber" name="L115" href="#L115">115</a> Assertions.assertTrue(p <= dist.cumulativeProbability(ret));
+<a class="jxr_linenumber" name="L116" href="#L116">116</a> Assertions.assertTrue(p > dist.cumulativeProbability(ret - 1));
+<a class="jxr_linenumber" name="L117" href="#L117">117</a> } <strong class="jxr_keyword">catch</strong> (<strong class="jxr_keyword">final</strong> AssertionError ex) {
+<a class="jxr_linenumber" name="L118" href="#L118">118</a> Assertions.fail(<span class="jxr_string">"mean of "</span> + mean + <span class="jxr_string">" and p of "</span> + p + <span class="jxr_string">" caused "</span> + ex.getMessage());
+<a class="jxr_linenumber" name="L119" href="#L119">119</a> }
+<a class="jxr_linenumber" name="L120" href="#L120">120</a> p += dp;
+<a class="jxr_linenumber" name="L121" href="#L121">121</a> }
+<a class="jxr_linenumber" name="L122" href="#L122">122</a> mean *= 10.0;
+<a class="jxr_linenumber" name="L123" href="#L123">123</a> }
+<a class="jxr_linenumber" name="L124" href="#L124">124</a> }
+<a class="jxr_linenumber" name="L125" href="#L125">125</a>
+<a class="jxr_linenumber" name="L126" href="#L126">126</a> @Test
+<a class="jxr_linenumber" name="L127" href="#L127">127</a> <strong class="jxr_keyword">void</strong> testAdditionalCumulativeProbabilityHighPrecision() {
+<a class="jxr_linenumber" name="L128" href="#L128">128</a> <em class="jxr_comment">// computed using R version 3.4.4</em>
+<a class="jxr_linenumber" name="L129" href="#L129">129</a> testCumulativeProbabilityHighPrecision(
+<a class="jxr_linenumber" name="L130" href="#L130">130</a> PoissonDistribution.of(100),
+<a class="jxr_linenumber" name="L131" href="#L131">131</a> <strong class="jxr_keyword">new</strong> <strong class="jxr_keyword">int</strong>[] {28, 25},
+<a class="jxr_linenumber" name="L132" href="#L132">132</a> <strong class="jxr_keyword">new</strong> <strong class="jxr_keyword">double</strong>[] {1.6858675763053070496e-17, 3.184075559619425735e-19},
+<a class="jxr_linenumber" name="L133" href="#L133">133</a> DoubleTolerances.relative(5e-14));
+<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">/**</em>
+<a class="jxr_linenumber" name="L137" href="#L137">137</a> <em class="jxr_javadoccomment"> * Test creation of a sampler with a large mean that computes valid probabilities.</em>
+<a class="jxr_linenumber" name="L138" href="#L138">138</a> <em class="jxr_javadoccomment"> */</em>
+<a class="jxr_linenumber" name="L139" href="#L139">139</a> @Test
+<a class="jxr_linenumber" name="L140" href="#L140">140</a> <strong class="jxr_keyword">void</strong> testCreateSamplerWithLargeMean() {
+<a class="jxr_linenumber" name="L141" href="#L141">141</a> <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">int</strong> mean = Integer.MAX_VALUE;
+<a class="jxr_linenumber" name="L142" href="#L142">142</a> <strong class="jxr_keyword">final</strong> PoissonDistribution dist = PoissonDistribution.of(mean);
+<a class="jxr_linenumber" name="L143" href="#L143">143</a> <em class="jxr_comment">// The mean is roughly the median for large mean</em>
+<a class="jxr_linenumber" name="L144" href="#L144">144</a> Assertions.assertEquals(0.5, dist.cumulativeProbability(mean), 0.05);
+<a class="jxr_linenumber" name="L145" href="#L145">145</a> <strong class="jxr_keyword">final</strong> UniformRandomProvider rng = RandomSource.SPLIT_MIX_64.create();
+<a class="jxr_linenumber" name="L146" href="#L146">146</a> dist.createSampler(rng)
+<a class="jxr_linenumber" name="L147" href="#L147">147</a> .samples(50)
+<a class="jxr_linenumber" name="L148" href="#L148">148</a> .forEach(i -> Assertions.assertTrue(i >= 0, () -> <span class="jxr_string">"Bad sample: "</span> + i));
+<a class="jxr_linenumber" name="L149" href="#L149">149</a> }
+<a class="jxr_linenumber" name="L150" href="#L150">150</a> }
+</pre>
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