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+<div id="overview"><a href="../../../../../../testapidocs/org/apache/commons/statistics/distribution/GammaDistributionTest.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> java.io.BufferedReader;
+<a class="jxr_linenumber" name="L21" href="#L21">21</a> <strong class="jxr_keyword">import</strong> java.io.IOException;
+<a class="jxr_linenumber" name="L22" href="#L22">22</a> <strong class="jxr_keyword">import</strong> java.io.InputStream;
+<a class="jxr_linenumber" name="L23" href="#L23">23</a> <strong class="jxr_keyword">import</strong> java.io.InputStreamReader;
+<a class="jxr_linenumber" name="L24" href="#L24">24</a> <strong class="jxr_keyword">import</strong> java.util.stream.Stream;
+<a class="jxr_linenumber" name="L25" href="#L25">25</a> <strong class="jxr_keyword">import</strong> org.apache.commons.math3.stat.descriptive.SummaryStatistics;
+<a class="jxr_linenumber" name="L26" href="#L26">26</a> <strong class="jxr_keyword">import</strong> org.apache.commons.numbers.gamma.LanczosApproximation;
+<a class="jxr_linenumber" name="L27" href="#L27">27</a> <strong class="jxr_keyword">import</strong> org.junit.jupiter.api.Assertions;
+<a class="jxr_linenumber" name="L28" href="#L28">28</a> <strong class="jxr_keyword">import</strong> org.junit.jupiter.params.ParameterizedTest;
+<a class="jxr_linenumber" name="L29" href="#L29">29</a> <strong class="jxr_keyword">import</strong> org.junit.jupiter.params.provider.Arguments;
+<a class="jxr_linenumber" name="L30" href="#L30">30</a> <strong class="jxr_keyword">import</strong> org.junit.jupiter.params.provider.CsvSource;
+<a class="jxr_linenumber" name="L31" href="#L31">31</a> <strong class="jxr_keyword">import</strong> org.junit.jupiter.params.provider.MethodSource;
+<a class="jxr_linenumber" name="L32" href="#L32">32</a>
+<a class="jxr_linenumber" name="L33" href="#L33">33</a> <em class="jxr_javadoccomment">/**</em>
+<a class="jxr_linenumber" name="L34" href="#L34">34</a> <em class="jxr_javadoccomment"> * Test cases for {@link GammaDistribution}.</em>
+<a class="jxr_linenumber" name="L35" href="#L35">35</a> <em class="jxr_javadoccomment"> * Extends {@link BaseContinuousDistributionTest}. See javadoc of that class for details.</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">class</strong> <a name="GammaDistributionTest" href="../../../../../org/apache/commons/statistics/distribution/GammaDistributionTest.html#GammaDistributionTest">GammaDistributionTest</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="L38" href="#L38">38</a> <strong class="jxr_keyword">private</strong> <strong class="jxr_keyword">static</strong> <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> HALF_LOG_2_PI = 0.5 * Math.log(2.0 * Math.PI);
+<a class="jxr_linenumber" name="L39" href="#L39">39</a>
+<a class="jxr_linenumber" name="L40" href="#L40">40</a> @Override
+<a class="jxr_linenumber" name="L41" href="#L41">41</a> ContinuousDistribution makeDistribution(Object... parameters) {
+<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[0];
+<a class="jxr_linenumber" name="L43" href="#L43">43</a> <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> scale = (Double) parameters[1];
+<a class="jxr_linenumber" name="L44" href="#L44">44</a> <strong class="jxr_keyword">return</strong> GammaDistribution.of(shape, scale);
+<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> @Override
+<a class="jxr_linenumber" name="L48" href="#L48">48</a> Object[][] makeInvalidParameters() {
+<a class="jxr_linenumber" name="L49" href="#L49">49</a> <strong class="jxr_keyword">return</strong> <strong class="jxr_keyword">new</strong> Object[][] {
+<a class="jxr_linenumber" name="L50" href="#L50">50</a> {0.0, 1.0},
+<a class="jxr_linenumber" name="L51" href="#L51">51</a> {-0.1, 1.0},
+<a class="jxr_linenumber" name="L52" href="#L52">52</a> {1.0, 0.0},
+<a class="jxr_linenumber" name="L53" href="#L53">53</a> {1.0, -0.1},
+<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">"Shape"</span>, <span class="jxr_string">"Scale"</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> <em class="jxr_comment">// Tolerance is 8.881784197001252E-16</em>
+<a class="jxr_linenumber" name="L65" href="#L65">65</a> <strong class="jxr_keyword">return</strong> 4 * RELATIVE_EPS;
+<a class="jxr_linenumber" name="L66" href="#L66">66</a> }
+<a class="jxr_linenumber" name="L67" href="#L67">67</a>
+<a class="jxr_linenumber" name="L68" href="#L68">68</a> <em class="jxr_comment">//-------------------- Additional test cases -------------------------------</em>
+<a class="jxr_linenumber" name="L69" href="#L69">69</a>
+<a class="jxr_linenumber" name="L70" href="#L70">70</a> @ParameterizedTest
+<a class="jxr_linenumber" name="L71" href="#L71">71</a> @MethodSource
+<a class="jxr_linenumber" name="L72" href="#L72">72</a> <strong class="jxr_keyword">void</strong> testAdditionalMoments(<strong class="jxr_keyword">double</strong> shape, <strong class="jxr_keyword">double</strong> scale, <strong class="jxr_keyword">double</strong> mean, <strong class="jxr_keyword">double</strong> variance) {
+<a class="jxr_linenumber" name="L73" href="#L73">73</a> <strong class="jxr_keyword">final</strong> GammaDistribution dist = GammaDistribution.of(shape, scale);
+<a class="jxr_linenumber" name="L74" href="#L74">74</a> testMoments(dist, mean, variance, DoubleTolerances.equals());
+<a class="jxr_linenumber" name="L75" href="#L75">75</a> }
+<a class="jxr_linenumber" name="L76" href="#L76">76</a>
+<a class="jxr_linenumber" name="L77" href="#L77">77</a> <strong class="jxr_keyword">static</strong> Stream<Arguments> testAdditionalMoments() {
+<a class="jxr_linenumber" name="L78" href="#L78">78</a> <strong class="jxr_keyword">return</strong> Stream.of(
+<a class="jxr_linenumber" name="L79" href="#L79">79</a> Arguments.of(1, 2, 2, 4),
+<a class="jxr_linenumber" name="L80" href="#L80">80</a> Arguments.of(1.1, 4.2, 1.1 * 4.2, 1.1 * 4.2 * 4.2),
+<a class="jxr_linenumber" name="L81" href="#L81">81</a> <em class="jxr_comment">// scipy.stats.gamma(shape, scale=scale).stats()</em>
+<a class="jxr_linenumber" name="L82" href="#L82">82</a> Arguments.of(0.5, 10, 5, 50),
+<a class="jxr_linenumber" name="L83" href="#L83">83</a> Arguments.of(0.5, 7.5, 3.75, 28.125),
+<a class="jxr_linenumber" name="L84" href="#L84">84</a> Arguments.of(0.25, 10, 2.5, 25)
+<a class="jxr_linenumber" name="L85" href="#L85">85</a> );
+<a class="jxr_linenumber" name="L86" href="#L86">86</a> }
+<a class="jxr_linenumber" name="L87" href="#L87">87</a>
+<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">"4.0, 2.0, -1.0, 0.0"</span>,
+<a class="jxr_linenumber" name="L91" href="#L91">91</a> <span class="jxr_string">"4.0, 2.0, 15.501, 0.94989465156755404"</span>,
+<a class="jxr_linenumber" name="L92" href="#L92">92</a> <span class="jxr_string">"4.0, 1.0, 0.504, 0.0018026739713985257"</span>,
+<a class="jxr_linenumber" name="L93" href="#L93">93</a> <span class="jxr_string">"1.0, 2.0, 10.011, 0.99329900998454213"</span>,
+<a class="jxr_linenumber" name="L94" href="#L94">94</a> <span class="jxr_string">"2.0, 2.0, 5.000, 0.71270250481635422"</span>,
+<a class="jxr_linenumber" name="L95" href="#L95">95</a> })
+<a class="jxr_linenumber" name="L96" href="#L96">96</a> <strong class="jxr_keyword">void</strong> testAdditionalCumulativeProbability(<strong class="jxr_keyword">double</strong> a, <strong class="jxr_keyword">double</strong> b, <strong class="jxr_keyword">double</strong> x, <strong class="jxr_keyword">double</strong> expected) {
+<a class="jxr_linenumber" name="L97" href="#L97">97</a> <strong class="jxr_keyword">final</strong> GammaDistribution dist = GammaDistribution.of(a, b);
+<a class="jxr_linenumber" name="L98" href="#L98">98</a> <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> actual = dist.cumulativeProbability(x);
+<a class="jxr_linenumber" name="L99" href="#L99">99</a> Assertions.assertEquals(expected, actual, expected * 1e-15, () -> <span class="jxr_string">"probability for "</span> + x);
+<a class="jxr_linenumber" name="L100" href="#L100">100</a> }
+<a class="jxr_linenumber" name="L101" href="#L101">101</a>
+<a class="jxr_linenumber" name="L102" href="#L102">102</a> @ParameterizedTest
+<a class="jxr_linenumber" name="L103" href="#L103">103</a> @CsvSource({
+<a class="jxr_linenumber" name="L104" href="#L104">104</a> <span class="jxr_string">"4.0, 2.0, 0.94989465156755404, 15.501"</span>,
+<a class="jxr_linenumber" name="L105" href="#L105">105</a> <span class="jxr_string">"4.0, 1.0, 0.0018026739713985257, 0.504"</span>,
+<a class="jxr_linenumber" name="L106" href="#L106">106</a> <span class="jxr_string">"1.0, 2.0, 0.99329900998454213, 10.011"</span>,
+<a class="jxr_linenumber" name="L107" href="#L107">107</a> <span class="jxr_string">"2.0, 2.0, 0.71270250481635422, 5.0"</span>,
+<a class="jxr_linenumber" name="L108" href="#L108">108</a> })
+<a class="jxr_linenumber" name="L109" href="#L109">109</a> <strong class="jxr_keyword">void</strong> testAdditionalInverseCumulativeProbability(<strong class="jxr_keyword">double</strong> a, <strong class="jxr_keyword">double</strong> b, <strong class="jxr_keyword">double</strong> p, <strong class="jxr_keyword">double</strong> expected) {
+<a class="jxr_linenumber" name="L110" href="#L110">110</a> <strong class="jxr_keyword">final</strong> GammaDistribution dist = GammaDistribution.of(a, b);
+<a class="jxr_linenumber" name="L111" href="#L111">111</a> <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> actual = dist.inverseCumulativeProbability(p);
+<a class="jxr_linenumber" name="L112" href="#L112">112</a> Assertions.assertEquals(expected, actual, expected * 5e-15, () -> <span class="jxr_string">"critical value for "</span> + p);
+<a class="jxr_linenumber" name="L113" href="#L113">113</a> }
+<a class="jxr_linenumber" name="L114" href="#L114">114</a>
+<a class="jxr_linenumber" name="L115" href="#L115">115</a> @ParameterizedTest
+<a class="jxr_linenumber" name="L116" href="#L116">116</a> @MethodSource
+<a class="jxr_linenumber" name="L117" href="#L117">117</a> <strong class="jxr_keyword">void</strong> testAdditionalDensity(<strong class="jxr_keyword">double</strong> alpha, <strong class="jxr_keyword">double</strong> rate, <strong class="jxr_keyword">double</strong>[] x, <strong class="jxr_keyword">double</strong>[] expected) {
+<a class="jxr_linenumber" name="L118" href="#L118">118</a> <strong class="jxr_keyword">final</strong> GammaDistribution dist = GammaDistribution.of(alpha, 1 / rate);
+<a class="jxr_linenumber" name="L119" href="#L119">119</a> testDensity(dist, x, expected, createRelTolerance(1e-9));
+<a class="jxr_linenumber" name="L120" href="#L120">120</a> }
+<a class="jxr_linenumber" name="L121" href="#L121">121</a>
+<a class="jxr_linenumber" name="L122" href="#L122">122</a> <strong class="jxr_keyword">static</strong> Stream<Arguments> testAdditionalDensity() {
+<a class="jxr_linenumber" name="L123" href="#L123">123</a> <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong>[] x = {-0.1, 1e-6, 0.5, 1, 2, 5};
+<a class="jxr_linenumber" name="L124" href="#L124">124</a> <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong>[] x1 = <strong class="jxr_keyword">new</strong> <strong class="jxr_keyword">double</strong>[]{1e-100, 1e-10, 1e-5, 0.1};
+<a class="jxr_linenumber" name="L125" href="#L125">125</a> <strong class="jxr_keyword">return</strong> Stream.of(
+<a class="jxr_linenumber" name="L126" href="#L126">126</a> <em class="jxr_comment">// R2.5: print(dgamma((x, shape=1, rate=1), digits=10)</em>
+<a class="jxr_linenumber" name="L127" href="#L127">127</a> Arguments.of(1, 1, x, <strong class="jxr_keyword">new</strong> <strong class="jxr_keyword">double</strong>[]{0.000000000000, 0.999999000001, 0.606530659713, 0.367879441171, 0.135335283237, 0.006737946999}),
+<a class="jxr_linenumber" name="L128" href="#L128">128</a> <em class="jxr_comment">// R2.5: print(dgamma((x, shape=2, rate=1), digits=10)</em>
+<a class="jxr_linenumber" name="L129" href="#L129">129</a> Arguments.of(2, 1, x, <strong class="jxr_keyword">new</strong> <strong class="jxr_keyword">double</strong>[]{0.000000000000, 0.000000999999, 0.303265329856, 0.367879441171, 0.270670566473, 0.033689734995}),
+<a class="jxr_linenumber" name="L130" href="#L130">130</a> <em class="jxr_comment">// R2.5: print(dgamma((x, shape=4, rate=1), digits=10)</em>
+<a class="jxr_linenumber" name="L131" href="#L131">131</a> Arguments.of(4, 1, x, <strong class="jxr_keyword">new</strong> <strong class="jxr_keyword">double</strong>[]{0.000000000e+00, 1.666665000e-19, 1.263605541e-02, 6.131324020e-02, 1.804470443e-01, 1.403738958e-01}),
+<a class="jxr_linenumber" name="L132" href="#L132">132</a> <em class="jxr_comment">// R2.5: print(dgamma((x, shape=4, rate=10), digits=10)</em>
+<a class="jxr_linenumber" name="L133" href="#L133">133</a> Arguments.of(4, 10, x, <strong class="jxr_keyword">new</strong> <strong class="jxr_keyword">double</strong>[]{0.000000000e+00, 1.666650000e-15, 1.403738958e+00, 7.566654960e-02, 2.748204830e-05, 4.018228850e-17}),
+<a class="jxr_linenumber" name="L134" href="#L134">134</a> <em class="jxr_comment">// R2.5: print(dgamma((x, shape=.1, rate=10), digits=10)</em>
+<a class="jxr_linenumber" name="L135" href="#L135">135</a> Arguments.of(0.1, 10, x, <strong class="jxr_keyword">new</strong> <strong class="jxr_keyword">double</strong>[]{0.000000000e+00, 3.323953832e+04, 1.663849010e-03, 6.007786726e-06, 1.461647647e-10, 5.996008322e-24}),
+<a class="jxr_linenumber" name="L136" href="#L136">136</a> <em class="jxr_comment">// R2.5: print(dgamma((x, shape=.1, rate=20), digits=10)</em>
+<a class="jxr_linenumber" name="L137" href="#L137">137</a> Arguments.of(0.1, 20, x, <strong class="jxr_keyword">new</strong> <strong class="jxr_keyword">double</strong>[]{0.000000000e+00, 3.562489883e+04, 1.201557345e-05, 2.923295295e-10, 3.228910843e-19, 1.239484589e-45}),
+<a class="jxr_linenumber" name="L138" href="#L138">138</a> <em class="jxr_comment">// R2.5: print(dgamma((x, shape=.1, rate=4), digits=10)</em>
+<a class="jxr_linenumber" name="L139" href="#L139">139</a> Arguments.of(0.1, 4, x, <strong class="jxr_keyword">new</strong> <strong class="jxr_keyword">double</strong>[]{0.000000000e+00, 3.032938388e+04, 3.049322494e-02, 2.211502311e-03, 2.170613371e-05, 5.846590589e-11}),
+<a class="jxr_linenumber" name="L140" href="#L140">140</a> <em class="jxr_comment">// R2.5: print(dgamma((x, shape=.1, rate=1), digits=10)</em>
+<a class="jxr_linenumber" name="L141" href="#L141">141</a> Arguments.of(0.1, 1, x, <strong class="jxr_keyword">new</strong> <strong class="jxr_keyword">double</strong>[]{0.000000000e+00, 2.640334143e+04, 1.189704437e-01, 3.866916944e-02, 7.623306235e-03, 1.663849010e-04}),
+<a class="jxr_linenumber" name="L142" href="#L142">142</a> <em class="jxr_comment">// To force overflow condition</em>
+<a class="jxr_linenumber" name="L143" href="#L143">143</a> <em class="jxr_comment">// R2.5: print(dgamma((x, shape=1000, rate=100), digits=10)</em>
+<a class="jxr_linenumber" name="L144" href="#L144">144</a> Arguments.of(1000, 100, x, <strong class="jxr_keyword">new</strong> <strong class="jxr_keyword">double</strong>[]{0.000000000e+00, 0.000000000e+00, 0.000000000e+00, 0.000000000e+00, 0.000000000e+00, 3.304830256e-84}),
+<a class="jxr_linenumber" name="L145" href="#L145">145</a>
+<a class="jxr_linenumber" name="L146" href="#L146">146</a> <em class="jxr_comment">// Test a shape far below 1.</em>
+<a class="jxr_linenumber" name="L147" href="#L147">147</a> <em class="jxr_comment">// Support for very small shape parameters was fixed in STATISTICS-39.</em>
+<a class="jxr_linenumber" name="L148" href="#L148">148</a> <em class="jxr_comment">// R2.5: print(dgamma((x1, shape=0.05, rate=1), digits=20)</em>
+<a class="jxr_linenumber" name="L149" href="#L149">149</a> Arguments.of(0.05, 1, x1,
+<a class="jxr_linenumber" name="L150" href="#L150">150</a> <strong class="jxr_keyword">new</strong> <strong class="jxr_keyword">double</strong>[] {
+<a class="jxr_linenumber" name="L151" href="#L151">151</a> 5.1360843263583843333e+93, 1.6241724724359893799e+08,
+<a class="jxr_linenumber" name="L152" href="#L152">152</a> 2.8882035841935007738e+03, 4.1419294512123655538e-01
+<a class="jxr_linenumber" name="L153" href="#L153">153</a> })
+<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> @ParameterizedTest
+<a class="jxr_linenumber" name="L158" href="#L158">158</a> @MethodSource
+<a class="jxr_linenumber" name="L159" href="#L159">159</a> <strong class="jxr_keyword">void</strong> testAdditionalLogDensity(<strong class="jxr_keyword">double</strong> alpha, <strong class="jxr_keyword">double</strong> rate, <strong class="jxr_keyword">double</strong>[] x, <strong class="jxr_keyword">double</strong>[] expected) {
+<a class="jxr_linenumber" name="L160" href="#L160">160</a> <strong class="jxr_keyword">final</strong> GammaDistribution dist = GammaDistribution.of(alpha, 1 / rate);
+<a class="jxr_linenumber" name="L161" href="#L161">161</a> testLogDensity(dist, x, expected, createRelTolerance(1e-9));
+<a class="jxr_linenumber" name="L162" href="#L162">162</a> }
+<a class="jxr_linenumber" name="L163" href="#L163">163</a>
+<a class="jxr_linenumber" name="L164" href="#L164">164</a> <strong class="jxr_keyword">static</strong> Stream<Arguments> testAdditionalLogDensity() {
+<a class="jxr_linenumber" name="L165" href="#L165">165</a> <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong>[] x = {-0.1, 1e-6, 0.5, 1, 2, 5};
+<a class="jxr_linenumber" name="L166" href="#L166">166</a> <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong>[] x1 = {1e-315, 1e-320, 1e-323};
+<a class="jxr_linenumber" name="L167" href="#L167">167</a> <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> inf = Double.POSITIVE_INFINITY;
+<a class="jxr_linenumber" name="L168" href="#L168">168</a> <strong class="jxr_keyword">return</strong> Stream.of(
+<a class="jxr_linenumber" name="L169" href="#L169">169</a> <em class="jxr_comment">// R2.5: print(dgamma((x, shape=1, rate=1, log=TRUE), digits=10)</em>
+<a class="jxr_linenumber" name="L170" href="#L170">170</a> Arguments.of(1, 1, x, <strong class="jxr_keyword">new</strong> <strong class="jxr_keyword">double</strong>[]{-inf, -1e-06, -5e-01, -1e+00, -2e+00, -5e+00}),
+<a class="jxr_linenumber" name="L171" href="#L171">171</a> <em class="jxr_comment">// R2.5: print(dgamma((x, shape=2, rate=1, log=TRUE), digits=10)</em>
+<a class="jxr_linenumber" name="L172" href="#L172">172</a> Arguments.of(2, 1, x, <strong class="jxr_keyword">new</strong> <strong class="jxr_keyword">double</strong>[]{-inf, -13.815511558, -1.193147181, -1.000000000, -1.306852819, -3.390562088}),
+<a class="jxr_linenumber" name="L173" href="#L173">173</a> <em class="jxr_comment">// R2.5: print(dgamma((x, shape=4, rate=1, log=TRUE), digits=10)</em>
+<a class="jxr_linenumber" name="L174" href="#L174">174</a> Arguments.of(4, 1, x, <strong class="jxr_keyword">new</strong> <strong class="jxr_keyword">double</strong>[]{-inf, -43.238292143, -4.371201011, -2.791759469, -1.712317928, -1.963445732}),
+<a class="jxr_linenumber" name="L175" href="#L175">175</a> <em class="jxr_comment">// R2.5: print(dgamma((x, shape=4, rate=10, log=TRUE), digits=10)</em>
+<a class="jxr_linenumber" name="L176" href="#L176">176</a> Arguments.of(4, 10, x, <strong class="jxr_keyword">new</strong> <strong class="jxr_keyword">double</strong>[]{-inf, -34.0279607711, 0.3391393611, -2.5814190973, -10.5019775556, -37.7531053599}),
+<a class="jxr_linenumber" name="L177" href="#L177">177</a> <em class="jxr_comment">// R2.5: print(dgamma((x, shape=.1, rate=10, log=TRUE), digits=10)</em>
+<a class="jxr_linenumber" name="L178" href="#L178">178</a> Arguments.of(0.1, 10, x, <strong class="jxr_keyword">new</strong> <strong class="jxr_keyword">double</strong>[]{-inf, 10.41149536, -6.39862168, -12.02245414, -22.64628660, -53.47094826}),
+<a class="jxr_linenumber" name="L179" href="#L179">179</a> <em class="jxr_comment">// R2.5: print(dgamma((x, shape=.1, rate=20, log=TRUE), digits=10)</em>
+<a class="jxr_linenumber" name="L180" href="#L180">180</a> Arguments.of(0.1, 20, x, <strong class="jxr_keyword">new</strong> <strong class="jxr_keyword">double</strong>[]{-inf, 10.48080008, -11.32930696, -21.95313942, -42.57697189, -103.40163355}),
+<a class="jxr_linenumber" name="L181" href="#L181">181</a> <em class="jxr_comment">// R2.5: print(dgamma((x, shape=.1, rate=4, log=TRUE), digits=10)</em>
+<a class="jxr_linenumber" name="L182" href="#L182">182</a> Arguments.of(0.1, 4, x, <strong class="jxr_keyword">new</strong> <strong class="jxr_keyword">double</strong>[]{-inf, 10.319872287, -3.490250753, -6.114083216, -10.737915678, -23.562577337}),
+<a class="jxr_linenumber" name="L183" href="#L183">183</a> <em class="jxr_comment">// R2.5: print(dgamma((x, shape=.1, rate=1, log=TRUE), digits=10)</em>
+<a class="jxr_linenumber" name="L184" href="#L184">184</a> Arguments.of(0.1, 1, x, <strong class="jxr_keyword">new</strong> <strong class="jxr_keyword">double</strong>[]{-inf, 10.181245850, -2.128880189, -3.252712652, -4.876545114, -8.701206773}),
+<a class="jxr_linenumber" name="L185" href="#L185">185</a> <em class="jxr_comment">// To force overflow condition to pdf=zero</em>
+<a class="jxr_linenumber" name="L186" href="#L186">186</a> <em class="jxr_comment">// R2.5: print(dgamma((x, shape=1000, rate=100, log=TRUE), digits=10)</em>
+<a class="jxr_linenumber" name="L187" href="#L187">187</a> Arguments.of(1000, 100, x, <strong class="jxr_keyword">new</strong> <strong class="jxr_keyword">double</strong>[]{-inf, -15101.7453846, -2042.5042706, -1400.0502372, -807.5962038, -192.2217627}),
+<a class="jxr_linenumber" name="L188" href="#L188">188</a> <em class="jxr_comment">// To force overflow condition to pdf=infinity</em>
+<a class="jxr_linenumber" name="L189" href="#L189">189</a> <em class="jxr_comment">// scipy.stats gamma(1e-2).logpdf(x1)</em>
+<a class="jxr_linenumber" name="L190" href="#L190">190</a> Arguments.of(0.01, 1, x1,
+<a class="jxr_linenumber" name="L191" href="#L191">191</a> <strong class="jxr_keyword">new</strong> <strong class="jxr_keyword">double</strong>[]{713.46168137365419, 724.85948860402209, 731.70997561537104})
+<a class="jxr_linenumber" name="L192" href="#L192">192</a> );
+<a class="jxr_linenumber" name="L193" href="#L193">193</a> }
+<a class="jxr_linenumber" name="L194" href="#L194">194</a>
+<a class="jxr_linenumber" name="L195" href="#L195">195</a> <strong class="jxr_keyword">private</strong> <strong class="jxr_keyword">static</strong> <strong class="jxr_keyword">double</strong> logGamma(<strong class="jxr_keyword">double</strong> x) {
+<a class="jxr_linenumber" name="L196" href="#L196">196</a> <em class="jxr_comment">/*</em>
+<a class="jxr_linenumber" name="L197" href="#L197">197</a> <em class="jxr_comment"> * This is a copy of</em>
+<a class="jxr_linenumber" name="L198" href="#L198">198</a> <em class="jxr_comment"> * double Gamma.logGamma(double)</em>
+<a class="jxr_linenumber" name="L199" href="#L199">199</a> <em class="jxr_comment"> * prior to MATH-849</em>
+<a class="jxr_linenumber" name="L200" href="#L200">200</a> <em class="jxr_comment"> */</em>
+<a class="jxr_linenumber" name="L201" href="#L201">201</a> <strong class="jxr_keyword">if</strong> (Double.isNaN(x) || x <= 0.0) {
+<a class="jxr_linenumber" name="L202" href="#L202">202</a> <strong class="jxr_keyword">return</strong> Double.NaN;
+<a class="jxr_linenumber" name="L203" href="#L203">203</a> }
+<a class="jxr_linenumber" name="L204" href="#L204">204</a> <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> sum = LanczosApproximation.value(x);
+<a class="jxr_linenumber" name="L205" href="#L205">205</a> <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> tmp = x + LanczosApproximation.g() + .5;
+<a class="jxr_linenumber" name="L206" href="#L206">206</a> <strong class="jxr_keyword">return</strong> ((x + .5) * Math.log(tmp)) - tmp +
+<a class="jxr_linenumber" name="L207" href="#L207">207</a> HALF_LOG_2_PI + Math.log(sum / x);
+<a class="jxr_linenumber" name="L208" href="#L208">208</a> }
+<a class="jxr_linenumber" name="L209" href="#L209">209</a>
+<a class="jxr_linenumber" name="L210" href="#L210">210</a> <strong class="jxr_keyword">private</strong> <strong class="jxr_keyword">static</strong> <strong class="jxr_keyword">double</strong> density(<strong class="jxr_keyword">double</strong> x,
+<a class="jxr_linenumber" name="L211" href="#L211">211</a> <strong class="jxr_keyword">double</strong> shape,
+<a class="jxr_linenumber" name="L212" href="#L212">212</a> <strong class="jxr_keyword">double</strong> scale) {
+<a class="jxr_linenumber" name="L213" href="#L213">213</a> <em class="jxr_comment">/*</em>
+<a class="jxr_linenumber" name="L214" href="#L214">214</a> <em class="jxr_comment"> * This is a copy of</em>
+<a class="jxr_linenumber" name="L215" href="#L215">215</a> <em class="jxr_comment"> * double GammaDistribution.density(double)</em>
+<a class="jxr_linenumber" name="L216" href="#L216">216</a> <em class="jxr_comment"> * prior to MATH-753.</em>
+<a class="jxr_linenumber" name="L217" href="#L217">217</a> <em class="jxr_comment"> */</em>
+<a class="jxr_linenumber" name="L218" href="#L218">218</a> <strong class="jxr_keyword">if</strong> (x < 0) {
+<a class="jxr_linenumber" name="L219" href="#L219">219</a> <strong class="jxr_keyword">return</strong> 0;
+<a class="jxr_linenumber" name="L220" href="#L220">220</a> }
+<a class="jxr_linenumber" name="L221" href="#L221">221</a> <strong class="jxr_keyword">return</strong> Math.pow(x / scale, shape - 1) / scale *
+<a class="jxr_linenumber" name="L222" href="#L222">222</a> Math.exp(-x / scale) / Math.exp(logGamma(shape));
+<a class="jxr_linenumber" name="L223" href="#L223">223</a> }
+<a class="jxr_linenumber" name="L224" href="#L224">224</a>
+<a class="jxr_linenumber" name="L225" href="#L225">225</a> <em class="jxr_javadoccomment">/**</em>
+<a class="jxr_linenumber" name="L226" href="#L226">226</a> <em class="jxr_javadoccomment"> * MATH-753: large values of x or shape parameter cause density(double) to</em>
+<a class="jxr_linenumber" name="L227" href="#L227">227</a> <em class="jxr_javadoccomment"> * overflow. Reference data is generated with the Maxima script</em>
+<a class="jxr_linenumber" name="L228" href="#L228">228</a> <em class="jxr_javadoccomment"> * gamma-distribution.mac, which can be found in</em>
+<a class="jxr_linenumber" name="L229" href="#L229">229</a> <em class="jxr_javadoccomment"> * src/test/resources/org/apache/commons/statistics/distribution.</em>
+<a class="jxr_linenumber" name="L230" href="#L230">230</a> <em class="jxr_javadoccomment"> *</em>
+<a class="jxr_linenumber" name="L231" href="#L231">231</a> <em class="jxr_javadoccomment"> * @param shape Shape of gamma distribution (scale is assumed to be 1)</em>
+<a class="jxr_linenumber" name="L232" href="#L232">232</a> <em class="jxr_javadoccomment"> * @param meanNoOF Allowed mean ULP error when the computed value does not overflow using the old method</em>
+<a class="jxr_linenumber" name="L233" href="#L233">233</a> <em class="jxr_javadoccomment"> * @param sdNoOF Allowed SD ULP error when the computed value does not overflow using the old method</em>
+<a class="jxr_linenumber" name="L234" href="#L234">234</a> <em class="jxr_javadoccomment"> * @param meanOF Allowed mean ULP error when the computed value overflows using the old method</em>
+<a class="jxr_linenumber" name="L235" href="#L235">235</a> <em class="jxr_javadoccomment"> * @param sdOF Allowed SD ULP error when the computed value overflows using the old method</em>
+<a class="jxr_linenumber" name="L236" href="#L236">236</a> <em class="jxr_javadoccomment"> * @param resourceName Resource name containing a pair of comma separated values for the</em>
+<a class="jxr_linenumber" name="L237" href="#L237">237</a> <em class="jxr_javadoccomment"> * random variable x and the expected value of the gamma distribution: x, gamma(x; shape, scale=1)</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> @ParameterizedTest
+<a class="jxr_linenumber" name="L240" href="#L240">240</a> @MethodSource
+<a class="jxr_linenumber" name="L241" href="#L241">241</a> <strong class="jxr_keyword">void</strong> testMath753(<strong class="jxr_keyword">double</strong> shape,
+<a class="jxr_linenumber" name="L242" href="#L242">242</a> <strong class="jxr_keyword">double</strong> meanNoOF, <strong class="jxr_keyword">double</strong> sdNoOF,
+<a class="jxr_linenumber" name="L243" href="#L243">243</a> <strong class="jxr_keyword">double</strong> meanOF, <strong class="jxr_keyword">double</strong> sdOF,
+<a class="jxr_linenumber" name="L244" href="#L244">244</a> String resourceName) {
+<a class="jxr_linenumber" name="L245" href="#L245">245</a> <strong class="jxr_keyword">final</strong> GammaDistribution dist = GammaDistribution.of(shape, 1.0);
+<a class="jxr_linenumber" name="L246" href="#L246">246</a> <strong class="jxr_keyword">final</strong> SummaryStatistics statOld = <strong class="jxr_keyword">new</strong> SummaryStatistics();
+<a class="jxr_linenumber" name="L247" href="#L247">247</a> <em class="jxr_comment">// statNewNoOF = No overflow of old function</em>
+<a class="jxr_linenumber" name="L248" href="#L248">248</a> <em class="jxr_comment">// statNewOF = Overflow of old function</em>
+<a class="jxr_linenumber" name="L249" href="#L249">249</a> <strong class="jxr_keyword">final</strong> SummaryStatistics statNewNoOF = <strong class="jxr_keyword">new</strong> SummaryStatistics();
+<a class="jxr_linenumber" name="L250" href="#L250">250</a> <strong class="jxr_keyword">final</strong> SummaryStatistics statNewOF = <strong class="jxr_keyword">new</strong> SummaryStatistics();
+<a class="jxr_linenumber" name="L251" href="#L251">251</a>
+<a class="jxr_linenumber" name="L252" href="#L252">252</a> <strong class="jxr_keyword">final</strong> InputStream resourceAsStream = <strong class="jxr_keyword">this</strong>.getClass().getResourceAsStream(resourceName);
+<a class="jxr_linenumber" name="L253" href="#L253">253</a> Assertions.assertNotNull(resourceAsStream, () -> <span class="jxr_string">"Could not find resource "</span> + resourceName);
+<a class="jxr_linenumber" name="L254" href="#L254">254</a>
+<a class="jxr_linenumber" name="L255" href="#L255">255</a> <strong class="jxr_keyword">try</strong> (BufferedReader in = <strong class="jxr_keyword">new</strong> BufferedReader(<strong class="jxr_keyword">new</strong> InputStreamReader(resourceAsStream))) {
+<a class="jxr_linenumber" name="L256" href="#L256">256</a> <strong class="jxr_keyword">for</strong> (String line = in.readLine(); line != <strong class="jxr_keyword">null</strong>; line = in.readLine()) {
+<a class="jxr_linenumber" name="L257" href="#L257">257</a> <strong class="jxr_keyword">if</strong> (line.startsWith(<span class="jxr_string">"#"</span>)) {
+<a class="jxr_linenumber" name="L258" href="#L258">258</a> <strong class="jxr_keyword">continue</strong>;
+<a class="jxr_linenumber" name="L259" href="#L259">259</a> }
+<a class="jxr_linenumber" name="L260" href="#L260">260</a> <strong class="jxr_keyword">final</strong> String[] tokens = line.split(<span class="jxr_string">", "</span>);
+<a class="jxr_linenumber" name="L261" href="#L261">261</a> Assertions.assertEquals(2, tokens.length, <span class="jxr_string">"expected two floating-point values"</span>);
+<a class="jxr_linenumber" name="L262" href="#L262">262</a> <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> x = Double.parseDouble(tokens[0]);
+<a class="jxr_linenumber" name="L263" href="#L263">263</a> <strong class="jxr_keyword">final</strong> String msg = <span class="jxr_string">"x = "</span> + x + <span class="jxr_string">", shape = "</span> + shape +
+<a class="jxr_linenumber" name="L264" href="#L264">264</a> <span class="jxr_string">", scale = 1.0"</span>;
+<a class="jxr_linenumber" name="L265" href="#L265">265</a> <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> expected = Double.parseDouble(tokens[1]);
+<a class="jxr_linenumber" name="L266" href="#L266">266</a> <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> ulp = Math.ulp(expected);
+<a class="jxr_linenumber" name="L267" href="#L267">267</a> <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> actualOld = density(x, shape, 1.0);
+<a class="jxr_linenumber" name="L268" href="#L268">268</a> <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> actualNew = dist.density(x);
+<a class="jxr_linenumber" name="L269" href="#L269">269</a> <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> errOld = Math.abs((actualOld - expected) / ulp);
+<a class="jxr_linenumber" name="L270" href="#L270">270</a> <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> errNew = Math.abs((actualNew - expected) / ulp);
+<a class="jxr_linenumber" name="L271" href="#L271">271</a>
+<a class="jxr_linenumber" name="L272" href="#L272">272</a> <strong class="jxr_keyword">if</strong> (!Double.isFinite(actualOld)) {
+<a class="jxr_linenumber" name="L273" href="#L273">273</a> Assertions.assertTrue(Double.isFinite(actualNew), msg);
+<a class="jxr_linenumber" name="L274" href="#L274">274</a> statNewOF.addValue(errNew);
+<a class="jxr_linenumber" name="L275" href="#L275">275</a> } <strong class="jxr_keyword">else</strong> {
+<a class="jxr_linenumber" name="L276" href="#L276">276</a> statOld.addValue(errOld);
+<a class="jxr_linenumber" name="L277" href="#L277">277</a> statNewNoOF.addValue(errNew);
+<a class="jxr_linenumber" name="L278" href="#L278">278</a> }
+<a class="jxr_linenumber" name="L279" href="#L279">279</a> }
+<a class="jxr_linenumber" name="L280" href="#L280">280</a> <strong class="jxr_keyword">if</strong> (statOld.getN() != 0) {
+<a class="jxr_linenumber" name="L281" href="#L281">281</a> <em class="jxr_comment">/*</em>
+<a class="jxr_linenumber" name="L282" href="#L282">282</a> <em class="jxr_comment"> * If no overflow occurs, check that new implementation is</em>
+<a class="jxr_linenumber" name="L283" href="#L283">283</a> <em class="jxr_comment"> * better than old one.</em>
+<a class="jxr_linenumber" name="L284" href="#L284">284</a> <em class="jxr_comment"> */</em>
+<a class="jxr_linenumber" name="L285" href="#L285">285</a> <strong class="jxr_keyword">final</strong> StringBuilder sb = <strong class="jxr_keyword">new</strong> StringBuilder(<span class="jxr_string">"shape = "</span>);
+<a class="jxr_linenumber" name="L286" href="#L286">286</a> sb.append(shape);
+<a class="jxr_linenumber" name="L287" href="#L287">287</a> sb.append(<span class="jxr_string">", scale = 1.0\n"</span>);
+<a class="jxr_linenumber" name="L288" href="#L288">288</a> sb.append(<span class="jxr_string">"Old implementation\n"</span>);
+<a class="jxr_linenumber" name="L289" href="#L289">289</a> sb.append(<span class="jxr_string">"------------------\n"</span>);
+<a class="jxr_linenumber" name="L290" href="#L290">290</a> sb.append(statOld.toString());
+<a class="jxr_linenumber" name="L291" href="#L291">291</a> sb.append(<span class="jxr_string">"New implementation\n"</span>);
+<a class="jxr_linenumber" name="L292" href="#L292">292</a> sb.append(<span class="jxr_string">"------------------\n"</span>);
+<a class="jxr_linenumber" name="L293" href="#L293">293</a> sb.append(statNewNoOF.toString());
+<a class="jxr_linenumber" name="L294" href="#L294">294</a> <strong class="jxr_keyword">final</strong> String msg = sb.toString();
+<a class="jxr_linenumber" name="L295" href="#L295">295</a>
+<a class="jxr_linenumber" name="L296" href="#L296">296</a> <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> oldMin = statOld.getMin();
+<a class="jxr_linenumber" name="L297" href="#L297">297</a> <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> newMin = statNewNoOF.getMin();
+<a class="jxr_linenumber" name="L298" href="#L298">298</a> Assertions.assertTrue(newMin <= oldMin, msg);
+<a class="jxr_linenumber" name="L299" href="#L299">299</a>
+<a class="jxr_linenumber" name="L300" href="#L300">300</a> <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> oldMax = statOld.getMax();
+<a class="jxr_linenumber" name="L301" href="#L301">301</a> <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> newMax = statNewNoOF.getMax();
+<a class="jxr_linenumber" name="L302" href="#L302">302</a> Assertions.assertTrue(newMax <= oldMax, msg);
+<a class="jxr_linenumber" name="L303" href="#L303">303</a>
+<a class="jxr_linenumber" name="L304" href="#L304">304</a> <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> oldMean = statOld.getMean();
+<a class="jxr_linenumber" name="L305" href="#L305">305</a> <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> newMean = statNewNoOF.getMean();
+<a class="jxr_linenumber" name="L306" href="#L306">306</a> Assertions.assertTrue(newMean <= oldMean, msg);
+<a class="jxr_linenumber" name="L307" href="#L307">307</a>
+<a class="jxr_linenumber" name="L308" href="#L308">308</a> <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> oldSd = statOld.getStandardDeviation();
+<a class="jxr_linenumber" name="L309" href="#L309">309</a> <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> newSd = statNewNoOF.getStandardDeviation();
+<a class="jxr_linenumber" name="L310" href="#L310">310</a> Assertions.assertTrue(newSd <= oldSd, msg);
+<a class="jxr_linenumber" name="L311" href="#L311">311</a>
+<a class="jxr_linenumber" name="L312" href="#L312">312</a> Assertions.assertTrue(newMean <= meanNoOF, msg);
+<a class="jxr_linenumber" name="L313" href="#L313">313</a> Assertions.assertTrue(newSd <= sdNoOF, msg);
+<a class="jxr_linenumber" name="L314" href="#L314">314</a> }
+<a class="jxr_linenumber" name="L315" href="#L315">315</a> <strong class="jxr_keyword">if</strong> (statNewOF.getN() != 0) {
+<a class="jxr_linenumber" name="L316" href="#L316">316</a> <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> newMean = statNewOF.getMean();
+<a class="jxr_linenumber" name="L317" href="#L317">317</a> <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> newSd = statNewOF.getStandardDeviation();
+<a class="jxr_linenumber" name="L318" href="#L318">318</a>
+<a class="jxr_linenumber" name="L319" href="#L319">319</a> <strong class="jxr_keyword">final</strong> StringBuilder sb = <strong class="jxr_keyword">new</strong> StringBuilder(<span class="jxr_string">"shape = "</span>);
+<a class="jxr_linenumber" name="L320" href="#L320">320</a> sb.append(shape);
+<a class="jxr_linenumber" name="L321" href="#L321">321</a> sb.append(<span class="jxr_string">", scale = 1.0"</span>);
+<a class="jxr_linenumber" name="L322" href="#L322">322</a> sb.append(<span class="jxr_string">", max. mean error (ulps) = "</span>);
+<a class="jxr_linenumber" name="L323" href="#L323">323</a> sb.append(meanOF);
+<a class="jxr_linenumber" name="L324" href="#L324">324</a> sb.append(<span class="jxr_string">", actual mean error (ulps) = "</span>);
+<a class="jxr_linenumber" name="L325" href="#L325">325</a> sb.append(newMean);
+<a class="jxr_linenumber" name="L326" href="#L326">326</a> sb.append(<span class="jxr_string">", max. sd of error (ulps) = "</span>);
+<a class="jxr_linenumber" name="L327" href="#L327">327</a> sb.append(sdOF);
+<a class="jxr_linenumber" name="L328" href="#L328">328</a> sb.append(<span class="jxr_string">", actual sd of error (ulps) = "</span>);
+<a class="jxr_linenumber" name="L329" href="#L329">329</a> sb.append(newSd);
+<a class="jxr_linenumber" name="L330" href="#L330">330</a> <strong class="jxr_keyword">final</strong> String msg = sb.toString();
+<a class="jxr_linenumber" name="L331" href="#L331">331</a>
+<a class="jxr_linenumber" name="L332" href="#L332">332</a> Assertions.assertTrue(newMean <= meanOF, msg);
+<a class="jxr_linenumber" name="L333" href="#L333">333</a> Assertions.assertTrue(newSd <= sdOF, msg);
+<a class="jxr_linenumber" name="L334" href="#L334">334</a> }
+<a class="jxr_linenumber" name="L335" href="#L335">335</a> } <strong class="jxr_keyword">catch</strong> (<strong class="jxr_keyword">final</strong> IOException e) {
+<a class="jxr_linenumber" name="L336" href="#L336">336</a> Assertions.fail(e);
+<a class="jxr_linenumber" name="L337" href="#L337">337</a> }
+<a class="jxr_linenumber" name="L338" href="#L338">338</a> }
+<a class="jxr_linenumber" name="L339" href="#L339">339</a>
+<a class="jxr_linenumber" name="L340" href="#L340">340</a> <strong class="jxr_keyword">static</strong> Stream<Arguments> testMath753() {
+<a class="jxr_linenumber" name="L341" href="#L341">341</a> <strong class="jxr_keyword">return</strong> Stream.of(
+<a class="jxr_linenumber" name="L342" href="#L342">342</a> Arguments.of(0.25, 1.0, 1.0, 0.0, 0.0, <span class="jxr_string">"gamma-distribution-shape-0.25.csv"</span>),
+<a class="jxr_linenumber" name="L343" href="#L343">343</a> Arguments.of(0.5, 1.0, 1.0, 0.0, 0.0, <span class="jxr_string">"gamma-distribution-shape-0.5.csv"</span>),
+<a class="jxr_linenumber" name="L344" href="#L344">344</a> Arguments.of(0.75, 1.0, 1.0, 0.0, 0.0, <span class="jxr_string">"gamma-distribution-shape-0.75.csv"</span>),
+<a class="jxr_linenumber" name="L345" href="#L345">345</a> Arguments.of(1.0, 1.0, 0.5, 0.0, 0.0, <span class="jxr_string">"gamma-distribution-shape-1.csv"</span>),
+<a class="jxr_linenumber" name="L346" href="#L346">346</a> Arguments.of(8.0, 1.0, 1.0, 0.0, 0.0, <span class="jxr_string">"gamma-distribution-shape-8.csv"</span>),
+<a class="jxr_linenumber" name="L347" href="#L347">347</a> Arguments.of(10.0, 1.0, 1.0, 0.0, 0.0, <span class="jxr_string">"gamma-distribution-shape-10.csv"</span>),
+<a class="jxr_linenumber" name="L348" href="#L348">348</a> Arguments.of(100.0, 2.0, 1.0, 0.0, 0.0, <span class="jxr_string">"gamma-distribution-shape-100.csv"</span>),
+<a class="jxr_linenumber" name="L349" href="#L349">349</a> Arguments.of(142.0, 1.5, 1.0, 40.0, 40.0, <span class="jxr_string">"gamma-distribution-shape-142.csv"</span>),
+<a class="jxr_linenumber" name="L350" href="#L350">350</a> Arguments.of(1000.0, 1.0, 1.0, 160.0, 200.0, <span class="jxr_string">"gamma-distribution-shape-1000.csv"</span>)
+<a class="jxr_linenumber" name="L351" href="#L351">351</a> );
+<a class="jxr_linenumber" name="L352" href="#L352">352</a> }
+<a class="jxr_linenumber" name="L353" href="#L353">353</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/GeometricDistributionTest.html
==============================================================================
--- dev/commons/statistics/1.0-RC1/site/xref-test/org/apache/commons/statistics/distribution/GeometricDistributionTest.html (added)
+++ dev/commons/statistics/1.0-RC1/site/xref-test/org/apache/commons/statistics/distribution/GeometricDistributionTest.html Thu Dec 1 16:47:12 2022
@@ -0,0 +1,261 @@
+<!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>GeometricDistributionTest xref</title>
+<link type="text/css" rel="stylesheet" href="../../../../../stylesheet.css" />
+</head>
+<body>
+<div id="overview"><a href="../../../../../../testapidocs/org/apache/commons/statistics/distribution/GeometricDistributionTest.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.Arrays;
+<a class="jxr_linenumber" name="L20" href="#L20">20</a> <strong class="jxr_keyword">import</strong> java.util.stream.Stream;
+<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.Arguments;
+<a class="jxr_linenumber" name="L25" href="#L25">25</a> <strong class="jxr_keyword">import</strong> org.junit.jupiter.params.provider.MethodSource;
+<a class="jxr_linenumber" name="L26" href="#L26">26</a> <strong class="jxr_keyword">import</strong> org.junit.jupiter.params.provider.ValueSource;
+<a class="jxr_linenumber" name="L27" href="#L27">27</a>
+<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"> * Test cases for {@link GeometricDistribution}.</em>
+<a class="jxr_linenumber" name="L30" href="#L30">30</a> <em class="jxr_javadoccomment"> * Extends {@link BaseDiscreteDistributionTest}. See javadoc of that class for details.</em>
+<a class="jxr_linenumber" name="L31" href="#L31">31</a> <em class="jxr_javadoccomment"> */</em>
+<a class="jxr_linenumber" name="L32" href="#L32">32</a> <strong class="jxr_keyword">class</strong> <a name="GeometricDistributionTest" href="../../../../../org/apache/commons/statistics/distribution/GeometricDistributionTest.html#GeometricDistributionTest">GeometricDistributionTest</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="L33" href="#L33">33</a> @Override
+<a class="jxr_linenumber" name="L34" href="#L34">34</a> DiscreteDistribution makeDistribution(Object... parameters) {
+<a class="jxr_linenumber" name="L35" href="#L35">35</a> <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> p = (Double) parameters[0];
+<a class="jxr_linenumber" name="L36" href="#L36">36</a> <strong class="jxr_keyword">return</strong> GeometricDistribution.of(p);
+<a class="jxr_linenumber" name="L37" href="#L37">37</a> }
+<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> Object[][] makeInvalidParameters() {
+<a class="jxr_linenumber" name="L41" href="#L41">41</a> <strong class="jxr_keyword">return</strong> <strong class="jxr_keyword">new</strong> Object[][] {
+<a class="jxr_linenumber" name="L42" href="#L42">42</a> {-0.1},
+<a class="jxr_linenumber" name="L43" href="#L43">43</a> {0.0},
+<a class="jxr_linenumber" name="L44" href="#L44">44</a> {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">"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> 2 * RELATIVE_EPS;
+<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">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> GeometricDistribution dist = GeometricDistribution.of(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(0.5, (1.0 - 0.5) / 0.5, (1.0 - 0.5) / (0.5 * 0.5)),
+<a class="jxr_linenumber" name="L70" href="#L70">70</a> Arguments.of(0.3, (1.0 - 0.3) / 0.3, (1.0 - 0.3) / (0.3 * 0.3))
+<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>
+<a class="jxr_linenumber" name="L74" href="#L74">74</a> <em class="jxr_javadoccomment">/**</em>
+<a class="jxr_linenumber" name="L75" href="#L75">75</a> <em class="jxr_javadoccomment"> * Test the PMF is computed using the power function when p is above 0.5.</em>
+<a class="jxr_linenumber" name="L76" href="#L76">76</a> <em class="jxr_javadoccomment"> * <p>Note: The geometric distribution PMF is defined as:</em>
+<a class="jxr_linenumber" name="L77" href="#L77">77</a> <em class="jxr_javadoccomment"> * <pre></em>
+<a class="jxr_linenumber" name="L78" href="#L78">78</a> <em class="jxr_javadoccomment"> * pmf(x) = (1-p)^x * p</em>
+<a class="jxr_linenumber" name="L79" href="#L79">79</a> <em class="jxr_javadoccomment"> * </pre></em>
+<a class="jxr_linenumber" name="L80" href="#L80">80</a> <em class="jxr_javadoccomment"> * <p>As {@code p -> 0} use of the power function should be avoided as it will</em>
+<a class="jxr_linenumber" name="L81" href="#L81">81</a> <em class="jxr_javadoccomment"> * propagate the inexact computation of {@code 1 - p}. The implementation can</em>
+<a class="jxr_linenumber" name="L82" href="#L82">82</a> <em class="jxr_javadoccomment"> * switch to using a rearrangement with the exponential function which avoid</em>
+<a class="jxr_linenumber" name="L83" href="#L83">83</a> <em class="jxr_javadoccomment"> * computing {@code 1 - p}.</em>
+<a class="jxr_linenumber" name="L84" href="#L84">84</a> <em class="jxr_javadoccomment"> * <p>See STATISTICS-34.</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"> * @param p Probability of success</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> @ValueSource(doubles = {0.5, 0.6658665, 0.75, 0.8125347, 0.9, 0.95, 0.99})
+<a class="jxr_linenumber" name="L90" href="#L90">90</a> <strong class="jxr_keyword">void</strong> testPMF(<strong class="jxr_keyword">double</strong> p) {
+<a class="jxr_linenumber" name="L91" href="#L91">91</a> <strong class="jxr_keyword">final</strong> GeometricDistribution dist = GeometricDistribution.of(p);
+<a class="jxr_linenumber" name="L92" href="#L92">92</a> <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">int</strong>[] x = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 20, 30, 40};
+<a class="jxr_linenumber" name="L93" href="#L93">93</a> <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong>[] values = Arrays.stream(x).mapToDouble(k -> p * Math.pow(1 - p, k)).toArray();
+<a class="jxr_linenumber" name="L94" href="#L94">94</a> <em class="jxr_comment">// The PMF should be an exact match to the direct implementation with Math.pow.</em>
+<a class="jxr_linenumber" name="L95" href="#L95">95</a> testProbability(dist, x, values, DoubleTolerances.equals());
+<a class="jxr_linenumber" name="L96" href="#L96">96</a> }
+<a class="jxr_linenumber" name="L97" href="#L97">97</a>
+<a class="jxr_linenumber" name="L98" href="#L98">98</a> <em class="jxr_javadoccomment">/**</em>
+<a class="jxr_linenumber" name="L99" href="#L99">99</a> <em class="jxr_javadoccomment"> * Test the inverse CDF returns the correct x from the CDF result.</em>
+<a class="jxr_linenumber" name="L100" href="#L100">100</a> <em class="jxr_javadoccomment"> * Cases were identified using various probabilities to discover a mismatch</em>
+<a class="jxr_linenumber" name="L101" href="#L101">101</a> <em class="jxr_javadoccomment"> * of x != icdf(cdf(x)). This occurs due to rounding errors on the inversion.</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> @ParameterizedTest
+<a class="jxr_linenumber" name="L104" href="#L104">104</a> @ValueSource(doubles = {
+<a class="jxr_linenumber" name="L105" href="#L105">105</a> 0.2,
+<a class="jxr_linenumber" name="L106" href="#L106">106</a> 0.8,
+<a class="jxr_linenumber" name="L107" href="#L107">107</a> <em class="jxr_comment">// icdf(cdf(x)) requires rounding up</em>
+<a class="jxr_linenumber" name="L108" href="#L108">108</a> 0.07131208016887369,
+<a class="jxr_linenumber" name="L109" href="#L109">109</a> 0.14441285445326058,
+<a class="jxr_linenumber" name="L110" href="#L110">110</a> 0.272118157703929,
+<a class="jxr_linenumber" name="L111" href="#L111">111</a> 0.424656239093432,
+<a class="jxr_linenumber" name="L112" href="#L112">112</a> 0.00899452845634574,
+<a class="jxr_linenumber" name="L113" href="#L113">113</a> <em class="jxr_comment">// icdf(cdf(x)) requires rounding down</em>
+<a class="jxr_linenumber" name="L114" href="#L114">114</a> 0.3441320118140774,
+<a class="jxr_linenumber" name="L115" href="#L115">115</a> 0.5680886873083258,
+<a class="jxr_linenumber" name="L116" href="#L116">116</a> 0.8738746761971425,
+<a class="jxr_linenumber" name="L117" href="#L117">117</a> 0.17373328785967923,
+<a class="jxr_linenumber" name="L118" href="#L118">118</a> 0.09252030895185881,
+<a class="jxr_linenumber" name="L119" href="#L119">119</a> })
+<a class="jxr_linenumber" name="L120" href="#L120">120</a> <strong class="jxr_keyword">void</strong> testInverseCDF(<strong class="jxr_keyword">double</strong> p) {
+<a class="jxr_linenumber" name="L121" href="#L121">121</a> <strong class="jxr_keyword">final</strong> GeometricDistribution dist = GeometricDistribution.of(p);
+<a class="jxr_linenumber" name="L122" href="#L122">122</a> <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">int</strong>[] x = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10};
+<a class="jxr_linenumber" name="L123" href="#L123">123</a> testCumulativeProbabilityInverseMapping(dist, x);
+<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> <em class="jxr_javadoccomment">/**</em>
+<a class="jxr_linenumber" name="L127" href="#L127">127</a> <em class="jxr_javadoccomment"> * Test the inverse SF returns the correct x from the SF result.</em>
+<a class="jxr_linenumber" name="L128" href="#L128">128</a> <em class="jxr_javadoccomment"> * Cases were identified using various probabilities to discover a mismatch</em>
+<a class="jxr_linenumber" name="L129" href="#L129">129</a> <em class="jxr_javadoccomment"> * of x != isf(sf(x)). This occurs due to rounding errors on the inversion.</em>
+<a class="jxr_linenumber" name="L130" href="#L130">130</a> <em class="jxr_javadoccomment"> */</em>
+<a class="jxr_linenumber" name="L131" href="#L131">131</a> @ParameterizedTest
+<a class="jxr_linenumber" name="L132" href="#L132">132</a> @ValueSource(doubles = {
+<a class="jxr_linenumber" name="L133" href="#L133">133</a> 0.2,
+<a class="jxr_linenumber" name="L134" href="#L134">134</a> 0.8,
+<a class="jxr_linenumber" name="L135" href="#L135">135</a> <em class="jxr_comment">// isf(sf(x)) requires rounding up</em>
+<a class="jxr_linenumber" name="L136" href="#L136">136</a> 0.9625911263689207,
+<a class="jxr_linenumber" name="L137" href="#L137">137</a> 0.2858964038911178,
+<a class="jxr_linenumber" name="L138" href="#L138">138</a> 0.31872883511135996,
+<a class="jxr_linenumber" name="L139" href="#L139">139</a> 0.46149078212832284,
+<a class="jxr_linenumber" name="L140" href="#L140">140</a> 0.3701613946505057,
+<a class="jxr_linenumber" name="L141" href="#L141">141</a> <em class="jxr_comment">// isf(sf(x)) requires rounding down</em>
+<a class="jxr_linenumber" name="L142" href="#L142">142</a> 0.3796493606864414,
+<a class="jxr_linenumber" name="L143" href="#L143">143</a> 0.1113177920615187,
+<a class="jxr_linenumber" name="L144" href="#L144">144</a> 0.2587259503484439,
+<a class="jxr_linenumber" name="L145" href="#L145">145</a> 0.8996839434455458,
+<a class="jxr_linenumber" name="L146" href="#L146">146</a> 0.450704136259792,
+<a class="jxr_linenumber" name="L147" href="#L147">147</a> })
+<a class="jxr_linenumber" name="L148" href="#L148">148</a> <strong class="jxr_keyword">void</strong> testInverseSF(<strong class="jxr_keyword">double</strong> p) {
+<a class="jxr_linenumber" name="L149" href="#L149">149</a> <strong class="jxr_keyword">final</strong> GeometricDistribution dist = GeometricDistribution.of(p);
+<a class="jxr_linenumber" name="L150" href="#L150">150</a> <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">int</strong>[] x = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10};
+<a class="jxr_linenumber" name="L151" href="#L151">151</a> testSurvivalProbabilityInverseMapping(dist, x);
+<a class="jxr_linenumber" name="L152" href="#L152">152</a> }
+<a class="jxr_linenumber" name="L153" href="#L153">153</a>
+<a class="jxr_linenumber" name="L154" href="#L154">154</a> <em class="jxr_javadoccomment">/**</em>
+<a class="jxr_linenumber" name="L155" href="#L155">155</a> <em class="jxr_javadoccomment"> * Test the most extreme parameters. Uses a small enough value of p that the distribution is</em>
+<a class="jxr_linenumber" name="L156" href="#L156">156</a> <em class="jxr_javadoccomment"> * truncated by the maximum integer value. This creates a case where (x+1) will overflow.</em>
+<a class="jxr_linenumber" name="L157" href="#L157">157</a> <em class="jxr_javadoccomment"> * This occurs in the cumulative and survival function computations.</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> @Test
+<a class="jxr_linenumber" name="L160" href="#L160">160</a> <strong class="jxr_keyword">void</strong> testExtremeParameters() {
+<a class="jxr_linenumber" name="L161" href="#L161">161</a> <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> p = Double.MIN_VALUE;
+<a class="jxr_linenumber" name="L162" href="#L162">162</a> <strong class="jxr_keyword">final</strong> GeometricDistribution dist = GeometricDistribution.of(p);
+<a class="jxr_linenumber" name="L163" href="#L163">163</a>
+<a class="jxr_linenumber" name="L164" href="#L164">164</a> <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">int</strong> x = Integer.MAX_VALUE;
+<a class="jxr_linenumber" name="L165" href="#L165">165</a> <em class="jxr_comment">// CDF = 1 - (1-p)^(x+1)</em>
+<a class="jxr_linenumber" name="L166" href="#L166">166</a> <em class="jxr_comment">// Compute with log for accuracy with small p</em>
+<a class="jxr_linenumber" name="L167" href="#L167">167</a> <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> cdf = -Math.expm1(Math.log1p(-p) * (x + 1.0));
+<a class="jxr_linenumber" name="L168" href="#L168">168</a> Assertions.assertNotEquals(1.0, cdf);
+<a class="jxr_linenumber" name="L169" href="#L169">169</a> Assertions.assertEquals(cdf, dist.cumulativeProbability(x));
+<a class="jxr_linenumber" name="L170" href="#L170">170</a> <strong class="jxr_keyword">for</strong> (<strong class="jxr_keyword">int</strong> i = 0; i < 5; i++) {
+<a class="jxr_linenumber" name="L171" href="#L171">171</a> Assertions.assertEquals(x - i, dist.inverseCumulativeProbability(dist.cumulativeProbability(x - i)));
+<a class="jxr_linenumber" name="L172" href="#L172">172</a> }
+<a class="jxr_linenumber" name="L173" href="#L173">173</a>
+<a class="jxr_linenumber" name="L174" href="#L174">174</a> <em class="jxr_comment">// CDF(x=0) = p</em>
+<a class="jxr_linenumber" name="L175" href="#L175">175</a> Assertions.assertEquals(p, dist.cumulativeProbability(0));
+<a class="jxr_linenumber" name="L176" href="#L176">176</a> Assertions.assertEquals(0, dist.inverseCumulativeProbability(p));
+<a class="jxr_linenumber" name="L177" href="#L177">177</a> Assertions.assertEquals(1, dist.inverseCumulativeProbability(Math.nextUp(p)));
+<a class="jxr_linenumber" name="L178" href="#L178">178</a> <strong class="jxr_keyword">for</strong> (<strong class="jxr_keyword">int</strong> i = 1; i < 5; i++) {
+<a class="jxr_linenumber" name="L179" href="#L179">179</a> Assertions.assertEquals(i, dist.inverseCumulativeProbability(dist.cumulativeProbability(i)));
+<a class="jxr_linenumber" name="L180" href="#L180">180</a> }
+<a class="jxr_linenumber" name="L181" href="#L181">181</a>
+<a class="jxr_linenumber" name="L182" href="#L182">182</a> <em class="jxr_comment">// SF = (1-p)^(x+1)</em>
+<a class="jxr_linenumber" name="L183" href="#L183">183</a> <em class="jxr_comment">// Compute with log for accuracy with small p</em>
+<a class="jxr_linenumber" name="L184" href="#L184">184</a> <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> sf = Math.exp(Math.log1p(-p) * (x + 1.0));
+<a class="jxr_linenumber" name="L185" href="#L185">185</a> Assertions.assertEquals(1.0 - cdf, sf);
+<a class="jxr_linenumber" name="L186" href="#L186">186</a> Assertions.assertEquals(sf, dist.survivalProbability(x));
+<a class="jxr_linenumber" name="L187" href="#L187">187</a> <em class="jxr_comment">// SF is too close to 1 to be able to invert</em>
+<a class="jxr_linenumber" name="L188" href="#L188">188</a> Assertions.assertEquals(1.0, sf);
+<a class="jxr_linenumber" name="L189" href="#L189">189</a> Assertions.assertEquals(x, dist.inverseSurvivalProbability(Math.nextDown(1.0)));
+<a class="jxr_linenumber" name="L190" href="#L190">190</a> }
+<a class="jxr_linenumber" name="L191" href="#L191">191</a>
+<a class="jxr_linenumber" name="L192" href="#L192">192</a> <em class="jxr_javadoccomment">/**</em>
+<a class="jxr_linenumber" name="L193" href="#L193">193</a> <em class="jxr_javadoccomment"> * Test the most extreme parameters. Uses a large enough value of p that the distribution is</em>
+<a class="jxr_linenumber" name="L194" href="#L194">194</a> <em class="jxr_javadoccomment"> * compacted to x=0.</em>
+<a class="jxr_linenumber" name="L195" href="#L195">195</a> <em class="jxr_javadoccomment"> *</em>
+<a class="jxr_linenumber" name="L196" href="#L196">196</a> <em class="jxr_javadoccomment"> * <p>p is one ULP down from 1.0.</em>
+<a class="jxr_linenumber" name="L197" href="#L197">197</a> <em class="jxr_javadoccomment"> */</em>
+<a class="jxr_linenumber" name="L198" href="#L198">198</a> @Test
+<a class="jxr_linenumber" name="L199" href="#L199">199</a> <strong class="jxr_keyword">void</strong> testExtremeParameters2() {
+<a class="jxr_linenumber" name="L200" href="#L200">200</a> <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> p = Math.nextDown(1.0);
+<a class="jxr_linenumber" name="L201" href="#L201">201</a> <strong class="jxr_keyword">final</strong> GeometricDistribution dist = GeometricDistribution.of(p);
+<a class="jxr_linenumber" name="L202" href="#L202">202</a>
+<a class="jxr_linenumber" name="L203" href="#L203">203</a> <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">int</strong> x = 0;
+<a class="jxr_linenumber" name="L204" href="#L204">204</a> <em class="jxr_comment">// CDF = 1 - (1-p)^(x+1)</em>
+<a class="jxr_linenumber" name="L205" href="#L205">205</a> <em class="jxr_comment">// CDF(x=0) = p</em>
+<a class="jxr_linenumber" name="L206" href="#L206">206</a> Assertions.assertEquals(p, dist.cumulativeProbability(0));
+<a class="jxr_linenumber" name="L207" href="#L207">207</a> Assertions.assertEquals(0, dist.inverseCumulativeProbability(p));
+<a class="jxr_linenumber" name="L208" href="#L208">208</a> <em class="jxr_comment">// CDF is too close to 1 to be able to invert next value</em>
+<a class="jxr_linenumber" name="L209" href="#L209">209</a> Assertions.assertEquals(Integer.MAX_VALUE, dist.inverseCumulativeProbability(Math.nextUp(p)));
+<a class="jxr_linenumber" name="L210" href="#L210">210</a>
+<a class="jxr_linenumber" name="L211" href="#L211">211</a> <em class="jxr_comment">// SF = (1-p)^(x+1)</em>
+<a class="jxr_linenumber" name="L212" href="#L212">212</a> <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> sf = 1 - p;
+<a class="jxr_linenumber" name="L213" href="#L213">213</a> Assertions.assertNotEquals(0.0, sf);
+<a class="jxr_linenumber" name="L214" href="#L214">214</a> Assertions.assertEquals(sf, dist.survivalProbability(x));
+<a class="jxr_linenumber" name="L215" href="#L215">215</a> <strong class="jxr_keyword">for</strong> (<strong class="jxr_keyword">int</strong> i = 1; i < 5; i++) {
+<a class="jxr_linenumber" name="L216" href="#L216">216</a> Assertions.assertEquals(i, dist.inverseSurvivalProbability(dist.survivalProbability(i)));
+<a class="jxr_linenumber" name="L217" href="#L217">217</a> }
+<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"> * Test the most extreme parameters. Uses a large enough value of p that the distribution is</em>
+<a class="jxr_linenumber" name="L222" href="#L222">222</a> <em class="jxr_javadoccomment"> * compacted to x=0.</em>
+<a class="jxr_linenumber" name="L223" href="#L223">223</a> <em class="jxr_javadoccomment"> *</em>
+<a class="jxr_linenumber" name="L224" href="#L224">224</a> <em class="jxr_javadoccomment"> * <p>p is two ULP down from 1.0.</em>
+<a class="jxr_linenumber" name="L225" href="#L225">225</a> <em class="jxr_javadoccomment"> */</em>
+<a class="jxr_linenumber" name="L226" href="#L226">226</a> @Test
+<a class="jxr_linenumber" name="L227" href="#L227">227</a> <strong class="jxr_keyword">void</strong> testExtremeParameters3() {
+<a class="jxr_linenumber" name="L228" href="#L228">228</a> <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> p = Math.nextDown(Math.nextDown(1.0));
+<a class="jxr_linenumber" name="L229" href="#L229">229</a> <strong class="jxr_keyword">final</strong> GeometricDistribution dist = GeometricDistribution.of(p);
+<a class="jxr_linenumber" name="L230" href="#L230">230</a>
+<a class="jxr_linenumber" name="L231" href="#L231">231</a> <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">int</strong> x = 0;
+<a class="jxr_linenumber" name="L232" href="#L232">232</a> <em class="jxr_comment">// CDF = 1 - (1-p)^(x+1)</em>
+<a class="jxr_linenumber" name="L233" href="#L233">233</a> <em class="jxr_comment">// CDF(x=0) = p</em>
+<a class="jxr_linenumber" name="L234" href="#L234">234</a> Assertions.assertEquals(p, dist.cumulativeProbability(0));
+<a class="jxr_linenumber" name="L235" href="#L235">235</a> Assertions.assertEquals(0, dist.inverseCumulativeProbability(p));
+<a class="jxr_linenumber" name="L236" href="#L236">236</a> Assertions.assertEquals(1, dist.inverseCumulativeProbability(Math.nextUp(p)));
+<a class="jxr_linenumber" name="L237" href="#L237">237</a> <em class="jxr_comment">// CDF is too close to 1 to be able to invert next value</em>
+<a class="jxr_linenumber" name="L238" href="#L238">238</a> Assertions.assertEquals(Integer.MAX_VALUE, dist.inverseCumulativeProbability(Math.nextUp(Math.nextUp(p))));
+<a class="jxr_linenumber" name="L239" href="#L239">239</a>
+<a class="jxr_linenumber" name="L240" href="#L240">240</a> <em class="jxr_comment">// SF = (1-p)^(x+1)</em>
+<a class="jxr_linenumber" name="L241" href="#L241">241</a> <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> sf = 1 - p;
+<a class="jxr_linenumber" name="L242" href="#L242">242</a> Assertions.assertNotEquals(0.0, sf);
+<a class="jxr_linenumber" name="L243" href="#L243">243</a> Assertions.assertEquals(sf, dist.survivalProbability(x));
+<a class="jxr_linenumber" name="L244" href="#L244">244</a> <strong class="jxr_keyword">for</strong> (<strong class="jxr_keyword">int</strong> i = 1; i < 5; i++) {
+<a class="jxr_linenumber" name="L245" href="#L245">245</a> Assertions.assertEquals(i, dist.inverseSurvivalProbability(dist.survivalProbability(i)));
+<a class="jxr_linenumber" name="L246" href="#L246">246</a> }
+<a class="jxr_linenumber" name="L247" href="#L247">247</a> }
+<a class="jxr_linenumber" name="L248" href="#L248">248</a> }
+</pre>
+<hr/>
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