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+<div id="overview"><a href="../../../../../../testapidocs/org/apache/commons/statistics/distribution/AbstractContinuousDistributionTest.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.math3.analysis.UnivariateFunction;
+<a class="jxr_linenumber" name="L20" href="#L20">20</a> <strong class="jxr_keyword">import</strong> org.apache.commons.math3.analysis.integration.RombergIntegrator;
+<a class="jxr_linenumber" name="L21" href="#L21">21</a> <strong class="jxr_keyword">import</strong> org.apache.commons.math3.analysis.integration.UnivariateIntegrator;
+<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>
+<a class="jxr_linenumber" name="L25" href="#L25">25</a> <em class="jxr_javadoccomment">/**</em>
+<a class="jxr_linenumber" name="L26" href="#L26">26</a> <em class="jxr_javadoccomment"> * Test cases for AbstractContinuousDistribution default implementations.</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="AbstractContinuousDistributionTest" href="../../../../../org/apache/commons/statistics/distribution/AbstractContinuousDistributionTest.html#AbstractContinuousDistributionTest">AbstractContinuousDistributionTest</a> {
+<a class="jxr_linenumber" name="L29" href="#L29">29</a>
+<a class="jxr_linenumber" name="L30" href="#L30">30</a> <em class="jxr_javadoccomment">/** Various tests related to MATH-699. */</em>
+<a class="jxr_linenumber" name="L31" href="#L31">31</a> @Test
+<a class="jxr_linenumber" name="L32" href="#L32">32</a> <strong class="jxr_keyword">void</strong> testContinuous() {
+<a class="jxr_linenumber" name="L33" href="#L33">33</a> <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> x0 = 0.0;
+<a class="jxr_linenumber" name="L34" href="#L34">34</a> <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> x1 = 1.0;
+<a class="jxr_linenumber" name="L35" href="#L35">35</a> <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> x2 = 2.0;
+<a class="jxr_linenumber" name="L36" href="#L36">36</a> <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> x3 = 3.0;
+<a class="jxr_linenumber" name="L37" href="#L37">37</a> <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> p12 = 0.5;
+<a class="jxr_linenumber" name="L38" href="#L38">38</a> <strong class="jxr_keyword">final</strong> AbstractContinuousDistribution distribution;
+<a class="jxr_linenumber" name="L39" href="#L39">39</a> distribution = <strong class="jxr_keyword">new</strong> AbstractContinuousDistribution() {
+<a class="jxr_linenumber" name="L40" href="#L40">40</a> @Override
+<a class="jxr_linenumber" name="L41" href="#L41">41</a> <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">double</strong> cumulativeProbability(<strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> x) {
+<a class="jxr_linenumber" name="L42" href="#L42">42</a> <strong class="jxr_keyword">if</strong> (x < x0 ||
+<a class="jxr_linenumber" name="L43" href="#L43">43</a> x > x3) {
+<a class="jxr_linenumber" name="L44" href="#L44">44</a> <strong class="jxr_keyword">throw</strong> <strong class="jxr_keyword">new</strong> DistributionException(DistributionException.OUT_OF_RANGE, x, x0, x3);
+<a class="jxr_linenumber" name="L45" href="#L45">45</a> }
+<a class="jxr_linenumber" name="L46" href="#L46">46</a> <strong class="jxr_keyword">if</strong> (x <= x1) {
+<a class="jxr_linenumber" name="L47" href="#L47">47</a> <strong class="jxr_keyword">return</strong> p12 * (x - x0) / (x1 - x0);
+<a class="jxr_linenumber" name="L48" href="#L48">48</a> } <strong class="jxr_keyword">else</strong> <strong class="jxr_keyword">if</strong> (x <= x2) {
+<a class="jxr_linenumber" name="L49" href="#L49">49</a> <strong class="jxr_keyword">return</strong> p12;
+<a class="jxr_linenumber" name="L50" href="#L50">50</a> } <strong class="jxr_keyword">else</strong> <strong class="jxr_keyword">if</strong> (x <= x3) {
+<a class="jxr_linenumber" name="L51" href="#L51">51</a> <strong class="jxr_keyword">return</strong> p12 + (1.0 - p12) * (x - x2) / (x3 - x2);
+<a class="jxr_linenumber" name="L52" href="#L52">52</a> }
+<a class="jxr_linenumber" name="L53" href="#L53">53</a> <strong class="jxr_keyword">return</strong> 0.0;
+<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> @Override
+<a class="jxr_linenumber" name="L57" href="#L57">57</a> <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">double</strong> density(<strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> x) {
+<a class="jxr_linenumber" name="L58" href="#L58">58</a> <strong class="jxr_keyword">if</strong> (x < x0 ||
+<a class="jxr_linenumber" name="L59" href="#L59">59</a> x > x3) {
+<a class="jxr_linenumber" name="L60" href="#L60">60</a> <strong class="jxr_keyword">throw</strong> <strong class="jxr_keyword">new</strong> DistributionException(DistributionException.OUT_OF_RANGE, x, x0, x3);
+<a class="jxr_linenumber" name="L61" href="#L61">61</a> }
+<a class="jxr_linenumber" name="L62" href="#L62">62</a> <strong class="jxr_keyword">if</strong> (x <= x1) {
+<a class="jxr_linenumber" name="L63" href="#L63">63</a> <strong class="jxr_keyword">return</strong> p12 / (x1 - x0);
+<a class="jxr_linenumber" name="L64" href="#L64">64</a> } <strong class="jxr_keyword">else</strong> <strong class="jxr_keyword">if</strong> (x <= x2) {
+<a class="jxr_linenumber" name="L65" href="#L65">65</a> <strong class="jxr_keyword">return</strong> 0.0;
+<a class="jxr_linenumber" name="L66" href="#L66">66</a> } <strong class="jxr_keyword">else</strong> <strong class="jxr_keyword">if</strong> (x <= x3) {
+<a class="jxr_linenumber" name="L67" href="#L67">67</a> <strong class="jxr_keyword">return</strong> (1.0 - p12) / (x3 - x2);
+<a class="jxr_linenumber" name="L68" href="#L68">68</a> }
+<a class="jxr_linenumber" name="L69" href="#L69">69</a> <strong class="jxr_keyword">return</strong> 0.0;
+<a class="jxr_linenumber" name="L70" href="#L70">70</a> }
+<a class="jxr_linenumber" name="L71" href="#L71">71</a>
+<a class="jxr_linenumber" name="L72" href="#L72">72</a> @Override
+<a class="jxr_linenumber" name="L73" href="#L73">73</a> <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">double</strong> getMean() {
+<a class="jxr_linenumber" name="L74" href="#L74">74</a> <strong class="jxr_keyword">return</strong> ((x0 + x1) * p12 + (x2 + x3) * (1.0 - p12)) / 2.0;
+<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> @Override
+<a class="jxr_linenumber" name="L78" href="#L78">78</a> <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">double</strong> getVariance() {
+<a class="jxr_linenumber" name="L79" href="#L79">79</a> <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> meanX = getMean();
+<a class="jxr_linenumber" name="L80" href="#L80">80</a> <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> meanX2;
+<a class="jxr_linenumber" name="L81" href="#L81">81</a> meanX2 = ((x0 * x0 + x0 * x1 + x1 * x1) * p12 +
+<a class="jxr_linenumber" name="L82" href="#L82">82</a> (x2 * x2 + x2 * x3 + x3 * x3) * (1.0 - p12)) / 3.0;
+<a class="jxr_linenumber" name="L83" href="#L83">83</a> <strong class="jxr_keyword">return</strong> meanX2 - meanX * meanX;
+<a class="jxr_linenumber" name="L84" href="#L84">84</a> }
+<a class="jxr_linenumber" name="L85" href="#L85">85</a>
+<a class="jxr_linenumber" name="L86" href="#L86">86</a> @Override
+<a class="jxr_linenumber" name="L87" href="#L87">87</a> <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">double</strong> getSupportLowerBound() {
+<a class="jxr_linenumber" name="L88" href="#L88">88</a> <strong class="jxr_keyword">return</strong> x0;
+<a class="jxr_linenumber" name="L89" href="#L89">89</a> }
+<a class="jxr_linenumber" name="L90" href="#L90">90</a>
+<a class="jxr_linenumber" name="L91" href="#L91">91</a> @Override
+<a class="jxr_linenumber" name="L92" href="#L92">92</a> <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">double</strong> getSupportUpperBound() {
+<a class="jxr_linenumber" name="L93" href="#L93">93</a> <strong class="jxr_keyword">return</strong> x3;
+<a class="jxr_linenumber" name="L94" href="#L94">94</a> }
+<a class="jxr_linenumber" name="L95" href="#L95">95</a>
+<a class="jxr_linenumber" name="L96" href="#L96">96</a> @Override
+<a class="jxr_linenumber" name="L97" href="#L97">97</a> <strong class="jxr_keyword">boolean</strong> isSupportConnected() {
+<a class="jxr_linenumber" name="L98" href="#L98">98</a> <em class="jxr_comment">// This is deliberately false; the functionality is the subject of this test</em>
+<a class="jxr_linenumber" name="L99" href="#L99">99</a> <strong class="jxr_keyword">return</strong> false;
+<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> <em class="jxr_comment">// CDF is continuous before x1 and after x2. Plateau in between:</em>
+<a class="jxr_linenumber" name="L103" href="#L103">103</a> <em class="jxr_comment">// CDF(x1 <= X <= x2) = p12.</em>
+<a class="jxr_linenumber" name="L104" href="#L104">104</a> <em class="jxr_comment">// The inverse returns the infimum.</em>
+<a class="jxr_linenumber" name="L105" href="#L105">105</a> <strong class="jxr_keyword">double</strong> expected = x1;
+<a class="jxr_linenumber" name="L106" href="#L106">106</a> <strong class="jxr_keyword">double</strong> actual = distribution.inverseCumulativeProbability(p12);
+<a class="jxr_linenumber" name="L107" href="#L107">107</a> Assertions.assertEquals(expected, actual, 1e-8, <span class="jxr_string">"Inverse CDF"</span>);
+<a class="jxr_linenumber" name="L108" href="#L108">108</a>
+<a class="jxr_linenumber" name="L109" href="#L109">109</a> actual = distribution.inverseSurvivalProbability(1 - p12);
+<a class="jxr_linenumber" name="L110" href="#L110">110</a> Assertions.assertEquals(expected, actual, 1e-8, <span class="jxr_string">"Inverse SF"</span>);
+<a class="jxr_linenumber" name="L111" href="#L111">111</a>
+<a class="jxr_linenumber" name="L112" href="#L112">112</a> <em class="jxr_comment">// Test the continuous region</em>
+<a class="jxr_linenumber" name="L113" href="#L113">113</a> expected = 0.5 * (x1 - x0);
+<a class="jxr_linenumber" name="L114" href="#L114">114</a> actual = distribution.inverseCumulativeProbability(p12 * 0.5);
+<a class="jxr_linenumber" name="L115" href="#L115">115</a> Assertions.assertEquals(expected, actual, 1e-8, <span class="jxr_string">"Inverse CDF"</span>);
+<a class="jxr_linenumber" name="L116" href="#L116">116</a>
+<a class="jxr_linenumber" name="L117" href="#L117">117</a> actual = distribution.inverseSurvivalProbability(1 - p12 * 0.5);
+<a class="jxr_linenumber" name="L118" href="#L118">118</a> Assertions.assertEquals(expected, actual, 1e-8, <span class="jxr_string">"Inverse SF"</span>);
+<a class="jxr_linenumber" name="L119" href="#L119">119</a>
+<a class="jxr_linenumber" name="L120" href="#L120">120</a> <em class="jxr_comment">// Edge case where the result is within the solver accuracy of the lower bound</em>
+<a class="jxr_linenumber" name="L121" href="#L121">121</a> expected = x0;
+<a class="jxr_linenumber" name="L122" href="#L122">122</a> actual = distribution.inverseCumulativeProbability(Double.MIN_VALUE);
+<a class="jxr_linenumber" name="L123" href="#L123">123</a> Assertions.assertEquals(expected, actual, 1e-8, <span class="jxr_string">"Inverse CDF"</span>);
+<a class="jxr_linenumber" name="L124" href="#L124">124</a>
+<a class="jxr_linenumber" name="L125" href="#L125">125</a> actual = distribution.inverseSurvivalProbability(Math.nextDown(1.0));
+<a class="jxr_linenumber" name="L126" href="#L126">126</a> Assertions.assertEquals(expected, actual, 1e-8, <span class="jxr_string">"Inverse SF"</span>);
+<a class="jxr_linenumber" name="L127" href="#L127">127</a> }
+<a class="jxr_linenumber" name="L128" href="#L128">128</a>
+<a class="jxr_linenumber" name="L129" href="#L129">129</a> <em class="jxr_javadoccomment">/** Various tests related to MATH-699. */</em>
+<a class="jxr_linenumber" name="L130" href="#L130">130</a> @Test
+<a class="jxr_linenumber" name="L131" href="#L131">131</a> <strong class="jxr_keyword">void</strong> testDiscontinuous() {
+<a class="jxr_linenumber" name="L132" href="#L132">132</a> <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> x0 = 0.0;
+<a class="jxr_linenumber" name="L133" href="#L133">133</a> <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> x1 = 0.25;
+<a class="jxr_linenumber" name="L134" href="#L134">134</a> <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> x2 = 0.5;
+<a class="jxr_linenumber" name="L135" href="#L135">135</a> <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> x3 = 0.75;
+<a class="jxr_linenumber" name="L136" href="#L136">136</a> <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> x4 = 1.0;
+<a class="jxr_linenumber" name="L137" href="#L137">137</a> <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> p12 = 1.0 / 3.0;
+<a class="jxr_linenumber" name="L138" href="#L138">138</a> <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> p23 = 2.0 / 3.0;
+<a class="jxr_linenumber" name="L139" href="#L139">139</a> <strong class="jxr_keyword">final</strong> AbstractContinuousDistribution distribution;
+<a class="jxr_linenumber" name="L140" href="#L140">140</a> distribution = <strong class="jxr_keyword">new</strong> AbstractContinuousDistribution() {
+<a class="jxr_linenumber" name="L141" href="#L141">141</a> @Override
+<a class="jxr_linenumber" name="L142" href="#L142">142</a> <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">double</strong> cumulativeProbability(<strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> x) {
+<a class="jxr_linenumber" name="L143" href="#L143">143</a> <strong class="jxr_keyword">if</strong> (x < x0 ||
+<a class="jxr_linenumber" name="L144" href="#L144">144</a> x > x4) {
+<a class="jxr_linenumber" name="L145" href="#L145">145</a> <strong class="jxr_keyword">throw</strong> <strong class="jxr_keyword">new</strong> DistributionException(DistributionException.OUT_OF_RANGE, x, x0, x4);
+<a class="jxr_linenumber" name="L146" href="#L146">146</a> }
+<a class="jxr_linenumber" name="L147" href="#L147">147</a> <strong class="jxr_keyword">if</strong> (x <= x1) {
+<a class="jxr_linenumber" name="L148" href="#L148">148</a> <strong class="jxr_keyword">return</strong> p12 * (x - x0) / (x1 - x0);
+<a class="jxr_linenumber" name="L149" href="#L149">149</a> } <strong class="jxr_keyword">else</strong> <strong class="jxr_keyword">if</strong> (x <= x2) {
+<a class="jxr_linenumber" name="L150" href="#L150">150</a> <strong class="jxr_keyword">return</strong> p12;
+<a class="jxr_linenumber" name="L151" href="#L151">151</a> } <strong class="jxr_keyword">else</strong> <strong class="jxr_keyword">if</strong> (x <= x3) {
+<a class="jxr_linenumber" name="L152" href="#L152">152</a> <strong class="jxr_keyword">return</strong> p23;
+<a class="jxr_linenumber" name="L153" href="#L153">153</a> } <strong class="jxr_keyword">else</strong> {
+<a class="jxr_linenumber" name="L154" href="#L154">154</a> <strong class="jxr_keyword">return</strong> (1.0 - p23) * (x - x3) / (x4 - x3) + p23;
+<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>
+<a class="jxr_linenumber" name="L158" href="#L158">158</a> @Override
+<a class="jxr_linenumber" name="L159" href="#L159">159</a> <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">double</strong> density(<strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> x) {
+<a class="jxr_linenumber" name="L160" href="#L160">160</a> <strong class="jxr_keyword">if</strong> (x < x0 ||
+<a class="jxr_linenumber" name="L161" href="#L161">161</a> x > x4) {
+<a class="jxr_linenumber" name="L162" href="#L162">162</a> <strong class="jxr_keyword">throw</strong> <strong class="jxr_keyword">new</strong> DistributionException(DistributionException.OUT_OF_RANGE, x, x0, x4);
+<a class="jxr_linenumber" name="L163" href="#L163">163</a> }
+<a class="jxr_linenumber" name="L164" href="#L164">164</a> <strong class="jxr_keyword">if</strong> (x <= x1) {
+<a class="jxr_linenumber" name="L165" href="#L165">165</a> <strong class="jxr_keyword">return</strong> p12 / (x1 - x0);
+<a class="jxr_linenumber" name="L166" href="#L166">166</a> } <strong class="jxr_keyword">else</strong> <strong class="jxr_keyword">if</strong> (x <= x2) {
+<a class="jxr_linenumber" name="L167" href="#L167">167</a> <strong class="jxr_keyword">return</strong> 0.0;
+<a class="jxr_linenumber" name="L168" href="#L168">168</a> } <strong class="jxr_keyword">else</strong> <strong class="jxr_keyword">if</strong> (x <= x3) {
+<a class="jxr_linenumber" name="L169" href="#L169">169</a> <strong class="jxr_keyword">return</strong> 0.0;
+<a class="jxr_linenumber" name="L170" href="#L170">170</a> } <strong class="jxr_keyword">else</strong> {
+<a class="jxr_linenumber" name="L171" href="#L171">171</a> <strong class="jxr_keyword">return</strong> (1.0 - p23) / (x4 - x3);
+<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>
+<a class="jxr_linenumber" name="L175" href="#L175">175</a> @Override
+<a class="jxr_linenumber" name="L176" href="#L176">176</a> <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">double</strong> getMean() {
+<a class="jxr_linenumber" name="L177" href="#L177">177</a> <strong class="jxr_keyword">final</strong> UnivariateFunction f = x -> x * density(x);
+<a class="jxr_linenumber" name="L178" href="#L178">178</a> <strong class="jxr_keyword">final</strong> UnivariateIntegrator integrator = <strong class="jxr_keyword">new</strong> RombergIntegrator();
+<a class="jxr_linenumber" name="L179" href="#L179">179</a> <strong class="jxr_keyword">return</strong> integrator.integrate(Integer.MAX_VALUE, f, x0, x4);
+<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> @Override
+<a class="jxr_linenumber" name="L183" href="#L183">183</a> <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">double</strong> getVariance() {
+<a class="jxr_linenumber" name="L184" href="#L184">184</a> <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> meanX = getMean();
+<a class="jxr_linenumber" name="L185" href="#L185">185</a> <strong class="jxr_keyword">final</strong> UnivariateFunction f = x -> x * x * density(x);
+<a class="jxr_linenumber" name="L186" href="#L186">186</a> <strong class="jxr_keyword">final</strong> UnivariateIntegrator integrator = <strong class="jxr_keyword">new</strong> RombergIntegrator();
+<a class="jxr_linenumber" name="L187" href="#L187">187</a> <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> meanX2 = integrator.integrate(Integer.MAX_VALUE,
+<a class="jxr_linenumber" name="L188" href="#L188">188</a> f, x0, x4);
+<a class="jxr_linenumber" name="L189" href="#L189">189</a> <strong class="jxr_keyword">return</strong> meanX2 - meanX * meanX;
+<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> @Override
+<a class="jxr_linenumber" name="L193" href="#L193">193</a> <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">double</strong> getSupportLowerBound() {
+<a class="jxr_linenumber" name="L194" href="#L194">194</a> <strong class="jxr_keyword">return</strong> x0;
+<a class="jxr_linenumber" name="L195" href="#L195">195</a> }
+<a class="jxr_linenumber" name="L196" href="#L196">196</a>
+<a class="jxr_linenumber" name="L197" href="#L197">197</a> @Override
+<a class="jxr_linenumber" name="L198" href="#L198">198</a> <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">double</strong> getSupportUpperBound() {
+<a class="jxr_linenumber" name="L199" href="#L199">199</a> <strong class="jxr_keyword">return</strong> x4;
+<a class="jxr_linenumber" name="L200" href="#L200">200</a> }
+<a class="jxr_linenumber" name="L201" href="#L201">201</a>
+<a class="jxr_linenumber" name="L202" href="#L202">202</a> @Override
+<a class="jxr_linenumber" name="L203" href="#L203">203</a> <strong class="jxr_keyword">boolean</strong> isSupportConnected() {
+<a class="jxr_linenumber" name="L204" href="#L204">204</a> <em class="jxr_comment">// This is deliberately false; the functionality is the subject of this test</em>
+<a class="jxr_linenumber" name="L205" href="#L205">205</a> <strong class="jxr_keyword">return</strong> false;
+<a class="jxr_linenumber" name="L206" href="#L206">206</a> }
+<a class="jxr_linenumber" name="L207" href="#L207">207</a> };
+<a class="jxr_linenumber" name="L208" href="#L208">208</a> <em class="jxr_comment">// CDF continuous before x1 and after x3. Two plateuas in between stepped at x2:</em>
+<a class="jxr_linenumber" name="L209" href="#L209">209</a> <em class="jxr_comment">// CDF(x1 <= X <= x2) = p12.</em>
+<a class="jxr_linenumber" name="L210" href="#L210">210</a> <em class="jxr_comment">// CDF(x2 <= X <= x3) = p23. The inverse returns the infimum.</em>
+<a class="jxr_linenumber" name="L211" href="#L211">211</a> <strong class="jxr_keyword">double</strong> expected = x2;
+<a class="jxr_linenumber" name="L212" href="#L212">212</a> <strong class="jxr_keyword">double</strong> actual = distribution.inverseCumulativeProbability(p23);
+<a class="jxr_linenumber" name="L213" href="#L213">213</a> Assertions.assertEquals(expected, actual, 1e-8, <span class="jxr_string">"Inverse CDF"</span>);
+<a class="jxr_linenumber" name="L214" href="#L214">214</a>
+<a class="jxr_linenumber" name="L215" href="#L215">215</a> actual = distribution.inverseSurvivalProbability(1 - p23);
+<a class="jxr_linenumber" name="L216" href="#L216">216</a> Assertions.assertEquals(expected, actual, 1e-8, <span class="jxr_string">"Inverse SF"</span>);
+<a class="jxr_linenumber" name="L217" href="#L217">217</a>
+<a class="jxr_linenumber" name="L218" href="#L218">218</a> <em class="jxr_comment">// Test the continuous region</em>
+<a class="jxr_linenumber" name="L219" href="#L219">219</a> expected = 0.5 * (x1 - x0);
+<a class="jxr_linenumber" name="L220" href="#L220">220</a> actual = distribution.inverseCumulativeProbability(p12 * 0.5);
+<a class="jxr_linenumber" name="L221" href="#L221">221</a> Assertions.assertEquals(expected, actual, 1e-8, <span class="jxr_string">"Inverse CDF"</span>);
+<a class="jxr_linenumber" name="L222" href="#L222">222</a>
+<a class="jxr_linenumber" name="L223" href="#L223">223</a> actual = distribution.inverseSurvivalProbability(1 - p12 * 0.5);
+<a class="jxr_linenumber" name="L224" href="#L224">224</a> Assertions.assertEquals(expected, actual, 1e-8, <span class="jxr_string">"Inverse SF"</span>);
+<a class="jxr_linenumber" name="L225" href="#L225">225</a>
+<a class="jxr_linenumber" name="L226" href="#L226">226</a> <em class="jxr_comment">// Edge case where the result is within the solver accuracy of the lower bound</em>
+<a class="jxr_linenumber" name="L227" href="#L227">227</a> expected = x0;
+<a class="jxr_linenumber" name="L228" href="#L228">228</a> actual = distribution.inverseCumulativeProbability(Double.MIN_VALUE);
+<a class="jxr_linenumber" name="L229" href="#L229">229</a> Assertions.assertEquals(expected, actual, 1e-8, <span class="jxr_string">"Inverse CDF"</span>);
+<a class="jxr_linenumber" name="L230" href="#L230">230</a>
+<a class="jxr_linenumber" name="L231" href="#L231">231</a> actual = distribution.inverseSurvivalProbability(Math.nextDown(1.0));
+<a class="jxr_linenumber" name="L232" href="#L232">232</a> Assertions.assertEquals(expected, actual, 1e-8, <span class="jxr_string">"Inverse SF"</span>);
+<a class="jxr_linenumber" name="L233" href="#L233">233</a> }
+<a class="jxr_linenumber" name="L234" href="#L234">234</a>
+<a class="jxr_linenumber" name="L235" href="#L235">235</a> <em class="jxr_javadoccomment">/**</em>
+<a class="jxr_linenumber" name="L236" href="#L236">236</a> <em class="jxr_javadoccomment"> * Test zero variance. This invalidates the Chebyshev inequality. If the mean is at</em>
+<a class="jxr_linenumber" name="L237" href="#L237">237</a> <em class="jxr_javadoccomment"> * one bound and the other bound is infinite then the inequality sets the other bound</em>
+<a class="jxr_linenumber" name="L238" href="#L238">238</a> <em class="jxr_javadoccomment"> * to the mean. This results in no bracket for the solver.</em>
+<a class="jxr_linenumber" name="L239" href="#L239">239</a> <em class="jxr_javadoccomment"> *</em>
+<a class="jxr_linenumber" name="L240" href="#L240">240</a> <em class="jxr_javadoccomment"> * <p>If the distribution is reporting the variance incorrectly then options are</em>
+<a class="jxr_linenumber" name="L241" href="#L241">241</a> <em class="jxr_javadoccomment"> * to throw an exception, or safely fall back to manual bracketing. This test verifies</em>
+<a class="jxr_linenumber" name="L242" href="#L242">242</a> <em class="jxr_javadoccomment"> * the solver reverts to manual bracketing and raises no exception.</em>
+<a class="jxr_linenumber" name="L243" href="#L243">243</a> <em class="jxr_javadoccomment"> */</em>
+<a class="jxr_linenumber" name="L244" href="#L244">244</a> @Test
+<a class="jxr_linenumber" name="L245" href="#L245">245</a> <strong class="jxr_keyword">void</strong> testZeroVariance() {
+<a class="jxr_linenumber" name="L246" href="#L246">246</a> <em class="jxr_comment">// Distribution must have an infinite bound but no variance.</em>
+<a class="jxr_linenumber" name="L247" href="#L247">247</a> <em class="jxr_comment">// This is an invalid case for the Chebyshev inequality.</em>
+<a class="jxr_linenumber" name="L248" href="#L248">248</a> <em class="jxr_comment">// E.g. It may occur in the Pareto distribution as it approaches a Dirac function.</em>
+<a class="jxr_linenumber" name="L249" href="#L249">249</a>
+<a class="jxr_linenumber" name="L250" href="#L250">250</a> <em class="jxr_comment">// Create a Dirac function at x=10</em>
+<a class="jxr_linenumber" name="L251" href="#L251">251</a> <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> x0 = 10.0;
+<a class="jxr_linenumber" name="L252" href="#L252">252</a> <strong class="jxr_keyword">final</strong> AbstractContinuousDistribution distribution;
+<a class="jxr_linenumber" name="L253" href="#L253">253</a> distribution = <strong class="jxr_keyword">new</strong> AbstractContinuousDistribution() {
+<a class="jxr_linenumber" name="L254" href="#L254">254</a> @Override
+<a class="jxr_linenumber" name="L255" href="#L255">255</a> <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">double</strong> cumulativeProbability(<strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> x) {
+<a class="jxr_linenumber" name="L256" href="#L256">256</a> <strong class="jxr_keyword">return</strong> x <= x0 ? 0.0 : 1.0;
+<a class="jxr_linenumber" name="L257" href="#L257">257</a> }
+<a class="jxr_linenumber" name="L258" href="#L258">258</a>
+<a class="jxr_linenumber" name="L259" href="#L259">259</a> @Override
+<a class="jxr_linenumber" name="L260" href="#L260">260</a> <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">double</strong> density(<strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> x) {
+<a class="jxr_linenumber" name="L261" href="#L261">261</a> <strong class="jxr_keyword">throw</strong> <strong class="jxr_keyword">new</strong> AssertionError();
+<a class="jxr_linenumber" name="L262" href="#L262">262</a> }
+<a class="jxr_linenumber" name="L263" href="#L263">263</a>
+<a class="jxr_linenumber" name="L264" href="#L264">264</a> @Override
+<a class="jxr_linenumber" name="L265" href="#L265">265</a> <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">double</strong> getMean() {
+<a class="jxr_linenumber" name="L266" href="#L266">266</a> <strong class="jxr_keyword">return</strong> x0;
+<a class="jxr_linenumber" name="L267" href="#L267">267</a> }
+<a class="jxr_linenumber" name="L268" href="#L268">268</a>
+<a class="jxr_linenumber" name="L269" href="#L269">269</a> @Override
+<a class="jxr_linenumber" name="L270" href="#L270">270</a> <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">double</strong> getVariance() {
+<a class="jxr_linenumber" name="L271" href="#L271">271</a> <strong class="jxr_keyword">return</strong> 0.0;
+<a class="jxr_linenumber" name="L272" href="#L272">272</a> }
+<a class="jxr_linenumber" name="L273" href="#L273">273</a>
+<a class="jxr_linenumber" name="L274" href="#L274">274</a> @Override
+<a class="jxr_linenumber" name="L275" href="#L275">275</a> <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">double</strong> getSupportLowerBound() {
+<a class="jxr_linenumber" name="L276" href="#L276">276</a> <strong class="jxr_keyword">return</strong> x0;
+<a class="jxr_linenumber" name="L277" href="#L277">277</a> }
+<a class="jxr_linenumber" name="L278" href="#L278">278</a>
+<a class="jxr_linenumber" name="L279" href="#L279">279</a> @Override
+<a class="jxr_linenumber" name="L280" href="#L280">280</a> <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">double</strong> getSupportUpperBound() {
+<a class="jxr_linenumber" name="L281" href="#L281">281</a> <strong class="jxr_keyword">return</strong> Double.POSITIVE_INFINITY;
+<a class="jxr_linenumber" name="L282" href="#L282">282</a> }
+<a class="jxr_linenumber" name="L283" href="#L283">283</a> };
+<a class="jxr_linenumber" name="L284" href="#L284">284</a> <strong class="jxr_keyword">double</strong> x = distribution.inverseCumulativeProbability(0.5);
+<a class="jxr_linenumber" name="L285" href="#L285">285</a> <em class="jxr_comment">// The value can be anything other than x0</em>
+<a class="jxr_linenumber" name="L286" href="#L286">286</a> Assertions.assertNotEquals(x0, x, <span class="jxr_string">"Inverse CDF"</span>);
+<a class="jxr_linenumber" name="L287" href="#L287">287</a> <em class="jxr_comment">// Ideally it would be the next value after x0 but accuracy is dependent</em>
+<a class="jxr_linenumber" name="L288" href="#L288">288</a> <em class="jxr_comment">// on the tolerance of the solver</em>
+<a class="jxr_linenumber" name="L289" href="#L289">289</a> Assertions.assertEquals(x0, x, 1e-8, <span class="jxr_string">"Inverse CDF"</span>);
+<a class="jxr_linenumber" name="L290" href="#L290">290</a>
+<a class="jxr_linenumber" name="L291" href="#L291">291</a> <em class="jxr_comment">// The same functionality should be supported for the inverse survival probability</em>
+<a class="jxr_linenumber" name="L292" href="#L292">292</a> x = distribution.inverseSurvivalProbability(0.5);
+<a class="jxr_linenumber" name="L293" href="#L293">293</a> Assertions.assertNotEquals(x0, x, <span class="jxr_string">"Inverse SF"</span>);
+<a class="jxr_linenumber" name="L294" href="#L294">294</a> Assertions.assertEquals(x0, x, 1e-8, <span class="jxr_string">"Inverse SF"</span>);
+<a class="jxr_linenumber" name="L295" href="#L295">295</a> }
+<a class="jxr_linenumber" name="L296" href="#L296">296</a>
+<a class="jxr_linenumber" name="L297" href="#L297">297</a> <em class="jxr_javadoccomment">/**</em>
+<a class="jxr_linenumber" name="L298" href="#L298">298</a> <em class="jxr_javadoccomment"> * Test infinite variance. This invalidates the Chebyshev inequality.</em>
+<a class="jxr_linenumber" name="L299" href="#L299">299</a> <em class="jxr_javadoccomment"> *</em>
+<a class="jxr_linenumber" name="L300" href="#L300">300</a> <em class="jxr_javadoccomment"> * <p>This test verifies the solver reverts to manual bracketing and raises no exception.</em>
+<a class="jxr_linenumber" name="L301" href="#L301">301</a> <em class="jxr_javadoccomment"> */</em>
+<a class="jxr_linenumber" name="L302" href="#L302">302</a> @Test
+<a class="jxr_linenumber" name="L303" href="#L303">303</a> <strong class="jxr_keyword">void</strong> testInfiniteVariance() {
+<a class="jxr_linenumber" name="L304" href="#L304">304</a> <em class="jxr_comment">// Distribution must have an infinite bound and infinite variance.</em>
+<a class="jxr_linenumber" name="L305" href="#L305">305</a> <em class="jxr_comment">// This is an invalid case for the Chebyshev inequality.</em>
+<a class="jxr_linenumber" name="L306" href="#L306">306</a>
+<a class="jxr_linenumber" name="L307" href="#L307">307</a> <em class="jxr_comment">// Create a triangle distribution: (a, c, b); a=lower, c=mode, b=upper</em>
+<a class="jxr_linenumber" name="L308" href="#L308">308</a> <em class="jxr_comment">// (-10, 0, 10)</em>
+<a class="jxr_linenumber" name="L309" href="#L309">309</a> <em class="jxr_comment">// Area of the first triangle [-10, 0] is set assuming the height is 10</em>
+<a class="jxr_linenumber" name="L310" href="#L310">310</a> <em class="jxr_comment">// => 10 * 10 * 2 / 2 = 100</em>
+<a class="jxr_linenumber" name="L311" href="#L311">311</a> <em class="jxr_comment">// Length of triangle to achieve half the area:</em>
+<a class="jxr_linenumber" name="L312" href="#L312">312</a> <em class="jxr_comment">// x = sqrt(50) = 7.07..</em>
+<a class="jxr_linenumber" name="L313" href="#L313">313</a>
+<a class="jxr_linenumber" name="L314" href="#L314">314</a> <strong class="jxr_keyword">final</strong> AbstractContinuousDistribution distribution;
+<a class="jxr_linenumber" name="L315" href="#L315">315</a> distribution = <strong class="jxr_keyword">new</strong> AbstractContinuousDistribution() {
+<a class="jxr_linenumber" name="L316" href="#L316">316</a> @Override
+<a class="jxr_linenumber" name="L317" href="#L317">317</a> <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">double</strong> cumulativeProbability(<strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> x) {
+<a class="jxr_linenumber" name="L318" href="#L318">318</a> <strong class="jxr_keyword">if</strong> (x > 0) {
+<a class="jxr_linenumber" name="L319" href="#L319">319</a> <em class="jxr_comment">// Use symmetry for the upper triangle</em>
+<a class="jxr_linenumber" name="L320" href="#L320">320</a> <strong class="jxr_keyword">return</strong> 1 - cumulativeProbability(-x);
+<a class="jxr_linenumber" name="L321" href="#L321">321</a> }
+<a class="jxr_linenumber" name="L322" href="#L322">322</a> <strong class="jxr_keyword">if</strong> (x < -10) {
+<a class="jxr_linenumber" name="L323" href="#L323">323</a> <strong class="jxr_keyword">return</strong> 0;
+<a class="jxr_linenumber" name="L324" href="#L324">324</a> }
+<a class="jxr_linenumber" name="L325" href="#L325">325</a> <strong class="jxr_keyword">return</strong> Math.pow(x + 10, 2) / 200;
+<a class="jxr_linenumber" name="L326" href="#L326">326</a> }
+<a class="jxr_linenumber" name="L327" href="#L327">327</a>
+<a class="jxr_linenumber" name="L328" href="#L328">328</a> @Override
+<a class="jxr_linenumber" name="L329" href="#L329">329</a> <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">double</strong> density(<strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> x) {
+<a class="jxr_linenumber" name="L330" href="#L330">330</a> <strong class="jxr_keyword">throw</strong> <strong class="jxr_keyword">new</strong> AssertionError();
+<a class="jxr_linenumber" name="L331" href="#L331">331</a> }
+<a class="jxr_linenumber" name="L332" href="#L332">332</a>
+<a class="jxr_linenumber" name="L333" href="#L333">333</a> @Override
+<a class="jxr_linenumber" name="L334" href="#L334">334</a> <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">double</strong> getMean() {
+<a class="jxr_linenumber" name="L335" href="#L335">335</a> <strong class="jxr_keyword">return</strong> 0;
+<a class="jxr_linenumber" name="L336" href="#L336">336</a> }
+<a class="jxr_linenumber" name="L337" href="#L337">337</a>
+<a class="jxr_linenumber" name="L338" href="#L338">338</a> @Override
+<a class="jxr_linenumber" name="L339" href="#L339">339</a> <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">double</strong> getVariance() {
+<a class="jxr_linenumber" name="L340" href="#L340">340</a> <em class="jxr_comment">// Report variance incorrectly</em>
+<a class="jxr_linenumber" name="L341" href="#L341">341</a> <strong class="jxr_keyword">return</strong> Double.POSITIVE_INFINITY;
+<a class="jxr_linenumber" name="L342" href="#L342">342</a> }
+<a class="jxr_linenumber" name="L343" href="#L343">343</a>
+<a class="jxr_linenumber" name="L344" href="#L344">344</a> @Override
+<a class="jxr_linenumber" name="L345" href="#L345">345</a> <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">double</strong> getSupportLowerBound() {
+<a class="jxr_linenumber" name="L346" href="#L346">346</a> <em class="jxr_comment">// Report lower bound incorrectly (it should be -10) to test cdf(0)</em>
+<a class="jxr_linenumber" name="L347" href="#L347">347</a> <strong class="jxr_keyword">return</strong> Double.NEGATIVE_INFINITY;
+<a class="jxr_linenumber" name="L348" href="#L348">348</a> }
+<a class="jxr_linenumber" name="L349" href="#L349">349</a>
+<a class="jxr_linenumber" name="L350" href="#L350">350</a> @Override
+<a class="jxr_linenumber" name="L351" href="#L351">351</a> <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">double</strong> getSupportUpperBound() {
+<a class="jxr_linenumber" name="L352" href="#L352">352</a> <em class="jxr_comment">// Report upper bound incorrectly (it should be 10) to test cdf(1)</em>
+<a class="jxr_linenumber" name="L353" href="#L353">353</a> <strong class="jxr_keyword">return</strong> Double.POSITIVE_INFINITY;
+<a class="jxr_linenumber" name="L354" href="#L354">354</a> }
+<a class="jxr_linenumber" name="L355" href="#L355">355</a> };
+<a class="jxr_linenumber" name="L356" href="#L356">356</a>
+<a class="jxr_linenumber" name="L357" href="#L357">357</a> <em class="jxr_comment">// Accuracy is dependent on the tolerance of the solver</em>
+<a class="jxr_linenumber" name="L358" href="#L358">358</a> <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> tolerance = 1e-8;
+<a class="jxr_linenumber" name="L359" href="#L359">359</a>
+<a class="jxr_linenumber" name="L360" href="#L360">360</a> <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> x = Math.sqrt(50);
+<a class="jxr_linenumber" name="L361" href="#L361">361</a> Assertions.assertEquals(Double.NEGATIVE_INFINITY, distribution.inverseCumulativeProbability(0), <span class="jxr_string">"Inverse CDF"</span>);
+<a class="jxr_linenumber" name="L362" href="#L362">362</a> Assertions.assertEquals(x - 10, distribution.inverseCumulativeProbability(0.25), tolerance, <span class="jxr_string">"Inverse CDF"</span>);
+<a class="jxr_linenumber" name="L363" href="#L363">363</a> Assertions.assertEquals(0, distribution.inverseCumulativeProbability(0.5), tolerance, <span class="jxr_string">"Inverse CDF"</span>);
+<a class="jxr_linenumber" name="L364" href="#L364">364</a> Assertions.assertEquals(10 - x, distribution.inverseCumulativeProbability(0.75), tolerance, <span class="jxr_string">"Inverse CDF"</span>);
+<a class="jxr_linenumber" name="L365" href="#L365">365</a> Assertions.assertEquals(Double.POSITIVE_INFINITY, distribution.inverseCumulativeProbability(1), <span class="jxr_string">"Inverse CDF"</span>);
+<a class="jxr_linenumber" name="L366" href="#L366">366</a>
+<a class="jxr_linenumber" name="L367" href="#L367">367</a> <em class="jxr_comment">// The same functionality should be supported for the inverse survival probability</em>
+<a class="jxr_linenumber" name="L368" href="#L368">368</a> Assertions.assertEquals(Double.NEGATIVE_INFINITY, distribution.inverseSurvivalProbability(1), <span class="jxr_string">"Inverse CDF"</span>);
+<a class="jxr_linenumber" name="L369" href="#L369">369</a> Assertions.assertEquals(x - 10, distribution.inverseSurvivalProbability(0.75), tolerance, <span class="jxr_string">"Inverse SF"</span>);
+<a class="jxr_linenumber" name="L370" href="#L370">370</a> Assertions.assertEquals(0, distribution.inverseSurvivalProbability(0.5), tolerance, <span class="jxr_string">"Inverse SF"</span>);
+<a class="jxr_linenumber" name="L371" href="#L371">371</a> Assertions.assertEquals(10 - x, distribution.inverseSurvivalProbability(0.25), tolerance, <span class="jxr_string">"Inverse SF"</span>);
+<a class="jxr_linenumber" name="L372" href="#L372">372</a> Assertions.assertEquals(Double.POSITIVE_INFINITY, distribution.inverseSurvivalProbability(0), <span class="jxr_string">"Inverse CDF"</span>);
+<a class="jxr_linenumber" name="L373" href="#L373">373</a> }
+<a class="jxr_linenumber" name="L374" href="#L374">374</a>
+<a class="jxr_linenumber" name="L375" href="#L375">375</a> <em class="jxr_javadoccomment">/**</em>
+<a class="jxr_linenumber" name="L376" href="#L376">376</a> <em class="jxr_javadoccomment"> * Create a distribution near positive infinity so that it is truncated by MAX_VALUE.</em>
+<a class="jxr_linenumber" name="L377" href="#L377">377</a> <em class="jxr_javadoccomment"> * This distribution reports the upper bound as infinite.</em>
+<a class="jxr_linenumber" name="L378" href="#L378">378</a> <em class="jxr_javadoccomment"> */</em>
+<a class="jxr_linenumber" name="L379" href="#L379">379</a> @Test
+<a class="jxr_linenumber" name="L380" href="#L380">380</a> <strong class="jxr_keyword">void</strong> testTruncatedDistributionAtPositiveInfinity() {
+<a class="jxr_linenumber" name="L381" href="#L381">381</a> assertTruncatedDistributionAtPositiveInfinity(false);
+<a class="jxr_linenumber" name="L382" href="#L382">382</a> }
+<a class="jxr_linenumber" name="L383" href="#L383">383</a>
+<a class="jxr_linenumber" name="L384" href="#L384">384</a> <em class="jxr_javadoccomment">/**</em>
+<a class="jxr_linenumber" name="L385" href="#L385">385</a> <em class="jxr_javadoccomment"> * Create a distribution near positive infinity so that it is truncated by MAX_VALUE.</em>
+<a class="jxr_linenumber" name="L386" href="#L386">386</a> <em class="jxr_javadoccomment"> * This distribution reports the upper bound as finite.</em>
+<a class="jxr_linenumber" name="L387" href="#L387">387</a> <em class="jxr_javadoccomment"> */</em>
+<a class="jxr_linenumber" name="L388" href="#L388">388</a> @Test
+<a class="jxr_linenumber" name="L389" href="#L389">389</a> <strong class="jxr_keyword">void</strong> testTruncatedDistributionAtPositiveInfinity2() {
+<a class="jxr_linenumber" name="L390" href="#L390">390</a> assertTruncatedDistributionAtPositiveInfinity(<strong class="jxr_keyword">true</strong>);
+<a class="jxr_linenumber" name="L391" href="#L391">391</a> }
+<a class="jxr_linenumber" name="L392" href="#L392">392</a>
+<a class="jxr_linenumber" name="L393" href="#L393">393</a> <strong class="jxr_keyword">private</strong> <strong class="jxr_keyword">static</strong> <strong class="jxr_keyword">void</strong> assertTruncatedDistributionAtPositiveInfinity(<strong class="jxr_keyword">boolean</strong> finiteBound) {
+<a class="jxr_linenumber" name="L394" href="#L394">394</a> <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> mean = Double.MAX_VALUE;
+<a class="jxr_linenumber" name="L395" href="#L395">395</a> <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> width = Double.MAX_VALUE / 2;
+<a class="jxr_linenumber" name="L396" href="#L396">396</a> <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> bound = finiteBound ? Double.MAX_VALUE : Double.POSITIVE_INFINITY;
+<a class="jxr_linenumber" name="L397" href="#L397">397</a> <strong class="jxr_keyword">final</strong> CentredUniformDistribution dist = <strong class="jxr_keyword">new</strong> CentredUniformDistribution(mean, width) {
+<a class="jxr_linenumber" name="L398" href="#L398">398</a> @Override
+<a class="jxr_linenumber" name="L399" href="#L399">399</a> <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">double</strong> getSupportUpperBound() {
+<a class="jxr_linenumber" name="L400" href="#L400">400</a> <strong class="jxr_keyword">return</strong> bound;
+<a class="jxr_linenumber" name="L401" href="#L401">401</a> }
+<a class="jxr_linenumber" name="L402" href="#L402">402</a> };
+<a class="jxr_linenumber" name="L403" href="#L403">403</a> <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> x = mean - width / 2;
+<a class="jxr_linenumber" name="L404" href="#L404">404</a> Assertions.assertEquals(0, dist.cumulativeProbability(x));
+<a class="jxr_linenumber" name="L405" href="#L405">405</a> Assertions.assertTrue(dist.cumulativeProbability(Math.nextUp(x)) > 0);
+<a class="jxr_linenumber" name="L406" href="#L406">406</a> Assertions.assertEquals(0.25, dist.cumulativeProbability(mean - width / 4));
+<a class="jxr_linenumber" name="L407" href="#L407">407</a> Assertions.assertEquals(0.5, dist.cumulativeProbability(mean));
+<a class="jxr_linenumber" name="L408" href="#L408">408</a>
+<a class="jxr_linenumber" name="L409" href="#L409">409</a> <em class="jxr_comment">// Truncated</em>
+<a class="jxr_linenumber" name="L410" href="#L410">410</a> Assertions.assertEquals(1.0, dist.cumulativeProbability(Math.nextUp(mean)));
+<a class="jxr_linenumber" name="L411" href="#L411">411</a>
+<a class="jxr_linenumber" name="L412" href="#L412">412</a> <em class="jxr_comment">// Inversion should be robust to return the upper infinite bound</em>
+<a class="jxr_linenumber" name="L413" href="#L413">413</a> Assertions.assertEquals(mean, dist.inverseCumulativeProbability(0.5));
+<a class="jxr_linenumber" name="L414" href="#L414">414</a> Assertions.assertEquals(mean, dist.inverseSurvivalProbability(0.5));
+<a class="jxr_linenumber" name="L415" href="#L415">415</a> Assertions.assertEquals(bound, dist.inverseCumulativeProbability(0.75));
+<a class="jxr_linenumber" name="L416" href="#L416">416</a> Assertions.assertEquals(bound, dist.inverseSurvivalProbability(0.25));
+<a class="jxr_linenumber" name="L417" href="#L417">417</a> }
+<a class="jxr_linenumber" name="L418" href="#L418">418</a>
+<a class="jxr_linenumber" name="L419" href="#L419">419</a> <em class="jxr_javadoccomment">/**</em>
+<a class="jxr_linenumber" name="L420" href="#L420">420</a> <em class="jxr_javadoccomment"> * Create a distribution near negative infinity so that it is truncated by -MAX_VALUE.</em>
+<a class="jxr_linenumber" name="L421" href="#L421">421</a> <em class="jxr_javadoccomment"> * This distribution reports the lower bound as infinite.</em>
+<a class="jxr_linenumber" name="L422" href="#L422">422</a> <em class="jxr_javadoccomment"> */</em>
+<a class="jxr_linenumber" name="L423" href="#L423">423</a> @Test
+<a class="jxr_linenumber" name="L424" href="#L424">424</a> <strong class="jxr_keyword">void</strong> testTruncatedDistributionAtNegativeInfinity() {
+<a class="jxr_linenumber" name="L425" href="#L425">425</a> assertTruncatedDistributionAtNegativeInfinity(false);
+<a class="jxr_linenumber" name="L426" href="#L426">426</a> }
+<a class="jxr_linenumber" name="L427" href="#L427">427</a>
+<a class="jxr_linenumber" name="L428" href="#L428">428</a> <em class="jxr_javadoccomment">/**</em>
+<a class="jxr_linenumber" name="L429" href="#L429">429</a> <em class="jxr_javadoccomment"> * Create a distribution near negative infinity so that it is truncated by -MAX_VALUE.</em>
+<a class="jxr_linenumber" name="L430" href="#L430">430</a> <em class="jxr_javadoccomment"> * This distribution reports the lower bound as finite.</em>
+<a class="jxr_linenumber" name="L431" href="#L431">431</a> <em class="jxr_javadoccomment"> */</em>
+<a class="jxr_linenumber" name="L432" href="#L432">432</a> @Test
+<a class="jxr_linenumber" name="L433" href="#L433">433</a> <strong class="jxr_keyword">void</strong> testTruncatedDistributionAtNegativeInfinity2() {
+<a class="jxr_linenumber" name="L434" href="#L434">434</a> assertTruncatedDistributionAtNegativeInfinity(<strong class="jxr_keyword">true</strong>);
+<a class="jxr_linenumber" name="L435" href="#L435">435</a> }
+<a class="jxr_linenumber" name="L436" href="#L436">436</a>
+<a class="jxr_linenumber" name="L437" href="#L437">437</a> <strong class="jxr_keyword">private</strong> <strong class="jxr_keyword">static</strong> <strong class="jxr_keyword">void</strong> assertTruncatedDistributionAtNegativeInfinity(<strong class="jxr_keyword">boolean</strong> finiteBound) {
+<a class="jxr_linenumber" name="L438" href="#L438">438</a> <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> mean = -Double.MAX_VALUE;
+<a class="jxr_linenumber" name="L439" href="#L439">439</a> <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> width = Double.MAX_VALUE / 2;
+<a class="jxr_linenumber" name="L440" href="#L440">440</a> <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> bound = finiteBound ? -Double.MAX_VALUE : Double.NEGATIVE_INFINITY;
+<a class="jxr_linenumber" name="L441" href="#L441">441</a> <strong class="jxr_keyword">final</strong> CentredUniformDistribution dist = <strong class="jxr_keyword">new</strong> CentredUniformDistribution(mean, width) {
+<a class="jxr_linenumber" name="L442" href="#L442">442</a> @Override
+<a class="jxr_linenumber" name="L443" href="#L443">443</a> <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">double</strong> getSupportLowerBound() {
+<a class="jxr_linenumber" name="L444" href="#L444">444</a> <strong class="jxr_keyword">return</strong> bound;
+<a class="jxr_linenumber" name="L445" href="#L445">445</a> }
+<a class="jxr_linenumber" name="L446" href="#L446">446</a> };
+<a class="jxr_linenumber" name="L447" href="#L447">447</a> <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> x = mean + width / 2;
+<a class="jxr_linenumber" name="L448" href="#L448">448</a> Assertions.assertEquals(1, dist.cumulativeProbability(x));
+<a class="jxr_linenumber" name="L449" href="#L449">449</a> Assertions.assertTrue(dist.cumulativeProbability(Math.nextDown(x)) < 1);
+<a class="jxr_linenumber" name="L450" href="#L450">450</a> Assertions.assertEquals(0.75, dist.cumulativeProbability(mean + width / 4));
+<a class="jxr_linenumber" name="L451" href="#L451">451</a> Assertions.assertEquals(0.5, dist.cumulativeProbability(mean));
+<a class="jxr_linenumber" name="L452" href="#L452">452</a>
+<a class="jxr_linenumber" name="L453" href="#L453">453</a> <em class="jxr_comment">// Truncated</em>
+<a class="jxr_linenumber" name="L454" href="#L454">454</a> Assertions.assertEquals(0.0, dist.cumulativeProbability(Math.nextDown(mean)));
+<a class="jxr_linenumber" name="L455" href="#L455">455</a>
+<a class="jxr_linenumber" name="L456" href="#L456">456</a> <em class="jxr_comment">// Inversion should be robust to return the lower infinite bound</em>
+<a class="jxr_linenumber" name="L457" href="#L457">457</a> Assertions.assertEquals(mean, dist.inverseCumulativeProbability(0.5));
+<a class="jxr_linenumber" name="L458" href="#L458">458</a> Assertions.assertEquals(mean, dist.inverseSurvivalProbability(0.5));
+<a class="jxr_linenumber" name="L459" href="#L459">459</a> Assertions.assertEquals(bound, dist.inverseCumulativeProbability(0.25));
+<a class="jxr_linenumber" name="L460" href="#L460">460</a> Assertions.assertEquals(bound, dist.inverseSurvivalProbability(0.75));
+<a class="jxr_linenumber" name="L461" href="#L461">461</a> }
+<a class="jxr_linenumber" name="L462" href="#L462">462</a>
+<a class="jxr_linenumber" name="L463" href="#L463">463</a> <em class="jxr_javadoccomment">/**</em>
+<a class="jxr_linenumber" name="L464" href="#L464">464</a> <em class="jxr_javadoccomment"> * Uniform distribution described with a centre and width.</em>
+<a class="jxr_linenumber" name="L465" href="#L465">465</a> <em class="jxr_javadoccomment"> * This can be use to place the centre of the distribution at the limit of a finite double</em>
+<a class="jxr_linenumber" name="L466" href="#L466">466</a> <em class="jxr_javadoccomment"> * value so that the distribution is truncated.</em>
+<a class="jxr_linenumber" name="L467" href="#L467">467</a> <em class="jxr_javadoccomment"> */</em>
+<a class="jxr_linenumber" name="L468" href="#L468">468</a> <strong class="jxr_keyword">static</strong> <strong class="jxr_keyword">class</strong> CentredUniformDistribution <strong class="jxr_keyword">extends</strong> AbstractContinuousDistribution {
+<a class="jxr_linenumber" name="L469" href="#L469">469</a> <strong class="jxr_keyword">private</strong> <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> mean;
+<a class="jxr_linenumber" name="L470" href="#L470">470</a> <strong class="jxr_keyword">private</strong> <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> width;
+<a class="jxr_linenumber" name="L471" href="#L471">471</a> <strong class="jxr_keyword">private</strong> <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> density;
+<a class="jxr_linenumber" name="L472" href="#L472">472</a> <strong class="jxr_keyword">private</strong> <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> lo;
+<a class="jxr_linenumber" name="L473" href="#L473">473</a> <strong class="jxr_keyword">private</strong> <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> hi;
+<a class="jxr_linenumber" name="L474" href="#L474">474</a>
+<a class="jxr_linenumber" name="L475" href="#L475">475</a> <em class="jxr_javadoccomment">/**</em>
+<a class="jxr_linenumber" name="L476" href="#L476">476</a> <em class="jxr_javadoccomment"> * @param mean Mean</em>
+<a class="jxr_linenumber" name="L477" href="#L477">477</a> <em class="jxr_javadoccomment"> * @param width Width</em>
+<a class="jxr_linenumber" name="L478" href="#L478">478</a> <em class="jxr_javadoccomment"> */</em>
+<a class="jxr_linenumber" name="L479" href="#L479">479</a> CentredUniformDistribution(<strong class="jxr_keyword">double</strong> mean, <strong class="jxr_keyword">double</strong> width) {
+<a class="jxr_linenumber" name="L480" href="#L480">480</a> <strong class="jxr_keyword">this</strong>.mean = mean;
+<a class="jxr_linenumber" name="L481" href="#L481">481</a> <strong class="jxr_keyword">this</strong>.width = width;
+<a class="jxr_linenumber" name="L482" href="#L482">482</a> density = 1 / width;
+<a class="jxr_linenumber" name="L483" href="#L483">483</a> lo = mean - width / 2;
+<a class="jxr_linenumber" name="L484" href="#L484">484</a> hi = mean + width / 2;
+<a class="jxr_linenumber" name="L485" href="#L485">485</a> }
+<a class="jxr_linenumber" name="L486" href="#L486">486</a>
+<a class="jxr_linenumber" name="L487" href="#L487">487</a> @Override
+<a class="jxr_linenumber" name="L488" href="#L488">488</a> <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">double</strong> density(<strong class="jxr_keyword">double</strong> x) {
+<a class="jxr_linenumber" name="L489" href="#L489">489</a> <strong class="jxr_keyword">return</strong> density;
+<a class="jxr_linenumber" name="L490" href="#L490">490</a> }
+<a class="jxr_linenumber" name="L491" href="#L491">491</a>
+<a class="jxr_linenumber" name="L492" href="#L492">492</a> @Override
+<a class="jxr_linenumber" name="L493" href="#L493">493</a> <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">double</strong> cumulativeProbability(<strong class="jxr_keyword">double</strong> x) {
+<a class="jxr_linenumber" name="L494" href="#L494">494</a> <strong class="jxr_keyword">if</strong> (x <= lo) {
+<a class="jxr_linenumber" name="L495" href="#L495">495</a> <strong class="jxr_keyword">return</strong> 0;
+<a class="jxr_linenumber" name="L496" href="#L496">496</a> }
+<a class="jxr_linenumber" name="L497" href="#L497">497</a> <strong class="jxr_keyword">if</strong> (x >= hi) {
+<a class="jxr_linenumber" name="L498" href="#L498">498</a> <strong class="jxr_keyword">return</strong> 1;
+<a class="jxr_linenumber" name="L499" href="#L499">499</a> }
+<a class="jxr_linenumber" name="L500" href="#L500">500</a> <strong class="jxr_keyword">return</strong> 0.5 + density * (x - mean);
+<a class="jxr_linenumber" name="L501" href="#L501">501</a> }
+<a class="jxr_linenumber" name="L502" href="#L502">502</a>
+<a class="jxr_linenumber" name="L503" href="#L503">503</a> @Override
+<a class="jxr_linenumber" name="L504" href="#L504">504</a> <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">double</strong> getMean() {
+<a class="jxr_linenumber" name="L505" href="#L505">505</a> <strong class="jxr_keyword">return</strong> mean;
+<a class="jxr_linenumber" name="L506" href="#L506">506</a> }
+<a class="jxr_linenumber" name="L507" href="#L507">507</a>
+<a class="jxr_linenumber" name="L508" href="#L508">508</a> @Override
+<a class="jxr_linenumber" name="L509" href="#L509">509</a> <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">double</strong> getVariance() {
+<a class="jxr_linenumber" name="L510" href="#L510">510</a> <strong class="jxr_keyword">return</strong> width * width / 12;
+<a class="jxr_linenumber" name="L511" href="#L511">511</a> }
+<a class="jxr_linenumber" name="L512" href="#L512">512</a>
+<a class="jxr_linenumber" name="L513" href="#L513">513</a> @Override
+<a class="jxr_linenumber" name="L514" href="#L514">514</a> <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">double</strong> getSupportLowerBound() {
+<a class="jxr_linenumber" name="L515" href="#L515">515</a> <strong class="jxr_keyword">return</strong> lo;
+<a class="jxr_linenumber" name="L516" href="#L516">516</a> }
+<a class="jxr_linenumber" name="L517" href="#L517">517</a>
+<a class="jxr_linenumber" name="L518" href="#L518">518</a> @Override
+<a class="jxr_linenumber" name="L519" href="#L519">519</a> <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">double</strong> getSupportUpperBound() {
+<a class="jxr_linenumber" name="L520" href="#L520">520</a> <strong class="jxr_keyword">return</strong> hi;
+<a class="jxr_linenumber" name="L521" href="#L521">521</a> }
+<a class="jxr_linenumber" name="L522" href="#L522">522</a> }
+<a class="jxr_linenumber" name="L523" href="#L523">523</a> }
+</pre>
+<hr/>
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