Added: dev/commons/statistics/1.0-RC1/site/xref/org/apache/commons/statistics/distribution/AbstractContinuousDistribution.html ============================================================================== --- dev/commons/statistics/1.0-RC1/site/xref/org/apache/commons/statistics/distribution/AbstractContinuousDistribution.html (added) +++ dev/commons/statistics/1.0-RC1/site/xref/org/apache/commons/statistics/distribution/AbstractContinuousDistribution.html Thu Dec 1 16:47:12 2022 @@ -0,0 +1,428 @@ +<!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>AbstractContinuousDistribution xref</title> +<link type="text/css" rel="stylesheet" href="../../../../../stylesheet.css" /> +</head> +<body> +<div id="overview"><a href="../../../../../../apidocs/org/apache/commons/statistics/distribution/AbstractContinuousDistribution.html">View Javadoc</a></div><pre> +<a class="jxr_linenumber" name="L1" href="#L1">1</a> <em class="jxr_comment">/*</em> +<a class="jxr_linenumber" name="L2" href="#L2">2</a> <em class="jxr_comment"> * Licensed to the Apache Software Foundation (ASF) under one or more</em> +<a class="jxr_linenumber" name="L3" href="#L3">3</a> <em class="jxr_comment"> * contributor license agreements. See the NOTICE file distributed with</em> +<a class="jxr_linenumber" name="L4" href="#L4">4</a> <em class="jxr_comment"> * this work for additional information regarding copyright ownership.</em> +<a class="jxr_linenumber" name="L5" href="#L5">5</a> <em class="jxr_comment"> * The ASF licenses this file to You under the Apache License, Version 2.0</em> +<a class="jxr_linenumber" name="L6" href="#L6">6</a> <em class="jxr_comment"> * (the "License"); you may not use this file except in compliance with</em> +<a class="jxr_linenumber" name="L7" href="#L7">7</a> <em class="jxr_comment"> * the License. You may obtain a copy of the License at</em> +<a class="jxr_linenumber" name="L8" href="#L8">8</a> <em class="jxr_comment"> *</em> +<a class="jxr_linenumber" name="L9" href="#L9">9</a> <em class="jxr_comment"> * <a href="http://www.apache.org/licenses/LICENSE-2.0"; target="alexandria_uri">http://www.apache.org/licenses/LICENSE-2.0</a></em> +<a class="jxr_linenumber" name="L10" href="#L10">10</a> <em class="jxr_comment"> *</em> +<a class="jxr_linenumber" name="L11" href="#L11">11</a> <em class="jxr_comment"> * Unless required by applicable law or agreed to in writing, software</em> +<a class="jxr_linenumber" name="L12" href="#L12">12</a> <em class="jxr_comment"> * distributed under the License is distributed on an "AS IS" BASIS,</em> +<a class="jxr_linenumber" name="L13" href="#L13">13</a> <em class="jxr_comment"> * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.</em> +<a class="jxr_linenumber" name="L14" href="#L14">14</a> <em class="jxr_comment"> * See the License for the specific language governing permissions and</em> +<a class="jxr_linenumber" name="L15" href="#L15">15</a> <em class="jxr_comment"> * limitations under the License.</em> +<a class="jxr_linenumber" name="L16" href="#L16">16</a> <em class="jxr_comment"> */</em> +<a class="jxr_linenumber" name="L17" href="#L17">17</a> <strong class="jxr_keyword">package</strong> org.apache.commons.statistics.distribution; +<a class="jxr_linenumber" name="L18" href="#L18">18</a> +<a class="jxr_linenumber" name="L19" href="#L19">19</a> <strong class="jxr_keyword">import</strong> java.util.function.DoubleBinaryOperator; +<a class="jxr_linenumber" name="L20" href="#L20">20</a> <strong class="jxr_keyword">import</strong> java.util.function.DoubleUnaryOperator; +<a class="jxr_linenumber" name="L21" href="#L21">21</a> <strong class="jxr_keyword">import</strong> org.apache.commons.numbers.rootfinder.BrentSolver; +<a class="jxr_linenumber" name="L22" href="#L22">22</a> <strong class="jxr_keyword">import</strong> org.apache.commons.rng.UniformRandomProvider; +<a class="jxr_linenumber" name="L23" href="#L23">23</a> <strong class="jxr_keyword">import</strong> org.apache.commons.rng.sampling.distribution.InverseTransformContinuousSampler; +<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"> * Base class for probability distributions on the reals.</em> +<a class="jxr_linenumber" name="L27" href="#L27">27</a> <em class="jxr_javadoccomment"> * Default implementations are provided for some of the methods</em> +<a class="jxr_linenumber" name="L28" href="#L28">28</a> <em class="jxr_javadoccomment"> * that do not vary from distribution to distribution.</em> +<a class="jxr_linenumber" name="L29" href="#L29">29</a> <em class="jxr_javadoccomment"> *</em> +<a class="jxr_linenumber" name="L30" href="#L30">30</a> <em class="jxr_javadoccomment"> * <p>This base class provides a default factory method for creating</em> +<a class="jxr_linenumber" name="L31" href="#L31">31</a> <em class="jxr_javadoccomment"> * a {@link ContinuousDistribution.Sampler sampler instance} that uses the</em> +<a class="jxr_linenumber" name="L32" href="#L32">32</a> <em class="jxr_javadoccomment"> * <a href="<a href="https://en.wikipedia.org/wiki/Inverse_transform_sampling"; target="alexandria_uri">https://en.wikipedia.org/wiki/Inverse_transform_sampling</a>"></em> +<a class="jxr_linenumber" name="L33" href="#L33">33</a> <em class="jxr_javadoccomment"> * inversion method</a> for generating random samples that follow the</em> +<a class="jxr_linenumber" name="L34" href="#L34">34</a> <em class="jxr_javadoccomment"> * distribution.</em> +<a class="jxr_linenumber" name="L35" href="#L35">35</a> <em class="jxr_javadoccomment"> *</em> +<a class="jxr_linenumber" name="L36" href="#L36">36</a> <em class="jxr_javadoccomment"> * <p>The class provides functionality to evaluate the probability in a range</em> +<a class="jxr_linenumber" name="L37" href="#L37">37</a> <em class="jxr_javadoccomment"> * using either the cumulative probability or the survival probability.</em> +<a class="jxr_linenumber" name="L38" href="#L38">38</a> <em class="jxr_javadoccomment"> * The survival probability is used if both arguments to</em> +<a class="jxr_linenumber" name="L39" href="#L39">39</a> <em class="jxr_javadoccomment"> * {@link #probability(double, double)} are above the median.</em> +<a class="jxr_linenumber" name="L40" href="#L40">40</a> <em class="jxr_javadoccomment"> * Child classes with a known median can override the default {@link #getMedian()}</em> +<a class="jxr_linenumber" name="L41" href="#L41">41</a> <em class="jxr_javadoccomment"> * method.</em> +<a class="jxr_linenumber" name="L42" href="#L42">42</a> <em class="jxr_javadoccomment"> */</em> +<a class="jxr_linenumber" name="L43" href="#L43">43</a> <strong class="jxr_keyword">abstract</strong> <strong class="jxr_keyword">class</strong> <a name="AbstractContinuousDistribution" href="../../../../../org/apache/commons/statistics/distribution/AbstractContinuousDistribution.html#AbstractContinuousDistribution">AbstractContinuousDistribution</a> +<a class="jxr_linenumber" name="L44" href="#L44">44</a> <strong class="jxr_keyword">implements</strong> <a name="ContinuousDistribution" href="../../../../../org/apache/commons/statistics/distribution/ContinuousDistribution.html#ContinuousDistribution">ContinuousDistribution</a> { +<a class="jxr_linenumber" name="L45" href="#L45">45</a> +<a class="jxr_linenumber" name="L46" href="#L46">46</a> <em class="jxr_comment">// Notes on the inverse probability implementation:</em> +<a class="jxr_linenumber" name="L47" href="#L47">47</a> <em class="jxr_comment">//</em> +<a class="jxr_linenumber" name="L48" href="#L48">48</a> <em class="jxr_comment">// The Brent solver does not allow a stopping criteria for the proximity</em> +<a class="jxr_linenumber" name="L49" href="#L49">49</a> <em class="jxr_comment">// to the root; it uses equality to zero within 1 ULP. The search is</em> +<a class="jxr_linenumber" name="L50" href="#L50">50</a> <em class="jxr_comment">// iterated until there is a small difference between the upper</em> +<a class="jxr_linenumber" name="L51" href="#L51">51</a> <em class="jxr_comment">// and lower bracket of the root, expressed as a combination of relative</em> +<a class="jxr_linenumber" name="L52" href="#L52">52</a> <em class="jxr_comment">// and absolute thresholds.</em> +<a class="jxr_linenumber" name="L53" href="#L53">53</a> +<a class="jxr_linenumber" name="L54" href="#L54">54</a> <em class="jxr_javadoccomment">/** BrentSolver relative accuracy.</em> +<a class="jxr_linenumber" name="L55" href="#L55">55</a> <em class="jxr_javadoccomment"> * This is used with {@code tol = 2 * relEps * abs(b) + absEps} so the minimum</em> +<a class="jxr_linenumber" name="L56" href="#L56">56</a> <em class="jxr_javadoccomment"> * non-zero value with an effect is half of machine epsilon (2^-53). */</em> +<a class="jxr_linenumber" name="L57" href="#L57">57</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> SOLVER_RELATIVE_ACCURACY = 0x1.0p-53; +<a class="jxr_linenumber" name="L58" href="#L58">58</a> <em class="jxr_javadoccomment">/** BrentSolver absolute accuracy.</em> +<a class="jxr_linenumber" name="L59" href="#L59">59</a> <em class="jxr_javadoccomment"> * This is used with {@code tol = 2 * relEps * abs(b) + absEps} so set to MIN_VALUE</em> +<a class="jxr_linenumber" name="L60" href="#L60">60</a> <em class="jxr_javadoccomment"> * so that when the relative epsilon has no effect (as b is too small) the tolerance</em> +<a class="jxr_linenumber" name="L61" href="#L61">61</a> <em class="jxr_javadoccomment"> * is at least 1 ULP for sub-normal numbers. */</em> +<a class="jxr_linenumber" name="L62" href="#L62">62</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> SOLVER_ABSOLUTE_ACCURACY = Double.MIN_VALUE; +<a class="jxr_linenumber" name="L63" href="#L63">63</a> <em class="jxr_javadoccomment">/** BrentSolver function value accuracy.</em> +<a class="jxr_linenumber" name="L64" href="#L64">64</a> <em class="jxr_javadoccomment"> * Determines if the Brent solver performs a search. It is not used during the search.</em> +<a class="jxr_linenumber" name="L65" href="#L65">65</a> <em class="jxr_javadoccomment"> * Set to a very low value to search using Brent's method unless</em> +<a class="jxr_linenumber" name="L66" href="#L66">66</a> <em class="jxr_javadoccomment"> * the starting point is correct, or within 1 ULP for sub-normal probabilities. */</em> +<a class="jxr_linenumber" name="L67" href="#L67">67</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> SOLVER_FUNCTION_VALUE_ACCURACY = Double.MIN_VALUE; +<a class="jxr_linenumber" name="L68" href="#L68">68</a> +<a class="jxr_linenumber" name="L69" href="#L69">69</a> <em class="jxr_javadoccomment">/** Cached value of the median. */</em> +<a class="jxr_linenumber" name="L70" href="#L70">70</a> <strong class="jxr_keyword">private</strong> <strong class="jxr_keyword">double</strong> median = Double.NaN; +<a class="jxr_linenumber" name="L71" href="#L71">71</a> +<a class="jxr_linenumber" name="L72" href="#L72">72</a> <em class="jxr_javadoccomment">/**</em> +<a class="jxr_linenumber" name="L73" href="#L73">73</a> <em class="jxr_javadoccomment"> * Gets the median. This is used to determine if the arguments to the</em> +<a class="jxr_linenumber" name="L74" href="#L74">74</a> <em class="jxr_javadoccomment"> * {@link #probability(double, double)} function are in the upper or lower domain.</em> +<a class="jxr_linenumber" name="L75" href="#L75">75</a> <em class="jxr_javadoccomment"> *</em> +<a class="jxr_linenumber" name="L76" href="#L76">76</a> <em class="jxr_javadoccomment"> * <p>The default implementation calls {@link #inverseCumulativeProbability(double)}</em> +<a class="jxr_linenumber" name="L77" href="#L77">77</a> <em class="jxr_javadoccomment"> * with a value of 0.5.</em> +<a class="jxr_linenumber" name="L78" href="#L78">78</a> <em class="jxr_javadoccomment"> *</em> +<a class="jxr_linenumber" name="L79" href="#L79">79</a> <em class="jxr_javadoccomment"> * @return the median</em> +<a class="jxr_linenumber" name="L80" href="#L80">80</a> <em class="jxr_javadoccomment"> */</em> +<a class="jxr_linenumber" name="L81" href="#L81">81</a> <strong class="jxr_keyword">double</strong> getMedian() { +<a class="jxr_linenumber" name="L82" href="#L82">82</a> <strong class="jxr_keyword">double</strong> m = median; +<a class="jxr_linenumber" name="L83" href="#L83">83</a> <strong class="jxr_keyword">if</strong> (Double.isNaN(m)) { +<a class="jxr_linenumber" name="L84" href="#L84">84</a> median = m = inverseCumulativeProbability(0.5); +<a class="jxr_linenumber" name="L85" href="#L85">85</a> } +<a class="jxr_linenumber" name="L86" href="#L86">86</a> <strong class="jxr_keyword">return</strong> m; +<a class="jxr_linenumber" name="L87" href="#L87">87</a> } +<a class="jxr_linenumber" name="L88" href="#L88">88</a> +<a class="jxr_linenumber" name="L89" href="#L89">89</a> <em class="jxr_javadoccomment">/** {@inheritDoc} */</em> +<a class="jxr_linenumber" name="L90" href="#L90">90</a> @Override +<a class="jxr_linenumber" name="L91" href="#L91">91</a> <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">double</strong> probability(<strong class="jxr_keyword">double</strong> x0, +<a class="jxr_linenumber" name="L92" href="#L92">92</a> <strong class="jxr_keyword">double</strong> x1) { +<a class="jxr_linenumber" name="L93" href="#L93">93</a> <strong class="jxr_keyword">if</strong> (x0 > x1) { +<a class="jxr_linenumber" name="L94" href="#L94">94</a> <strong class="jxr_keyword">throw</strong> <strong class="jxr_keyword">new</strong> <a name="DistributionException" href="../../../../../org/apache/commons/statistics/distribution/DistributionException.html#DistributionException">DistributionException</a>(DistributionException.INVALID_RANGE_LOW_GT_HIGH, x0, x1); +<a class="jxr_linenumber" name="L95" href="#L95">95</a> } +<a class="jxr_linenumber" name="L96" href="#L96">96</a> <em class="jxr_comment">// Use the survival probability when in the upper domain [3]:</em> +<a class="jxr_linenumber" name="L97" href="#L97">97</a> <em class="jxr_comment">//</em> +<a class="jxr_linenumber" name="L98" href="#L98">98</a> <em class="jxr_comment">// lower median upper</em> +<a class="jxr_linenumber" name="L99" href="#L99">99</a> <em class="jxr_comment">// | | |</em> +<a class="jxr_linenumber" name="L100" href="#L100">100</a> <em class="jxr_comment">// 1. |------|</em> +<a class="jxr_linenumber" name="L101" href="#L101">101</a> <em class="jxr_comment">// x0 x1</em> +<a class="jxr_linenumber" name="L102" href="#L102">102</a> <em class="jxr_comment">// 2. |----------|</em> +<a class="jxr_linenumber" name="L103" href="#L103">103</a> <em class="jxr_comment">// x0 x1</em> +<a class="jxr_linenumber" name="L104" href="#L104">104</a> <em class="jxr_comment">// 3. |--------|</em> +<a class="jxr_linenumber" name="L105" href="#L105">105</a> <em class="jxr_comment">// x0 x1</em> +<a class="jxr_linenumber" name="L106" href="#L106">106</a> +<a class="jxr_linenumber" name="L107" href="#L107">107</a> <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> m = getMedian(); +<a class="jxr_linenumber" name="L108" href="#L108">108</a> <strong class="jxr_keyword">if</strong> (x0 >= m) { +<a class="jxr_linenumber" name="L109" href="#L109">109</a> <strong class="jxr_keyword">return</strong> survivalProbability(x0) - survivalProbability(x1); +<a class="jxr_linenumber" name="L110" href="#L110">110</a> } +<a class="jxr_linenumber" name="L111" href="#L111">111</a> <strong class="jxr_keyword">return</strong> cumulativeProbability(x1) - cumulativeProbability(x0); +<a class="jxr_linenumber" name="L112" href="#L112">112</a> } +<a class="jxr_linenumber" name="L113" href="#L113">113</a> +<a class="jxr_linenumber" name="L114" href="#L114">114</a> <em class="jxr_javadoccomment">/**</em> +<a class="jxr_linenumber" name="L115" href="#L115">115</a> <em class="jxr_javadoccomment"> * {@inheritDoc}</em> +<a class="jxr_linenumber" name="L116" href="#L116">116</a> <em class="jxr_javadoccomment"> *</em> +<a class="jxr_linenumber" name="L117" href="#L117">117</a> <em class="jxr_javadoccomment"> * <p>The default implementation returns:</em> +<a class="jxr_linenumber" name="L118" href="#L118">118</a> <em class="jxr_javadoccomment"> * <ul></em> +<a class="jxr_linenumber" name="L119" href="#L119">119</a> <em class="jxr_javadoccomment"> * <li>{@link #getSupportLowerBound()} for {@code p = 0},</li></em> +<a class="jxr_linenumber" name="L120" href="#L120">120</a> <em class="jxr_javadoccomment"> * <li>{@link #getSupportUpperBound()} for {@code p = 1}, or</li></em> +<a class="jxr_linenumber" name="L121" href="#L121">121</a> <em class="jxr_javadoccomment"> * <li>the result of a search for a root between the lower and upper bound using</em> +<a class="jxr_linenumber" name="L122" href="#L122">122</a> <em class="jxr_javadoccomment"> * {@link #cumulativeProbability(double) cumulativeProbability(x) - p}.</em> +<a class="jxr_linenumber" name="L123" href="#L123">123</a> <em class="jxr_javadoccomment"> * The bounds may be bracketed for efficiency.</li></em> +<a class="jxr_linenumber" name="L124" href="#L124">124</a> <em class="jxr_javadoccomment"> * </ul></em> +<a class="jxr_linenumber" name="L125" href="#L125">125</a> <em class="jxr_javadoccomment"> *</em> +<a class="jxr_linenumber" name="L126" href="#L126">126</a> <em class="jxr_javadoccomment"> * @throws IllegalArgumentException if {@code p < 0} or {@code p > 1}</em> +<a class="jxr_linenumber" name="L127" href="#L127">127</a> <em class="jxr_javadoccomment"> */</em> +<a class="jxr_linenumber" name="L128" href="#L128">128</a> @Override +<a class="jxr_linenumber" name="L129" href="#L129">129</a> <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">double</strong> inverseCumulativeProbability(<strong class="jxr_keyword">double</strong> p) { +<a class="jxr_linenumber" name="L130" href="#L130">130</a> ArgumentUtils.checkProbability(p); +<a class="jxr_linenumber" name="L131" href="#L131">131</a> <strong class="jxr_keyword">return</strong> inverseProbability(p, 1 - p, false); +<a class="jxr_linenumber" name="L132" href="#L132">132</a> } +<a class="jxr_linenumber" name="L133" href="#L133">133</a> +<a class="jxr_linenumber" name="L134" href="#L134">134</a> <em class="jxr_javadoccomment">/**</em> +<a class="jxr_linenumber" name="L135" href="#L135">135</a> <em class="jxr_javadoccomment"> * {@inheritDoc}</em> +<a class="jxr_linenumber" name="L136" href="#L136">136</a> <em class="jxr_javadoccomment"> *</em> +<a class="jxr_linenumber" name="L137" href="#L137">137</a> <em class="jxr_javadoccomment"> * <p>The default implementation returns:</em> +<a class="jxr_linenumber" name="L138" href="#L138">138</a> <em class="jxr_javadoccomment"> * <ul></em> +<a class="jxr_linenumber" name="L139" href="#L139">139</a> <em class="jxr_javadoccomment"> * <li>{@link #getSupportLowerBound()} for {@code p = 1},</li></em> +<a class="jxr_linenumber" name="L140" href="#L140">140</a> <em class="jxr_javadoccomment"> * <li>{@link #getSupportUpperBound()} for {@code p = 0}, or</li></em> +<a class="jxr_linenumber" name="L141" href="#L141">141</a> <em class="jxr_javadoccomment"> * <li>the result of a search for a root between the lower and upper bound using</em> +<a class="jxr_linenumber" name="L142" href="#L142">142</a> <em class="jxr_javadoccomment"> * {@link #survivalProbability(double) survivalProbability(x) - p}.</em> +<a class="jxr_linenumber" name="L143" href="#L143">143</a> <em class="jxr_javadoccomment"> * The bounds may be bracketed for efficiency.</li></em> +<a class="jxr_linenumber" name="L144" href="#L144">144</a> <em class="jxr_javadoccomment"> * </ul></em> +<a class="jxr_linenumber" name="L145" href="#L145">145</a> <em class="jxr_javadoccomment"> *</em> +<a class="jxr_linenumber" name="L146" href="#L146">146</a> <em class="jxr_javadoccomment"> * @throws IllegalArgumentException if {@code p < 0} or {@code p > 1}</em> +<a class="jxr_linenumber" name="L147" href="#L147">147</a> <em class="jxr_javadoccomment"> */</em> +<a class="jxr_linenumber" name="L148" href="#L148">148</a> @Override +<a class="jxr_linenumber" name="L149" href="#L149">149</a> <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">double</strong> inverseSurvivalProbability(<strong class="jxr_keyword">double</strong> p) { +<a class="jxr_linenumber" name="L150" href="#L150">150</a> ArgumentUtils.checkProbability(p); +<a class="jxr_linenumber" name="L151" href="#L151">151</a> <strong class="jxr_keyword">return</strong> inverseProbability(1 - p, p, <strong class="jxr_keyword">true</strong>); +<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"> * Implementation for the inverse cumulative or survival probability.</em> +<a class="jxr_linenumber" name="L156" href="#L156">156</a> <em class="jxr_javadoccomment"> *</em> +<a class="jxr_linenumber" name="L157" href="#L157">157</a> <em class="jxr_javadoccomment"> * @param p Cumulative probability.</em> +<a class="jxr_linenumber" name="L158" href="#L158">158</a> <em class="jxr_javadoccomment"> * @param q Survival probability.</em> +<a class="jxr_linenumber" name="L159" href="#L159">159</a> <em class="jxr_javadoccomment"> * @param complement Set to true to compute the inverse survival probability</em> +<a class="jxr_linenumber" name="L160" href="#L160">160</a> <em class="jxr_javadoccomment"> * @return the value</em> +<a class="jxr_linenumber" name="L161" href="#L161">161</a> <em class="jxr_javadoccomment"> */</em> +<a class="jxr_linenumber" name="L162" href="#L162">162</a> <strong class="jxr_keyword">private</strong> <strong class="jxr_keyword">double</strong> inverseProbability(<strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> p, <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> q, <strong class="jxr_keyword">boolean</strong> complement) { +<a class="jxr_linenumber" name="L163" href="#L163">163</a> <em class="jxr_comment">/* IMPLEMENTATION NOTES</em> +<a class="jxr_linenumber" name="L164" href="#L164">164</a> <em class="jxr_comment"> * --------------------</em> +<a class="jxr_linenumber" name="L165" href="#L165">165</a> <em class="jxr_comment"> * Where applicable, use is made of the one-sided Chebyshev inequality</em> +<a class="jxr_linenumber" name="L166" href="#L166">166</a> <em class="jxr_comment"> * to bracket the root. This inequality states that</em> +<a class="jxr_linenumber" name="L167" href="#L167">167</a> <em class="jxr_comment"> * P(X - mu >= k * sig) <= 1 / (1 + k^2),</em> +<a class="jxr_linenumber" name="L168" href="#L168">168</a> <em class="jxr_comment"> * mu: mean, sig: standard deviation. Equivalently</em> +<a class="jxr_linenumber" name="L169" href="#L169">169</a> <em class="jxr_comment"> * 1 - P(X < mu + k * sig) <= 1 / (1 + k^2),</em> +<a class="jxr_linenumber" name="L170" href="#L170">170</a> <em class="jxr_comment"> * F(mu + k * sig) >= k^2 / (1 + k^2).</em> +<a class="jxr_linenumber" name="L171" href="#L171">171</a> <em class="jxr_comment"> *</em> +<a class="jxr_linenumber" name="L172" href="#L172">172</a> <em class="jxr_comment"> * For k = sqrt(p / (1 - p)), we find</em> +<a class="jxr_linenumber" name="L173" href="#L173">173</a> <em class="jxr_comment"> * F(mu + k * sig) >= p,</em> +<a class="jxr_linenumber" name="L174" href="#L174">174</a> <em class="jxr_comment"> * and (mu + k * sig) is an upper-bound for the root.</em> +<a class="jxr_linenumber" name="L175" href="#L175">175</a> <em class="jxr_comment"> *</em> +<a class="jxr_linenumber" name="L176" href="#L176">176</a> <em class="jxr_comment"> * Then, introducing Y = -X, mean(Y) = -mu, sd(Y) = sig, and</em> +<a class="jxr_linenumber" name="L177" href="#L177">177</a> <em class="jxr_comment"> * P(Y >= -mu + k * sig) <= 1 / (1 + k^2),</em> +<a class="jxr_linenumber" name="L178" href="#L178">178</a> <em class="jxr_comment"> * P(-X >= -mu + k * sig) <= 1 / (1 + k^2),</em> +<a class="jxr_linenumber" name="L179" href="#L179">179</a> <em class="jxr_comment"> * P(X <= mu - k * sig) <= 1 / (1 + k^2),</em> +<a class="jxr_linenumber" name="L180" href="#L180">180</a> <em class="jxr_comment"> * F(mu - k * sig) <= 1 / (1 + k^2).</em> +<a class="jxr_linenumber" name="L181" href="#L181">181</a> <em class="jxr_comment"> *</em> +<a class="jxr_linenumber" name="L182" href="#L182">182</a> <em class="jxr_comment"> * For k = sqrt((1 - p) / p), we find</em> +<a class="jxr_linenumber" name="L183" href="#L183">183</a> <em class="jxr_comment"> * F(mu - k * sig) <= p,</em> +<a class="jxr_linenumber" name="L184" href="#L184">184</a> <em class="jxr_comment"> * and (mu - k * sig) is a lower-bound for the root.</em> +<a class="jxr_linenumber" name="L185" href="#L185">185</a> <em class="jxr_comment"> *</em> +<a class="jxr_linenumber" name="L186" href="#L186">186</a> <em class="jxr_comment"> * In cases where the Chebyshev inequality does not apply, geometric</em> +<a class="jxr_linenumber" name="L187" href="#L187">187</a> <em class="jxr_comment"> * progressions 1, 2, 4, ... and -1, -2, -4, ... are used to bracket</em> +<a class="jxr_linenumber" name="L188" href="#L188">188</a> <em class="jxr_comment"> * the root.</em> +<a class="jxr_linenumber" name="L189" href="#L189">189</a> <em class="jxr_comment"> *</em> +<a class="jxr_linenumber" name="L190" href="#L190">190</a> <em class="jxr_comment"> * In the case of the survival probability the bracket can be set using the same</em> +<a class="jxr_linenumber" name="L191" href="#L191">191</a> <em class="jxr_comment"> * bound given that the argument p = 1 - q, with q the survival probability.</em> +<a class="jxr_linenumber" name="L192" href="#L192">192</a> <em class="jxr_comment"> */</em> +<a class="jxr_linenumber" name="L193" href="#L193">193</a> +<a class="jxr_linenumber" name="L194" href="#L194">194</a> <strong class="jxr_keyword">double</strong> lowerBound = getSupportLowerBound(); +<a class="jxr_linenumber" name="L195" href="#L195">195</a> <strong class="jxr_keyword">if</strong> (p == 0) { +<a class="jxr_linenumber" name="L196" href="#L196">196</a> <strong class="jxr_keyword">return</strong> lowerBound; +<a class="jxr_linenumber" name="L197" href="#L197">197</a> } +<a class="jxr_linenumber" name="L198" href="#L198">198</a> <strong class="jxr_keyword">double</strong> upperBound = getSupportUpperBound(); +<a class="jxr_linenumber" name="L199" href="#L199">199</a> <strong class="jxr_keyword">if</strong> (q == 0) { +<a class="jxr_linenumber" name="L200" href="#L200">200</a> <strong class="jxr_keyword">return</strong> upperBound; +<a class="jxr_linenumber" name="L201" href="#L201">201</a> } +<a class="jxr_linenumber" name="L202" href="#L202">202</a> +<a class="jxr_linenumber" name="L203" href="#L203">203</a> <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> mu = getMean(); +<a class="jxr_linenumber" name="L204" href="#L204">204</a> <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> sig = Math.sqrt(getVariance()); +<a class="jxr_linenumber" name="L205" href="#L205">205</a> <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">boolean</strong> chebyshevApplies = Double.isFinite(mu) && +<a class="jxr_linenumber" name="L206" href="#L206">206</a> ArgumentUtils.isFiniteStrictlyPositive(sig); +<a class="jxr_linenumber" name="L207" href="#L207">207</a> +<a class="jxr_linenumber" name="L208" href="#L208">208</a> <strong class="jxr_keyword">if</strong> (lowerBound == Double.NEGATIVE_INFINITY) { +<a class="jxr_linenumber" name="L209" href="#L209">209</a> lowerBound = createFiniteLowerBound(p, q, complement, upperBound, mu, sig, chebyshevApplies); +<a class="jxr_linenumber" name="L210" href="#L210">210</a> } +<a class="jxr_linenumber" name="L211" href="#L211">211</a> +<a class="jxr_linenumber" name="L212" href="#L212">212</a> <strong class="jxr_keyword">if</strong> (upperBound == Double.POSITIVE_INFINITY) { +<a class="jxr_linenumber" name="L213" href="#L213">213</a> upperBound = createFiniteUpperBound(p, q, complement, lowerBound, mu, sig, chebyshevApplies); +<a class="jxr_linenumber" name="L214" href="#L214">214</a> } +<a class="jxr_linenumber" name="L215" href="#L215">215</a> +<a class="jxr_linenumber" name="L216" href="#L216">216</a> <em class="jxr_comment">// Here the bracket [lower, upper] uses finite values. If the support</em> +<a class="jxr_linenumber" name="L217" href="#L217">217</a> <em class="jxr_comment">// is infinite the bracket can truncate the distribution and the target</em> +<a class="jxr_linenumber" name="L218" href="#L218">218</a> <em class="jxr_comment">// probability can be outside the range of [lower, upper].</em> +<a class="jxr_linenumber" name="L219" href="#L219">219</a> <strong class="jxr_keyword">if</strong> (upperBound == Double.MAX_VALUE) { +<a class="jxr_linenumber" name="L220" href="#L220">220</a> <strong class="jxr_keyword">if</strong> (complement) { +<a class="jxr_linenumber" name="L221" href="#L221">221</a> <strong class="jxr_keyword">if</strong> (survivalProbability(upperBound) > q) { +<a class="jxr_linenumber" name="L222" href="#L222">222</a> <strong class="jxr_keyword">return</strong> getSupportUpperBound(); +<a class="jxr_linenumber" name="L223" href="#L223">223</a> } +<a class="jxr_linenumber" name="L224" href="#L224">224</a> } <strong class="jxr_keyword">else</strong> <strong class="jxr_keyword">if</strong> (cumulativeProbability(upperBound) < p) { +<a class="jxr_linenumber" name="L225" href="#L225">225</a> <strong class="jxr_keyword">return</strong> getSupportUpperBound(); +<a class="jxr_linenumber" name="L226" href="#L226">226</a> } +<a class="jxr_linenumber" name="L227" href="#L227">227</a> } +<a class="jxr_linenumber" name="L228" href="#L228">228</a> <strong class="jxr_keyword">if</strong> (lowerBound == -Double.MAX_VALUE) { +<a class="jxr_linenumber" name="L229" href="#L229">229</a> <strong class="jxr_keyword">if</strong> (complement) { +<a class="jxr_linenumber" name="L230" href="#L230">230</a> <strong class="jxr_keyword">if</strong> (survivalProbability(lowerBound) < q) { +<a class="jxr_linenumber" name="L231" href="#L231">231</a> <strong class="jxr_keyword">return</strong> getSupportLowerBound(); +<a class="jxr_linenumber" name="L232" href="#L232">232</a> } +<a class="jxr_linenumber" name="L233" href="#L233">233</a> } <strong class="jxr_keyword">else</strong> <strong class="jxr_keyword">if</strong> (cumulativeProbability(lowerBound) > p) { +<a class="jxr_linenumber" name="L234" href="#L234">234</a> <strong class="jxr_keyword">return</strong> getSupportLowerBound(); +<a class="jxr_linenumber" name="L235" href="#L235">235</a> } +<a class="jxr_linenumber" name="L236" href="#L236">236</a> } +<a class="jxr_linenumber" name="L237" href="#L237">237</a> +<a class="jxr_linenumber" name="L238" href="#L238">238</a> <strong class="jxr_keyword">final</strong> DoubleUnaryOperator fun = complement ? +<a class="jxr_linenumber" name="L239" href="#L239">239</a> arg -> survivalProbability(arg) - q : +<a class="jxr_linenumber" name="L240" href="#L240">240</a> arg -> cumulativeProbability(arg) - p; +<a class="jxr_linenumber" name="L241" href="#L241">241</a> <em class="jxr_comment">// Note the initial value is robust to overflow.</em> +<a class="jxr_linenumber" name="L242" href="#L242">242</a> <em class="jxr_comment">// Do not use 0.5 * (lowerBound + upperBound).</em> +<a class="jxr_linenumber" name="L243" href="#L243">243</a> <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> x = <strong class="jxr_keyword">new</strong> BrentSolver(SOLVER_RELATIVE_ACCURACY, +<a class="jxr_linenumber" name="L244" href="#L244">244</a> SOLVER_ABSOLUTE_ACCURACY, +<a class="jxr_linenumber" name="L245" href="#L245">245</a> SOLVER_FUNCTION_VALUE_ACCURACY) +<a class="jxr_linenumber" name="L246" href="#L246">246</a> .findRoot(fun, +<a class="jxr_linenumber" name="L247" href="#L247">247</a> lowerBound, +<a class="jxr_linenumber" name="L248" href="#L248">248</a> lowerBound + 0.5 * (upperBound - lowerBound), +<a class="jxr_linenumber" name="L249" href="#L249">249</a> upperBound); +<a class="jxr_linenumber" name="L250" href="#L250">250</a> +<a class="jxr_linenumber" name="L251" href="#L251">251</a> <strong class="jxr_keyword">if</strong> (!isSupportConnected()) { +<a class="jxr_linenumber" name="L252" href="#L252">252</a> <strong class="jxr_keyword">return</strong> searchPlateau(complement, lowerBound, x); +<a class="jxr_linenumber" name="L253" href="#L253">253</a> } +<a class="jxr_linenumber" name="L254" href="#L254">254</a> <strong class="jxr_keyword">return</strong> x; +<a class="jxr_linenumber" name="L255" href="#L255">255</a> } +<a class="jxr_linenumber" name="L256" href="#L256">256</a> +<a class="jxr_linenumber" name="L257" href="#L257">257</a> <em class="jxr_javadoccomment">/**</em> +<a class="jxr_linenumber" name="L258" href="#L258">258</a> <em class="jxr_javadoccomment"> * Create a finite lower bound. Assumes the current lower bound is negative infinity.</em> +<a class="jxr_linenumber" name="L259" href="#L259">259</a> <em class="jxr_javadoccomment"> *</em> +<a class="jxr_linenumber" name="L260" href="#L260">260</a> <em class="jxr_javadoccomment"> * @param p Cumulative probability.</em> +<a class="jxr_linenumber" name="L261" href="#L261">261</a> <em class="jxr_javadoccomment"> * @param q Survival probability.</em> +<a class="jxr_linenumber" name="L262" href="#L262">262</a> <em class="jxr_javadoccomment"> * @param complement Set to true to compute the inverse survival probability</em> +<a class="jxr_linenumber" name="L263" href="#L263">263</a> <em class="jxr_javadoccomment"> * @param upperBound Current upper bound</em> +<a class="jxr_linenumber" name="L264" href="#L264">264</a> <em class="jxr_javadoccomment"> * @param mu Mean</em> +<a class="jxr_linenumber" name="L265" href="#L265">265</a> <em class="jxr_javadoccomment"> * @param sig Standard deviation</em> +<a class="jxr_linenumber" name="L266" href="#L266">266</a> <em class="jxr_javadoccomment"> * @param chebyshevApplies True if the Chebyshev inequality applies (mean is finite and {@code sig > 0}}</em> +<a class="jxr_linenumber" name="L267" href="#L267">267</a> <em class="jxr_javadoccomment"> * @return the finite lower bound</em> +<a class="jxr_linenumber" name="L268" href="#L268">268</a> <em class="jxr_javadoccomment"> */</em> +<a class="jxr_linenumber" name="L269" href="#L269">269</a> <strong class="jxr_keyword">private</strong> <strong class="jxr_keyword">double</strong> createFiniteLowerBound(<strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> p, <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> q, <strong class="jxr_keyword">boolean</strong> complement, +<a class="jxr_linenumber" name="L270" href="#L270">270</a> <strong class="jxr_keyword">double</strong> upperBound, <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> mu, <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> sig, <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">boolean</strong> chebyshevApplies) { +<a class="jxr_linenumber" name="L271" href="#L271">271</a> <strong class="jxr_keyword">double</strong> lowerBound; +<a class="jxr_linenumber" name="L272" href="#L272">272</a> <strong class="jxr_keyword">if</strong> (chebyshevApplies) { +<a class="jxr_linenumber" name="L273" href="#L273">273</a> lowerBound = mu - sig * Math.sqrt(q / p); +<a class="jxr_linenumber" name="L274" href="#L274">274</a> } <strong class="jxr_keyword">else</strong> { +<a class="jxr_linenumber" name="L275" href="#L275">275</a> lowerBound = Double.NEGATIVE_INFINITY; +<a class="jxr_linenumber" name="L276" href="#L276">276</a> } +<a class="jxr_linenumber" name="L277" href="#L277">277</a> <em class="jxr_comment">// Bound may have been set as infinite</em> +<a class="jxr_linenumber" name="L278" href="#L278">278</a> <strong class="jxr_keyword">if</strong> (lowerBound == Double.NEGATIVE_INFINITY) { +<a class="jxr_linenumber" name="L279" href="#L279">279</a> lowerBound = Math.min(-1, upperBound); +<a class="jxr_linenumber" name="L280" href="#L280">280</a> <strong class="jxr_keyword">if</strong> (complement) { +<a class="jxr_linenumber" name="L281" href="#L281">281</a> <strong class="jxr_keyword">while</strong> (survivalProbability(lowerBound) < q) { +<a class="jxr_linenumber" name="L282" href="#L282">282</a> lowerBound *= 2; +<a class="jxr_linenumber" name="L283" href="#L283">283</a> } +<a class="jxr_linenumber" name="L284" href="#L284">284</a> } <strong class="jxr_keyword">else</strong> { +<a class="jxr_linenumber" name="L285" href="#L285">285</a> <strong class="jxr_keyword">while</strong> (cumulativeProbability(lowerBound) >= p) { +<a class="jxr_linenumber" name="L286" href="#L286">286</a> lowerBound *= 2; +<a class="jxr_linenumber" name="L287" href="#L287">287</a> } +<a class="jxr_linenumber" name="L288" href="#L288">288</a> } +<a class="jxr_linenumber" name="L289" href="#L289">289</a> <em class="jxr_comment">// Ensure finite</em> +<a class="jxr_linenumber" name="L290" href="#L290">290</a> lowerBound = Math.max(lowerBound, -Double.MAX_VALUE); +<a class="jxr_linenumber" name="L291" href="#L291">291</a> } +<a class="jxr_linenumber" name="L292" href="#L292">292</a> <strong class="jxr_keyword">return</strong> lowerBound; +<a class="jxr_linenumber" name="L293" href="#L293">293</a> } +<a class="jxr_linenumber" name="L294" href="#L294">294</a> +<a class="jxr_linenumber" name="L295" href="#L295">295</a> <em class="jxr_javadoccomment">/**</em> +<a class="jxr_linenumber" name="L296" href="#L296">296</a> <em class="jxr_javadoccomment"> * Create a finite upper bound. Assumes the current upper bound is positive infinity.</em> +<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"> * @param p Cumulative probability.</em> +<a class="jxr_linenumber" name="L299" href="#L299">299</a> <em class="jxr_javadoccomment"> * @param q Survival probability.</em> +<a class="jxr_linenumber" name="L300" href="#L300">300</a> <em class="jxr_javadoccomment"> * @param complement Set to true to compute the inverse survival probability</em> +<a class="jxr_linenumber" name="L301" href="#L301">301</a> <em class="jxr_javadoccomment"> * @param lowerBound Current lower bound</em> +<a class="jxr_linenumber" name="L302" href="#L302">302</a> <em class="jxr_javadoccomment"> * @param mu Mean</em> +<a class="jxr_linenumber" name="L303" href="#L303">303</a> <em class="jxr_javadoccomment"> * @param sig Standard deviation</em> +<a class="jxr_linenumber" name="L304" href="#L304">304</a> <em class="jxr_javadoccomment"> * @param chebyshevApplies True if the Chebyshev inequality applies (mean is finite and {@code sig > 0}}</em> +<a class="jxr_linenumber" name="L305" href="#L305">305</a> <em class="jxr_javadoccomment"> * @return the finite lower bound</em> +<a class="jxr_linenumber" name="L306" href="#L306">306</a> <em class="jxr_javadoccomment"> */</em> +<a class="jxr_linenumber" name="L307" href="#L307">307</a> <strong class="jxr_keyword">private</strong> <strong class="jxr_keyword">double</strong> createFiniteUpperBound(<strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> p, <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> q, <strong class="jxr_keyword">boolean</strong> complement, +<a class="jxr_linenumber" name="L308" href="#L308">308</a> <strong class="jxr_keyword">double</strong> lowerBound, <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> mu, <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> sig, <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">boolean</strong> chebyshevApplies) { +<a class="jxr_linenumber" name="L309" href="#L309">309</a> <strong class="jxr_keyword">double</strong> upperBound; +<a class="jxr_linenumber" name="L310" href="#L310">310</a> <strong class="jxr_keyword">if</strong> (chebyshevApplies) { +<a class="jxr_linenumber" name="L311" href="#L311">311</a> upperBound = mu + sig * Math.sqrt(p / q); +<a class="jxr_linenumber" name="L312" href="#L312">312</a> } <strong class="jxr_keyword">else</strong> { +<a class="jxr_linenumber" name="L313" href="#L313">313</a> upperBound = Double.POSITIVE_INFINITY; +<a class="jxr_linenumber" name="L314" href="#L314">314</a> } +<a class="jxr_linenumber" name="L315" href="#L315">315</a> <em class="jxr_comment">// Bound may have been set as infinite</em> +<a class="jxr_linenumber" name="L316" href="#L316">316</a> <strong class="jxr_keyword">if</strong> (upperBound == Double.POSITIVE_INFINITY) { +<a class="jxr_linenumber" name="L317" href="#L317">317</a> upperBound = Math.max(1, lowerBound); +<a class="jxr_linenumber" name="L318" href="#L318">318</a> <strong class="jxr_keyword">if</strong> (complement) { +<a class="jxr_linenumber" name="L319" href="#L319">319</a> <strong class="jxr_keyword">while</strong> (survivalProbability(upperBound) >= q) { +<a class="jxr_linenumber" name="L320" href="#L320">320</a> upperBound *= 2; +<a class="jxr_linenumber" name="L321" href="#L321">321</a> } +<a class="jxr_linenumber" name="L322" href="#L322">322</a> } <strong class="jxr_keyword">else</strong> { +<a class="jxr_linenumber" name="L323" href="#L323">323</a> <strong class="jxr_keyword">while</strong> (cumulativeProbability(upperBound) < p) { +<a class="jxr_linenumber" name="L324" href="#L324">324</a> upperBound *= 2; +<a class="jxr_linenumber" name="L325" href="#L325">325</a> } +<a class="jxr_linenumber" name="L326" href="#L326">326</a> } +<a class="jxr_linenumber" name="L327" href="#L327">327</a> <em class="jxr_comment">// Ensure finite</em> +<a class="jxr_linenumber" name="L328" href="#L328">328</a> upperBound = Math.min(upperBound, Double.MAX_VALUE); +<a class="jxr_linenumber" name="L329" href="#L329">329</a> } +<a class="jxr_linenumber" name="L330" href="#L330">330</a> <strong class="jxr_keyword">return</strong> upperBound; +<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> <em class="jxr_javadoccomment">/**</em> +<a class="jxr_linenumber" name="L334" href="#L334">334</a> <em class="jxr_javadoccomment"> * Indicates whether the support is connected, i.e. whether all values between the</em> +<a class="jxr_linenumber" name="L335" href="#L335">335</a> <em class="jxr_javadoccomment"> * lower and upper bound of the support are included in the support.</em> +<a class="jxr_linenumber" name="L336" href="#L336">336</a> <em class="jxr_javadoccomment"> *</em> +<a class="jxr_linenumber" name="L337" href="#L337">337</a> <em class="jxr_javadoccomment"> * <p>This method is used in the default implementation of the inverse cumulative and</em> +<a class="jxr_linenumber" name="L338" href="#L338">338</a> <em class="jxr_javadoccomment"> * survival probability functions.</em> +<a class="jxr_linenumber" name="L339" href="#L339">339</a> <em class="jxr_javadoccomment"> *</em> +<a class="jxr_linenumber" name="L340" href="#L340">340</a> <em class="jxr_javadoccomment"> * <p>The default value is true which assumes the cdf and sf have no plateau regions</em> +<a class="jxr_linenumber" name="L341" href="#L341">341</a> <em class="jxr_javadoccomment"> * where the same probability value is returned for a large range of x.</em> +<a class="jxr_linenumber" name="L342" href="#L342">342</a> <em class="jxr_javadoccomment"> * Override this method if there are gaps in the support of the cdf and sf.</em> +<a class="jxr_linenumber" name="L343" href="#L343">343</a> <em class="jxr_javadoccomment"> *</em> +<a class="jxr_linenumber" name="L344" href="#L344">344</a> <em class="jxr_javadoccomment"> * <p>If false then the inverse will perform an additional step to ensure that the</em> +<a class="jxr_linenumber" name="L345" href="#L345">345</a> <em class="jxr_javadoccomment"> * lower-bound of the interval on which the cdf is constant should be returned. This</em> +<a class="jxr_linenumber" name="L346" href="#L346">346</a> <em class="jxr_javadoccomment"> * will search from the initial point x downwards if a smaller value also has the same</em> +<a class="jxr_linenumber" name="L347" href="#L347">347</a> <em class="jxr_javadoccomment"> * cumulative (survival) probability.</em> +<a class="jxr_linenumber" name="L348" href="#L348">348</a> <em class="jxr_javadoccomment"> *</em> +<a class="jxr_linenumber" name="L349" href="#L349">349</a> <em class="jxr_javadoccomment"> * <p>Any plateau with a width in x smaller than the inverse absolute accuracy will</em> +<a class="jxr_linenumber" name="L350" href="#L350">350</a> <em class="jxr_javadoccomment"> * not be searched.</em> +<a class="jxr_linenumber" name="L351" href="#L351">351</a> <em class="jxr_javadoccomment"> *</em> +<a class="jxr_linenumber" name="L352" href="#L352">352</a> <em class="jxr_javadoccomment"> * <p>Note: This method was public in commons math. It has been reduced to package private</em> +<a class="jxr_linenumber" name="L353" href="#L353">353</a> <em class="jxr_javadoccomment"> * in commons statistics as it is an implementation detail.</em> +<a class="jxr_linenumber" name="L354" href="#L354">354</a> <em class="jxr_javadoccomment"> *</em> +<a class="jxr_linenumber" name="L355" href="#L355">355</a> <em class="jxr_javadoccomment"> * @return whether the support is connected.</em> +<a class="jxr_linenumber" name="L356" href="#L356">356</a> <em class="jxr_javadoccomment"> * @see <a href="<a href="https://issues.apache.org/jira/browse/MATH-699"; target="alexandria_uri">https://issues.apache.org/jira/browse/MATH-699</a>">MATH-699</a></em> +<a class="jxr_linenumber" name="L357" href="#L357">357</a> <em class="jxr_javadoccomment"> */</em> +<a class="jxr_linenumber" name="L358" href="#L358">358</a> <strong class="jxr_keyword">boolean</strong> isSupportConnected() { +<a class="jxr_linenumber" name="L359" href="#L359">359</a> <strong class="jxr_keyword">return</strong> <strong class="jxr_keyword">true</strong>; +<a class="jxr_linenumber" name="L360" href="#L360">360</a> } +<a class="jxr_linenumber" name="L361" href="#L361">361</a> +<a class="jxr_linenumber" name="L362" href="#L362">362</a> <em class="jxr_javadoccomment">/**</em> +<a class="jxr_linenumber" name="L363" href="#L363">363</a> <em class="jxr_javadoccomment"> * Test the probability function for a plateau at the point x. If detected</em> +<a class="jxr_linenumber" name="L364" href="#L364">364</a> <em class="jxr_javadoccomment"> * search the plateau for the lowest point y such that</em> +<a class="jxr_linenumber" name="L365" href="#L365">365</a> <em class="jxr_javadoccomment"> * {@code inf{y in R | P(y) == P(x)}}.</em> +<a class="jxr_linenumber" name="L366" href="#L366">366</a> <em class="jxr_javadoccomment"> *</em> +<a class="jxr_linenumber" name="L367" href="#L367">367</a> <em class="jxr_javadoccomment"> * <p>This function is used when the distribution support is not connected</em> +<a class="jxr_linenumber" name="L368" href="#L368">368</a> <em class="jxr_javadoccomment"> * to satisfy the inverse probability requirements of {@link ContinuousDistribution}</em> +<a class="jxr_linenumber" name="L369" href="#L369">369</a> <em class="jxr_javadoccomment"> * on the returned value.</em> +<a class="jxr_linenumber" name="L370" href="#L370">370</a> <em class="jxr_javadoccomment"> *</em> +<a class="jxr_linenumber" name="L371" href="#L371">371</a> <em class="jxr_javadoccomment"> * @param complement Set to true to search the survival probability.</em> +<a class="jxr_linenumber" name="L372" href="#L372">372</a> <em class="jxr_javadoccomment"> * @param lower Lower bound used to limit the search downwards.</em> +<a class="jxr_linenumber" name="L373" href="#L373">373</a> <em class="jxr_javadoccomment"> * @param x Current value.</em> +<a class="jxr_linenumber" name="L374" href="#L374">374</a> <em class="jxr_javadoccomment"> * @return the infimum y</em> +<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> <strong class="jxr_keyword">private</strong> <strong class="jxr_keyword">double</strong> searchPlateau(<strong class="jxr_keyword">boolean</strong> complement, <strong class="jxr_keyword">double</strong> lower, <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> x) { +<a class="jxr_linenumber" name="L377" href="#L377">377</a> <em class="jxr_comment">// Test for plateau. Lower the value x if the probability is the same.</em> +<a class="jxr_linenumber" name="L378" href="#L378">378</a> <em class="jxr_comment">// Ensure the step is robust to the solver accuracy being less</em> +<a class="jxr_linenumber" name="L379" href="#L379">379</a> <em class="jxr_comment">// than 1 ulp of x (e.g. dx=0 will infinite loop)</em> +<a class="jxr_linenumber" name="L380" href="#L380">380</a> <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> dx = Math.max(SOLVER_ABSOLUTE_ACCURACY, Math.ulp(x)); +<a class="jxr_linenumber" name="L381" href="#L381">381</a> <strong class="jxr_keyword">if</strong> (x - dx >= lower) { +<a class="jxr_linenumber" name="L382" href="#L382">382</a> <strong class="jxr_keyword">final</strong> DoubleUnaryOperator fun = complement ? +<a class="jxr_linenumber" name="L383" href="#L383">383</a> <strong class="jxr_keyword">this</strong>::survivalProbability : +<a class="jxr_linenumber" name="L384" href="#L384">384</a> <strong class="jxr_keyword">this</strong>::cumulativeProbability; +<a class="jxr_linenumber" name="L385" href="#L385">385</a> <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> px = fun.applyAsDouble(x); +<a class="jxr_linenumber" name="L386" href="#L386">386</a> <strong class="jxr_keyword">if</strong> (fun.applyAsDouble(x - dx) == px) { +<a class="jxr_linenumber" name="L387" href="#L387">387</a> <strong class="jxr_keyword">double</strong> upperBound = x; +<a class="jxr_linenumber" name="L388" href="#L388">388</a> <strong class="jxr_keyword">double</strong> lowerBound = lower; +<a class="jxr_linenumber" name="L389" href="#L389">389</a> <em class="jxr_comment">// Bisection search</em> +<a class="jxr_linenumber" name="L390" href="#L390">390</a> <em class="jxr_comment">// Require cdf(x) < px and sf(x) > px to move the lower bound</em> +<a class="jxr_linenumber" name="L391" href="#L391">391</a> <em class="jxr_comment">// to the midpoint.</em> +<a class="jxr_linenumber" name="L392" href="#L392">392</a> <strong class="jxr_keyword">final</strong> DoubleBinaryOperator cmp = complement ? +<a class="jxr_linenumber" name="L393" href="#L393">393</a> (a, b) -> a > b ? -1 : 1 : +<a class="jxr_linenumber" name="L394" href="#L394">394</a> (a, b) -> a < b ? -1 : 1; +<a class="jxr_linenumber" name="L395" href="#L395">395</a> <strong class="jxr_keyword">while</strong> (upperBound - lowerBound > dx) { +<a class="jxr_linenumber" name="L396" href="#L396">396</a> <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> midPoint = 0.5 * (lowerBound + upperBound); +<a class="jxr_linenumber" name="L397" href="#L397">397</a> <strong class="jxr_keyword">if</strong> (cmp.applyAsDouble(fun.applyAsDouble(midPoint), px) < 0) { +<a class="jxr_linenumber" name="L398" href="#L398">398</a> lowerBound = midPoint; +<a class="jxr_linenumber" name="L399" href="#L399">399</a> } <strong class="jxr_keyword">else</strong> { +<a class="jxr_linenumber" name="L400" href="#L400">400</a> upperBound = midPoint; +<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">return</strong> upperBound; +<a class="jxr_linenumber" name="L404" href="#L404">404</a> } +<a class="jxr_linenumber" name="L405" href="#L405">405</a> } +<a class="jxr_linenumber" name="L406" href="#L406">406</a> <strong class="jxr_keyword">return</strong> x; +<a class="jxr_linenumber" name="L407" href="#L407">407</a> } +<a class="jxr_linenumber" name="L408" href="#L408">408</a> +<a class="jxr_linenumber" name="L409" href="#L409">409</a> <em class="jxr_javadoccomment">/** {@inheritDoc} */</em> +<a class="jxr_linenumber" name="L410" href="#L410">410</a> @Override +<a class="jxr_linenumber" name="L411" href="#L411">411</a> <strong class="jxr_keyword">public</strong> ContinuousDistribution.Sampler createSampler(<strong class="jxr_keyword">final</strong> UniformRandomProvider rng) { +<a class="jxr_linenumber" name="L412" href="#L412">412</a> <em class="jxr_comment">// Inversion method distribution sampler.</em> +<a class="jxr_linenumber" name="L413" href="#L413">413</a> <strong class="jxr_keyword">return</strong> InverseTransformContinuousSampler.of(rng, <strong class="jxr_keyword">this</strong>::inverseCumulativeProbability)::sample; +<a class="jxr_linenumber" name="L414" href="#L414">414</a> } +<a class="jxr_linenumber" name="L415" href="#L415">415</a> } +</pre> +<hr/> +<div id="footer">Copyright © 2018–2022 <a href="https://www.apache.org/";>The Apache Software Foundation</a>. 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