Added: dev/commons/statistics/1.0-RC1/site/xref/org/apache/commons/statistics/distribution/LogisticDistribution.html ============================================================================== --- dev/commons/statistics/1.0-RC1/site/xref/org/apache/commons/statistics/distribution/LogisticDistribution.html (added) +++ dev/commons/statistics/1.0-RC1/site/xref/org/apache/commons/statistics/distribution/LogisticDistribution.html Thu Dec 1 16:47:12 2022 @@ -0,0 +1,233 @@ +<!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>LogisticDistribution xref</title> +<link type="text/css" rel="stylesheet" href="../../../../../stylesheet.css" /> +</head> +<body> +<div id="overview"><a href="../../../../../../apidocs/org/apache/commons/statistics/distribution/LogisticDistribution.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> <em class="jxr_javadoccomment">/**</em> +<a class="jxr_linenumber" name="L20" href="#L20">20</a> <em class="jxr_javadoccomment"> * Implementation of the logistic distribution.</em> +<a class="jxr_linenumber" name="L21" href="#L21">21</a> <em class="jxr_javadoccomment"> *</em> +<a class="jxr_linenumber" name="L22" href="#L22">22</a> <em class="jxr_javadoccomment"> * <p>The probability density function of \( X \) is:</em> +<a class="jxr_linenumber" name="L23" href="#L23">23</a> <em class="jxr_javadoccomment"> *</em> +<a class="jxr_linenumber" name="L24" href="#L24">24</a> <em class="jxr_javadoccomment"> * <p>\[ f(x; \mu, s) = \frac{e^{-(x-\mu)/s}} {s\left(1+e^{-(x-\mu)/s}\right)^2} \]</em> +<a class="jxr_linenumber" name="L25" href="#L25">25</a> <em class="jxr_javadoccomment"> *</em> +<a class="jxr_linenumber" name="L26" href="#L26">26</a> <em class="jxr_javadoccomment"> * <p>for \( \mu \) the location,</em> +<a class="jxr_linenumber" name="L27" href="#L27">27</a> <em class="jxr_javadoccomment"> * \( s &gt; 0 \) the scale, and</em> +<a class="jxr_linenumber" name="L28" href="#L28">28</a> <em class="jxr_javadoccomment"> * \( x \in (-\infty, \infty) \).</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"> * @see <a href="<a href="https://en.wikipedia.org/wiki/Logistic_distribution"; target="alexandria_uri">https://en.wikipedia.org/wiki/Logistic_distribution</a>">Logistic distribution (Wikipedia)</a></em> +<a class="jxr_linenumber" name="L31" href="#L31">31</a> <em class="jxr_javadoccomment"> * @see <a href="<a href="https://mathworld.wolfram.com/LogisticDistribution.html"; target="alexandria_uri">https://mathworld.wolfram.com/LogisticDistribution.html</a>">Logistic distribution (MathWorld)</a></em> +<a class="jxr_linenumber" name="L32" href="#L32">32</a> <em class="jxr_javadoccomment"> */</em> +<a class="jxr_linenumber" name="L33" href="#L33">33</a> <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">class</strong> <a name="LogisticDistribution" href="../../../../../org/apache/commons/statistics/distribution/LogisticDistribution.html#LogisticDistribution">LogisticDistribution</a> <strong class="jxr_keyword">extends</strong> <a name="AbstractContinuousDistribution" href="../../../../../org/apache/commons/statistics/distribution/AbstractContinuousDistribution.html#AbstractContinuousDistribution">AbstractContinuousDistribution</a> { +<a class="jxr_linenumber" name="L34" href="#L34">34</a> <em class="jxr_javadoccomment">/** Support lower bound. */</em> +<a class="jxr_linenumber" name="L35" href="#L35">35</a> <strong class="jxr_keyword">private</strong> <strong class="jxr_keyword">static</strong> <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> SUPPORT_LO = Double.NEGATIVE_INFINITY; +<a class="jxr_linenumber" name="L36" href="#L36">36</a> <em class="jxr_javadoccomment">/** Support upper bound. */</em> +<a class="jxr_linenumber" name="L37" href="#L37">37</a> <strong class="jxr_keyword">private</strong> <strong class="jxr_keyword">static</strong> <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> SUPPORT_HI = Double.POSITIVE_INFINITY; +<a class="jxr_linenumber" name="L38" href="#L38">38</a> <em class="jxr_javadoccomment">/** &pi;<sup>2</sup>/3. */</em> +<a class="jxr_linenumber" name="L39" href="#L39">39</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> PI_SQUARED_OVER_THREE = Math.PI * Math.PI / 3; +<a class="jxr_linenumber" name="L40" href="#L40">40</a> <em class="jxr_javadoccomment">/** Location parameter. */</em> +<a class="jxr_linenumber" name="L41" href="#L41">41</a> <strong class="jxr_keyword">private</strong> <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> mu; +<a class="jxr_linenumber" name="L42" href="#L42">42</a> <em class="jxr_javadoccomment">/** Scale parameter. */</em> +<a class="jxr_linenumber" name="L43" href="#L43">43</a> <strong class="jxr_keyword">private</strong> <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> scale; +<a class="jxr_linenumber" name="L44" href="#L44">44</a> <em class="jxr_javadoccomment">/** Logarithm of "scale". */</em> +<a class="jxr_linenumber" name="L45" href="#L45">45</a> <strong class="jxr_keyword">private</strong> <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> logScale; +<a class="jxr_linenumber" name="L46" href="#L46">46</a> +<a class="jxr_linenumber" name="L47" href="#L47">47</a> <em class="jxr_javadoccomment">/**</em> +<a class="jxr_linenumber" name="L48" href="#L48">48</a> <em class="jxr_javadoccomment"> * @param mu Location parameter.</em> +<a class="jxr_linenumber" name="L49" href="#L49">49</a> <em class="jxr_javadoccomment"> * @param scale Scale parameter (must be positive).</em> +<a class="jxr_linenumber" name="L50" href="#L50">50</a> <em class="jxr_javadoccomment"> */</em> +<a class="jxr_linenumber" name="L51" href="#L51">51</a> <strong class="jxr_keyword">private</strong> <a name="LogisticDistribution" href="../../../../../org/apache/commons/statistics/distribution/LogisticDistribution.html#LogisticDistribution">LogisticDistribution</a>(<strong class="jxr_keyword">double</strong> mu, +<a class="jxr_linenumber" name="L52" href="#L52">52</a> <strong class="jxr_keyword">double</strong> scale) { +<a class="jxr_linenumber" name="L53" href="#L53">53</a> <strong class="jxr_keyword">this</strong>.mu = mu; +<a class="jxr_linenumber" name="L54" href="#L54">54</a> <strong class="jxr_keyword">this</strong>.scale = scale; +<a class="jxr_linenumber" name="L55" href="#L55">55</a> <strong class="jxr_keyword">this</strong>.logScale = Math.log(scale); +<a class="jxr_linenumber" name="L56" href="#L56">56</a> } +<a class="jxr_linenumber" name="L57" href="#L57">57</a> +<a class="jxr_linenumber" name="L58" href="#L58">58</a> <em class="jxr_javadoccomment">/**</em> +<a class="jxr_linenumber" name="L59" href="#L59">59</a> <em class="jxr_javadoccomment"> * Creates a logistic distribution.</em> +<a class="jxr_linenumber" name="L60" href="#L60">60</a> <em class="jxr_javadoccomment"> *</em> +<a class="jxr_linenumber" name="L61" href="#L61">61</a> <em class="jxr_javadoccomment"> * @param mu Location parameter.</em> +<a class="jxr_linenumber" name="L62" href="#L62">62</a> <em class="jxr_javadoccomment"> * @param scale Scale parameter (must be positive).</em> +<a class="jxr_linenumber" name="L63" href="#L63">63</a> <em class="jxr_javadoccomment"> * @return the distribution</em> +<a class="jxr_linenumber" name="L64" href="#L64">64</a> <em class="jxr_javadoccomment"> * @throws IllegalArgumentException if {@code scale <= 0}.</em> +<a class="jxr_linenumber" name="L65" href="#L65">65</a> <em class="jxr_javadoccomment"> */</em> +<a class="jxr_linenumber" name="L66" href="#L66">66</a> <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">static</strong> <a name="LogisticDistribution" href="../../../../../org/apache/commons/statistics/distribution/LogisticDistribution.html#LogisticDistribution">LogisticDistribution</a> of(<strong class="jxr_keyword">double</strong> mu, +<a class="jxr_linenumber" name="L67" href="#L67">67</a> <strong class="jxr_keyword">double</strong> scale) { +<a class="jxr_linenumber" name="L68" href="#L68">68</a> <strong class="jxr_keyword">if</strong> (scale <= 0) { +<a class="jxr_linenumber" name="L69" href="#L69">69</a> <strong class="jxr_keyword">throw</strong> <strong class="jxr_keyword">new</strong> <a name="DistributionException" href="../../../../../org/apache/commons/statistics/distribution/DistributionException.html#DistributionException">DistributionException</a>(DistributionException.NOT_STRICTLY_POSITIVE, +<a class="jxr_linenumber" name="L70" href="#L70">70</a> scale); +<a class="jxr_linenumber" name="L71" href="#L71">71</a> } +<a class="jxr_linenumber" name="L72" href="#L72">72</a> <strong class="jxr_keyword">return</strong> <strong class="jxr_keyword">new</strong> <a name="LogisticDistribution" href="../../../../../org/apache/commons/statistics/distribution/LogisticDistribution.html#LogisticDistribution">LogisticDistribution</a>(mu, scale); +<a class="jxr_linenumber" name="L73" href="#L73">73</a> } +<a class="jxr_linenumber" name="L74" href="#L74">74</a> +<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"> * Gets the location parameter of this distribution.</em> +<a class="jxr_linenumber" name="L77" href="#L77">77</a> <em class="jxr_javadoccomment"> *</em> +<a class="jxr_linenumber" name="L78" href="#L78">78</a> <em class="jxr_javadoccomment"> * @return the location parameter.</em> +<a class="jxr_linenumber" name="L79" href="#L79">79</a> <em class="jxr_javadoccomment"> */</em> +<a class="jxr_linenumber" name="L80" href="#L80">80</a> <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">double</strong> getLocation() { +<a class="jxr_linenumber" name="L81" href="#L81">81</a> <strong class="jxr_keyword">return</strong> mu; +<a class="jxr_linenumber" name="L82" href="#L82">82</a> } +<a class="jxr_linenumber" name="L83" href="#L83">83</a> +<a class="jxr_linenumber" name="L84" href="#L84">84</a> <em class="jxr_javadoccomment">/**</em> +<a class="jxr_linenumber" name="L85" href="#L85">85</a> <em class="jxr_javadoccomment"> * Gets the scale parameter of this distribution.</em> +<a class="jxr_linenumber" name="L86" href="#L86">86</a> <em class="jxr_javadoccomment"> *</em> +<a class="jxr_linenumber" name="L87" href="#L87">87</a> <em class="jxr_javadoccomment"> * @return the scale parameter.</em> +<a class="jxr_linenumber" name="L88" href="#L88">88</a> <em class="jxr_javadoccomment"> */</em> +<a class="jxr_linenumber" name="L89" href="#L89">89</a> <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">double</strong> getScale() { +<a class="jxr_linenumber" name="L90" href="#L90">90</a> <strong class="jxr_keyword">return</strong> scale; +<a class="jxr_linenumber" name="L91" href="#L91">91</a> } +<a class="jxr_linenumber" name="L92" href="#L92">92</a> +<a class="jxr_linenumber" name="L93" href="#L93">93</a> <em class="jxr_javadoccomment">/** {@inheritDoc} */</em> +<a class="jxr_linenumber" name="L94" href="#L94">94</a> @Override +<a class="jxr_linenumber" name="L95" href="#L95">95</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="L96" href="#L96">96</a> <strong class="jxr_keyword">if</strong> (x <= SUPPORT_LO || +<a class="jxr_linenumber" name="L97" href="#L97">97</a> x >= SUPPORT_HI) { +<a class="jxr_linenumber" name="L98" href="#L98">98</a> <strong class="jxr_keyword">return</strong> 0; +<a class="jxr_linenumber" name="L99" href="#L99">99</a> } +<a class="jxr_linenumber" name="L100" href="#L100">100</a> +<a class="jxr_linenumber" name="L101" href="#L101">101</a> <em class="jxr_comment">// Ensure symmetry around location by using the absolute.</em> +<a class="jxr_linenumber" name="L102" href="#L102">102</a> <em class="jxr_comment">// This also ensures exp(z) is between 1 and 0 and avoids</em> +<a class="jxr_linenumber" name="L103" href="#L103">103</a> <em class="jxr_comment">// overflow for large negative values of (x - mu).</em> +<a class="jxr_linenumber" name="L104" href="#L104">104</a> <em class="jxr_comment">// Exploits the reciprocal relation: exp(-x) == 1 / exp(x)</em> +<a class="jxr_linenumber" name="L105" href="#L105">105</a> <em class="jxr_comment">// exp(-z) 1 exp(z) exp(z)</em> +<a class="jxr_linenumber" name="L106" href="#L106">106</a> <em class="jxr_comment">// --------------- = -------------------------- * ------ = --------------</em> +<a class="jxr_linenumber" name="L107" href="#L107">107</a> <em class="jxr_comment">// (1 + exp(-z))^2 exp(z) (1 + 1 / exp(z))^2 exp(z) (1 + exp(z))^2</em> +<a class="jxr_linenumber" name="L108" href="#L108">108</a> <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> z = -Math.abs(x - mu) / scale; +<a class="jxr_linenumber" name="L109" href="#L109">109</a> <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> v = Math.exp(z); +<a class="jxr_linenumber" name="L110" href="#L110">110</a> <strong class="jxr_keyword">return</strong> v / ((1 + v) * (1 + v)) / scale; +<a class="jxr_linenumber" name="L111" href="#L111">111</a> } +<a class="jxr_linenumber" name="L112" href="#L112">112</a> +<a class="jxr_linenumber" name="L113" href="#L113">113</a> <em class="jxr_javadoccomment">/** {@inheritDoc} */</em> +<a class="jxr_linenumber" name="L114" href="#L114">114</a> @Override +<a class="jxr_linenumber" name="L115" href="#L115">115</a> <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">double</strong> logDensity(<strong class="jxr_keyword">double</strong> x) { +<a class="jxr_linenumber" name="L116" href="#L116">116</a> <strong class="jxr_keyword">if</strong> (x <= SUPPORT_LO || +<a class="jxr_linenumber" name="L117" href="#L117">117</a> x >= SUPPORT_HI) { +<a class="jxr_linenumber" name="L118" href="#L118">118</a> <strong class="jxr_keyword">return</strong> Double.NEGATIVE_INFINITY; +<a class="jxr_linenumber" name="L119" href="#L119">119</a> } +<a class="jxr_linenumber" name="L120" href="#L120">120</a> +<a class="jxr_linenumber" name="L121" href="#L121">121</a> <em class="jxr_comment">// Ensure symmetry around location by using the absolute</em> +<a class="jxr_linenumber" name="L122" href="#L122">122</a> <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> z = -Math.abs(x - mu) / scale; +<a class="jxr_linenumber" name="L123" href="#L123">123</a> <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> v = Math.exp(z); +<a class="jxr_linenumber" name="L124" href="#L124">124</a> <strong class="jxr_keyword">return</strong> z - 2 * Math.log1p(v) - logScale; +<a class="jxr_linenumber" name="L125" href="#L125">125</a> } +<a class="jxr_linenumber" name="L126" href="#L126">126</a> +<a class="jxr_linenumber" name="L127" href="#L127">127</a> <em class="jxr_javadoccomment">/** {@inheritDoc} */</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> cumulativeProbability(<strong class="jxr_keyword">double</strong> x) { +<a class="jxr_linenumber" name="L130" href="#L130">130</a> <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> z = (x - mu) / scale; +<a class="jxr_linenumber" name="L131" href="#L131">131</a> <strong class="jxr_keyword">return</strong> 1 / (1 + Math.exp(-z)); +<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">/** {@inheritDoc} */</em> +<a class="jxr_linenumber" name="L135" href="#L135">135</a> @Override +<a class="jxr_linenumber" name="L136" href="#L136">136</a> <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">double</strong> survivalProbability(<strong class="jxr_keyword">double</strong> x) { +<a class="jxr_linenumber" name="L137" href="#L137">137</a> <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> z = (x - mu) / scale; +<a class="jxr_linenumber" name="L138" href="#L138">138</a> <strong class="jxr_keyword">return</strong> 1 / (1 + Math.exp(z)); +<a class="jxr_linenumber" name="L139" href="#L139">139</a> } +<a class="jxr_linenumber" name="L140" href="#L140">140</a> +<a class="jxr_linenumber" name="L141" href="#L141">141</a> <em class="jxr_javadoccomment">/** {@inheritDoc} */</em> +<a class="jxr_linenumber" name="L142" href="#L142">142</a> @Override +<a class="jxr_linenumber" name="L143" href="#L143">143</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="L144" href="#L144">144</a> ArgumentUtils.checkProbability(p); +<a class="jxr_linenumber" name="L145" href="#L145">145</a> <strong class="jxr_keyword">if</strong> (p == 0) { +<a class="jxr_linenumber" name="L146" href="#L146">146</a> <strong class="jxr_keyword">return</strong> SUPPORT_LO; +<a class="jxr_linenumber" name="L147" href="#L147">147</a> } <strong class="jxr_keyword">else</strong> <strong class="jxr_keyword">if</strong> (p == 1) { +<a class="jxr_linenumber" name="L148" href="#L148">148</a> <strong class="jxr_keyword">return</strong> SUPPORT_HI; +<a class="jxr_linenumber" name="L149" href="#L149">149</a> } <strong class="jxr_keyword">else</strong> { +<a class="jxr_linenumber" name="L150" href="#L150">150</a> <strong class="jxr_keyword">return</strong> scale * Math.log(p / (1 - p)) + mu; +<a class="jxr_linenumber" name="L151" href="#L151">151</a> } +<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">/** {@inheritDoc} */</em> +<a class="jxr_linenumber" name="L155" href="#L155">155</a> @Override +<a class="jxr_linenumber" name="L156" href="#L156">156</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="L157" href="#L157">157</a> ArgumentUtils.checkProbability(p); +<a class="jxr_linenumber" name="L158" href="#L158">158</a> <strong class="jxr_keyword">if</strong> (p == 1) { +<a class="jxr_linenumber" name="L159" href="#L159">159</a> <strong class="jxr_keyword">return</strong> SUPPORT_LO; +<a class="jxr_linenumber" name="L160" href="#L160">160</a> } <strong class="jxr_keyword">else</strong> <strong class="jxr_keyword">if</strong> (p == 0) { +<a class="jxr_linenumber" name="L161" href="#L161">161</a> <strong class="jxr_keyword">return</strong> SUPPORT_HI; +<a class="jxr_linenumber" name="L162" href="#L162">162</a> } <strong class="jxr_keyword">else</strong> { +<a class="jxr_linenumber" name="L163" href="#L163">163</a> <strong class="jxr_keyword">return</strong> scale * -Math.log(p / (1 - p)) + mu; +<a class="jxr_linenumber" name="L164" href="#L164">164</a> } +<a class="jxr_linenumber" name="L165" href="#L165">165</a> } +<a class="jxr_linenumber" name="L166" href="#L166">166</a> +<a class="jxr_linenumber" name="L167" href="#L167">167</a> <em class="jxr_javadoccomment">/**</em> +<a class="jxr_linenumber" name="L168" href="#L168">168</a> <em class="jxr_javadoccomment"> * {@inheritDoc}</em> +<a class="jxr_linenumber" name="L169" href="#L169">169</a> <em class="jxr_javadoccomment"> *</em> +<a class="jxr_linenumber" name="L170" href="#L170">170</a> <em class="jxr_javadoccomment"> * <p>The mean is equal to the {@link #getLocation() location}.</em> +<a class="jxr_linenumber" name="L171" href="#L171">171</a> <em class="jxr_javadoccomment"> */</em> +<a class="jxr_linenumber" name="L172" href="#L172">172</a> @Override +<a class="jxr_linenumber" name="L173" href="#L173">173</a> <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">double</strong> getMean() { +<a class="jxr_linenumber" name="L174" href="#L174">174</a> <strong class="jxr_keyword">return</strong> getLocation(); +<a class="jxr_linenumber" name="L175" href="#L175">175</a> } +<a class="jxr_linenumber" name="L176" href="#L176">176</a> +<a class="jxr_linenumber" name="L177" href="#L177">177</a> <em class="jxr_javadoccomment">/**</em> +<a class="jxr_linenumber" name="L178" href="#L178">178</a> <em class="jxr_javadoccomment"> * {@inheritDoc}</em> +<a class="jxr_linenumber" name="L179" href="#L179">179</a> <em class="jxr_javadoccomment"> *</em> +<a class="jxr_linenumber" name="L180" href="#L180">180</a> <em class="jxr_javadoccomment"> * <p>For scale parameter \( s \), the variance is:</em> +<a class="jxr_linenumber" name="L181" href="#L181">181</a> <em class="jxr_javadoccomment"> *</em> +<a class="jxr_linenumber" name="L182" href="#L182">182</a> <em class="jxr_javadoccomment"> * <p>\[ \frac{s^2 \pi^2}{3} \].</em> +<a class="jxr_linenumber" name="L183" href="#L183">183</a> <em class="jxr_javadoccomment"> */</em> +<a class="jxr_linenumber" name="L184" href="#L184">184</a> @Override +<a class="jxr_linenumber" name="L185" href="#L185">185</a> <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">double</strong> getVariance() { +<a class="jxr_linenumber" name="L186" href="#L186">186</a> <strong class="jxr_keyword">return</strong> scale * scale * PI_SQUARED_OVER_THREE; +<a class="jxr_linenumber" name="L187" href="#L187">187</a> } +<a class="jxr_linenumber" name="L188" href="#L188">188</a> +<a class="jxr_linenumber" name="L189" href="#L189">189</a> <em class="jxr_javadoccomment">/**</em> +<a class="jxr_linenumber" name="L190" href="#L190">190</a> <em class="jxr_javadoccomment"> * {@inheritDoc}</em> +<a class="jxr_linenumber" name="L191" href="#L191">191</a> <em class="jxr_javadoccomment"> *</em> +<a class="jxr_linenumber" name="L192" href="#L192">192</a> <em class="jxr_javadoccomment"> * <p>The lower bound of the support is always negative infinity.</em> +<a class="jxr_linenumber" name="L193" href="#L193">193</a> <em class="jxr_javadoccomment"> *</em> +<a class="jxr_linenumber" name="L194" href="#L194">194</a> <em class="jxr_javadoccomment"> * @return {@link Double#NEGATIVE_INFINITY negative infinity}.</em> +<a class="jxr_linenumber" name="L195" href="#L195">195</a> <em class="jxr_javadoccomment"> */</em> +<a class="jxr_linenumber" name="L196" href="#L196">196</a> @Override +<a class="jxr_linenumber" name="L197" href="#L197">197</a> <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">double</strong> getSupportLowerBound() { +<a class="jxr_linenumber" name="L198" href="#L198">198</a> <strong class="jxr_keyword">return</strong> SUPPORT_LO; +<a class="jxr_linenumber" name="L199" href="#L199">199</a> } +<a class="jxr_linenumber" name="L200" href="#L200">200</a> +<a class="jxr_linenumber" name="L201" href="#L201">201</a> <em class="jxr_javadoccomment">/**</em> +<a class="jxr_linenumber" name="L202" href="#L202">202</a> <em class="jxr_javadoccomment"> * {@inheritDoc}</em> +<a class="jxr_linenumber" name="L203" href="#L203">203</a> <em class="jxr_javadoccomment"> *</em> +<a class="jxr_linenumber" name="L204" href="#L204">204</a> <em class="jxr_javadoccomment"> * <p>The upper bound of the support is always positive infinity.</em> +<a class="jxr_linenumber" name="L205" href="#L205">205</a> <em class="jxr_javadoccomment"> *</em> +<a class="jxr_linenumber" name="L206" href="#L206">206</a> <em class="jxr_javadoccomment"> * @return {@link Double#POSITIVE_INFINITY positive infinity}.</em> +<a class="jxr_linenumber" name="L207" href="#L207">207</a> <em class="jxr_javadoccomment"> */</em> +<a class="jxr_linenumber" name="L208" href="#L208">208</a> @Override +<a class="jxr_linenumber" name="L209" href="#L209">209</a> <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">double</strong> getSupportUpperBound() { +<a class="jxr_linenumber" name="L210" href="#L210">210</a> <strong class="jxr_keyword">return</strong> SUPPORT_HI; +<a class="jxr_linenumber" name="L211" href="#L211">211</a> } +<a class="jxr_linenumber" name="L212" href="#L212">212</a> +<a class="jxr_linenumber" name="L213" href="#L213">213</a> <em class="jxr_javadoccomment">/** {@inheritDoc} */</em> +<a class="jxr_linenumber" name="L214" href="#L214">214</a> @Override +<a class="jxr_linenumber" name="L215" href="#L215">215</a> <strong class="jxr_keyword">double</strong> getMedian() { +<a class="jxr_linenumber" name="L216" href="#L216">216</a> <em class="jxr_comment">// Overridden for the probability(double, double) method.</em> +<a class="jxr_linenumber" name="L217" href="#L217">217</a> <em class="jxr_comment">// This is intentionally not a public method.</em> +<a class="jxr_linenumber" name="L218" href="#L218">218</a> <strong class="jxr_keyword">return</strong> mu; +<a class="jxr_linenumber" name="L219" href="#L219">219</a> } +<a class="jxr_linenumber" name="L220" href="#L220">220</a> } +</pre> +<hr/> +<div id="footer">Copyright © 2018–2022 <a href="https://www.apache.org/";>The Apache Software Foundation</a>. All rights reserved.</div> +</body> +</html>
Added: dev/commons/statistics/1.0-RC1/site/xref/org/apache/commons/statistics/distribution/NakagamiDistribution.html ============================================================================== --- dev/commons/statistics/1.0-RC1/site/xref/org/apache/commons/statistics/distribution/NakagamiDistribution.html (added) +++ dev/commons/statistics/1.0-RC1/site/xref/org/apache/commons/statistics/distribution/NakagamiDistribution.html Thu Dec 1 16:47:12 2022 @@ -0,0 +1,231 @@ +<!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>NakagamiDistribution xref</title> +<link type="text/css" rel="stylesheet" href="../../../../../stylesheet.css" /> +</head> +<body> +<div id="overview"><a href="../../../../../../apidocs/org/apache/commons/statistics/distribution/NakagamiDistribution.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.numbers.gamma.Gamma; +<a class="jxr_linenumber" name="L20" href="#L20">20</a> <strong class="jxr_keyword">import</strong> org.apache.commons.numbers.gamma.GammaRatio; +<a class="jxr_linenumber" name="L21" href="#L21">21</a> <strong class="jxr_keyword">import</strong> org.apache.commons.numbers.gamma.LogGamma; +<a class="jxr_linenumber" name="L22" href="#L22">22</a> <strong class="jxr_keyword">import</strong> org.apache.commons.numbers.gamma.RegularizedGamma; +<a class="jxr_linenumber" name="L23" href="#L23">23</a> <strong class="jxr_keyword">import</strong> org.apache.commons.rng.UniformRandomProvider; +<a class="jxr_linenumber" name="L24" href="#L24">24</a> <strong class="jxr_keyword">import</strong> org.apache.commons.rng.sampling.distribution.AhrensDieterMarsagliaTsangGammaSampler; +<a class="jxr_linenumber" name="L25" href="#L25">25</a> <strong class="jxr_keyword">import</strong> org.apache.commons.rng.sampling.distribution.SharedStateContinuousSampler; +<a class="jxr_linenumber" name="L26" href="#L26">26</a> +<a class="jxr_linenumber" name="L27" href="#L27">27</a> <em class="jxr_javadoccomment">/**</em> +<a class="jxr_linenumber" name="L28" href="#L28">28</a> <em class="jxr_javadoccomment"> * Implementation of the Nakagami 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>The probability density function of \( X \) is:</em> +<a class="jxr_linenumber" name="L31" href="#L31">31</a> <em class="jxr_javadoccomment"> *</em> +<a class="jxr_linenumber" name="L32" href="#L32">32</a> <em class="jxr_javadoccomment"> * <p>\[ f(x; \mu, \Omega) = \frac{2\mu^\mu}{\Gamma(\mu)\Omega^\mu}x^{2\mu-1}\exp\left(-\frac{\mu}{\Omega}x^2\right) \]</em> +<a class="jxr_linenumber" name="L33" href="#L33">33</a> <em class="jxr_javadoccomment"> *</em> +<a class="jxr_linenumber" name="L34" href="#L34">34</a> <em class="jxr_javadoccomment"> * <p>for \( \mu &gt; 0 \) the shape,</em> +<a class="jxr_linenumber" name="L35" href="#L35">35</a> <em class="jxr_javadoccomment"> * \( \Omega &gt; 0 \) the scale, and</em> +<a class="jxr_linenumber" name="L36" href="#L36">36</a> <em class="jxr_javadoccomment"> * \( x \in (0, \infty) \).</em> +<a class="jxr_linenumber" name="L37" href="#L37">37</a> <em class="jxr_javadoccomment"> *</em> +<a class="jxr_linenumber" name="L38" href="#L38">38</a> <em class="jxr_javadoccomment"> * @see <a href="<a href="https://en.wikipedia.org/wiki/Nakagami_distribution"; target="alexandria_uri">https://en.wikipedia.org/wiki/Nakagami_distribution</a>">Nakagami distribution (Wikipedia)</a></em> +<a class="jxr_linenumber" name="L39" href="#L39">39</a> <em class="jxr_javadoccomment"> */</em> +<a class="jxr_linenumber" name="L40" href="#L40">40</a> <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">class</strong> <a name="NakagamiDistribution" href="../../../../../org/apache/commons/statistics/distribution/NakagamiDistribution.html#NakagamiDistribution">NakagamiDistribution</a> <strong class="jxr_keyword">extends</strong> <a name="AbstractContinuousDistribution" href="../../../../../org/apache/commons/statistics/distribution/AbstractContinuousDistribution.html#AbstractContinuousDistribution">AbstractContinuousDistribution</a> { +<a class="jxr_linenumber" name="L41" href="#L41">41</a> <em class="jxr_javadoccomment">/** Support lower bound. */</em> +<a class="jxr_linenumber" name="L42" href="#L42">42</a> <strong class="jxr_keyword">private</strong> <strong class="jxr_keyword">static</strong> <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> SUPPORT_LO = 0; +<a class="jxr_linenumber" name="L43" href="#L43">43</a> <em class="jxr_javadoccomment">/** Support upper bound. */</em> +<a class="jxr_linenumber" name="L44" href="#L44">44</a> <strong class="jxr_keyword">private</strong> <strong class="jxr_keyword">static</strong> <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> SUPPORT_HI = Double.POSITIVE_INFINITY; +<a class="jxr_linenumber" name="L45" href="#L45">45</a> <em class="jxr_javadoccomment">/** Natural logarithm of 2. */</em> +<a class="jxr_linenumber" name="L46" href="#L46">46</a> <strong class="jxr_keyword">private</strong> <strong class="jxr_keyword">static</strong> <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> LN_2 = 0.6931471805599453094172321; +<a class="jxr_linenumber" name="L47" href="#L47">47</a> +<a class="jxr_linenumber" name="L48" href="#L48">48</a> <em class="jxr_javadoccomment">/** The shape parameter. */</em> +<a class="jxr_linenumber" name="L49" href="#L49">49</a> <strong class="jxr_keyword">private</strong> <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> mu; +<a class="jxr_linenumber" name="L50" href="#L50">50</a> <em class="jxr_javadoccomment">/** The scale parameter. */</em> +<a class="jxr_linenumber" name="L51" href="#L51">51</a> <strong class="jxr_keyword">private</strong> <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> omega; +<a class="jxr_linenumber" name="L52" href="#L52">52</a> <em class="jxr_javadoccomment">/** Density prefactor. */</em> +<a class="jxr_linenumber" name="L53" href="#L53">53</a> <strong class="jxr_keyword">private</strong> <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> densityPrefactor; +<a class="jxr_linenumber" name="L54" href="#L54">54</a> <em class="jxr_javadoccomment">/** Log density prefactor. */</em> +<a class="jxr_linenumber" name="L55" href="#L55">55</a> <strong class="jxr_keyword">private</strong> <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> logDensityPrefactor; +<a class="jxr_linenumber" name="L56" href="#L56">56</a> <em class="jxr_javadoccomment">/** Cached value for inverse probability function. */</em> +<a class="jxr_linenumber" name="L57" href="#L57">57</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="L58" href="#L58">58</a> <em class="jxr_javadoccomment">/** Cached value for inverse probability function. */</em> +<a class="jxr_linenumber" name="L59" href="#L59">59</a> <strong class="jxr_keyword">private</strong> <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> variance; +<a class="jxr_linenumber" name="L60" href="#L60">60</a> +<a class="jxr_linenumber" name="L61" href="#L61">61</a> <em class="jxr_javadoccomment">/**</em> +<a class="jxr_linenumber" name="L62" href="#L62">62</a> <em class="jxr_javadoccomment"> * @param mu Shape parameter (must be positive).</em> +<a class="jxr_linenumber" name="L63" href="#L63">63</a> <em class="jxr_javadoccomment"> * @param omega Scale parameter (must be positive). Controls the spread of the distribution.</em> +<a class="jxr_linenumber" name="L64" href="#L64">64</a> <em class="jxr_javadoccomment"> */</em> +<a class="jxr_linenumber" name="L65" href="#L65">65</a> <strong class="jxr_keyword">private</strong> <a name="NakagamiDistribution" href="../../../../../org/apache/commons/statistics/distribution/NakagamiDistribution.html#NakagamiDistribution">NakagamiDistribution</a>(<strong class="jxr_keyword">double</strong> mu, +<a class="jxr_linenumber" name="L66" href="#L66">66</a> <strong class="jxr_keyword">double</strong> omega) { +<a class="jxr_linenumber" name="L67" href="#L67">67</a> <strong class="jxr_keyword">this</strong>.mu = mu; +<a class="jxr_linenumber" name="L68" href="#L68">68</a> <strong class="jxr_keyword">this</strong>.omega = omega; +<a class="jxr_linenumber" name="L69" href="#L69">69</a> densityPrefactor = 2.0 * Math.pow(mu, mu) / (Gamma.value(mu) * Math.pow(omega, mu)); +<a class="jxr_linenumber" name="L70" href="#L70">70</a> logDensityPrefactor = LN_2 + Math.log(mu) * mu - LogGamma.value(mu) - Math.log(omega) * mu; +<a class="jxr_linenumber" name="L71" href="#L71">71</a> <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> v = GammaRatio.delta(mu, 0.5); +<a class="jxr_linenumber" name="L72" href="#L72">72</a> mean = Math.sqrt(omega / mu) / v; +<a class="jxr_linenumber" name="L73" href="#L73">73</a> variance = omega - (omega / mu) / v / v; +<a class="jxr_linenumber" name="L74" href="#L74">74</a> } +<a class="jxr_linenumber" name="L75" href="#L75">75</a> +<a class="jxr_linenumber" name="L76" href="#L76">76</a> <em class="jxr_javadoccomment">/**</em> +<a class="jxr_linenumber" name="L77" href="#L77">77</a> <em class="jxr_javadoccomment"> * Creates a Nakagami distribution.</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"> * @param mu Shape parameter (must be positive).</em> +<a class="jxr_linenumber" name="L80" href="#L80">80</a> <em class="jxr_javadoccomment"> * @param omega Scale parameter (must be positive). Controls the spread of the distribution.</em> +<a class="jxr_linenumber" name="L81" href="#L81">81</a> <em class="jxr_javadoccomment"> * @return the distribution</em> +<a class="jxr_linenumber" name="L82" href="#L82">82</a> <em class="jxr_javadoccomment"> * @throws IllegalArgumentException if {@code mu <= 0} or if</em> +<a class="jxr_linenumber" name="L83" href="#L83">83</a> <em class="jxr_javadoccomment"> * {@code omega <= 0}.</em> +<a class="jxr_linenumber" name="L84" href="#L84">84</a> <em class="jxr_javadoccomment"> */</em> +<a class="jxr_linenumber" name="L85" href="#L85">85</a> <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">static</strong> <a name="NakagamiDistribution" href="../../../../../org/apache/commons/statistics/distribution/NakagamiDistribution.html#NakagamiDistribution">NakagamiDistribution</a> of(<strong class="jxr_keyword">double</strong> mu, +<a class="jxr_linenumber" name="L86" href="#L86">86</a> <strong class="jxr_keyword">double</strong> omega) { +<a class="jxr_linenumber" name="L87" href="#L87">87</a> <strong class="jxr_keyword">if</strong> (mu <= 0) { +<a class="jxr_linenumber" name="L88" href="#L88">88</a> <strong class="jxr_keyword">throw</strong> <strong class="jxr_keyword">new</strong> <a name="DistributionException" href="../../../../../org/apache/commons/statistics/distribution/DistributionException.html#DistributionException">DistributionException</a>(DistributionException.NOT_STRICTLY_POSITIVE, mu); +<a class="jxr_linenumber" name="L89" href="#L89">89</a> } +<a class="jxr_linenumber" name="L90" href="#L90">90</a> <strong class="jxr_keyword">if</strong> (omega <= 0) { +<a class="jxr_linenumber" name="L91" href="#L91">91</a> <strong class="jxr_keyword">throw</strong> <strong class="jxr_keyword">new</strong> <a name="DistributionException" href="../../../../../org/apache/commons/statistics/distribution/DistributionException.html#DistributionException">DistributionException</a>(DistributionException.NOT_STRICTLY_POSITIVE, omega); +<a class="jxr_linenumber" name="L92" href="#L92">92</a> } +<a class="jxr_linenumber" name="L93" href="#L93">93</a> <strong class="jxr_keyword">return</strong> <strong class="jxr_keyword">new</strong> <a name="NakagamiDistribution" href="../../../../../org/apache/commons/statistics/distribution/NakagamiDistribution.html#NakagamiDistribution">NakagamiDistribution</a>(mu, omega); +<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> <em class="jxr_javadoccomment">/**</em> +<a class="jxr_linenumber" name="L97" href="#L97">97</a> <em class="jxr_javadoccomment"> * Gets the shape parameter of this distribution.</em> +<a class="jxr_linenumber" name="L98" href="#L98">98</a> <em class="jxr_javadoccomment"> *</em> +<a class="jxr_linenumber" name="L99" href="#L99">99</a> <em class="jxr_javadoccomment"> * @return the shape parameter.</em> +<a class="jxr_linenumber" name="L100" href="#L100">100</a> <em class="jxr_javadoccomment"> */</em> +<a class="jxr_linenumber" name="L101" href="#L101">101</a> <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">double</strong> getShape() { +<a class="jxr_linenumber" name="L102" href="#L102">102</a> <strong class="jxr_keyword">return</strong> mu; +<a class="jxr_linenumber" name="L103" href="#L103">103</a> } +<a class="jxr_linenumber" name="L104" href="#L104">104</a> +<a class="jxr_linenumber" name="L105" href="#L105">105</a> <em class="jxr_javadoccomment">/**</em> +<a class="jxr_linenumber" name="L106" href="#L106">106</a> <em class="jxr_javadoccomment"> * Gets the scale parameter of this distribution.</em> +<a class="jxr_linenumber" name="L107" href="#L107">107</a> <em class="jxr_javadoccomment"> *</em> +<a class="jxr_linenumber" name="L108" href="#L108">108</a> <em class="jxr_javadoccomment"> * @return the scale parameter.</em> +<a class="jxr_linenumber" name="L109" href="#L109">109</a> <em class="jxr_javadoccomment"> */</em> +<a class="jxr_linenumber" name="L110" href="#L110">110</a> <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">double</strong> getScale() { +<a class="jxr_linenumber" name="L111" href="#L111">111</a> <strong class="jxr_keyword">return</strong> omega; +<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">/** {@inheritDoc} */</em> +<a class="jxr_linenumber" name="L115" href="#L115">115</a> @Override +<a class="jxr_linenumber" name="L116" href="#L116">116</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="L117" href="#L117">117</a> <strong class="jxr_keyword">if</strong> (x <= SUPPORT_LO || +<a class="jxr_linenumber" name="L118" href="#L118">118</a> x >= SUPPORT_HI) { +<a class="jxr_linenumber" name="L119" href="#L119">119</a> <strong class="jxr_keyword">return</strong> 0; +<a class="jxr_linenumber" name="L120" href="#L120">120</a> } +<a class="jxr_linenumber" name="L121" href="#L121">121</a> +<a class="jxr_linenumber" name="L122" href="#L122">122</a> <strong class="jxr_keyword">return</strong> densityPrefactor * Math.pow(x, 2 * mu - 1) * Math.exp(-mu * x * x / omega); +<a class="jxr_linenumber" name="L123" href="#L123">123</a> } +<a class="jxr_linenumber" name="L124" href="#L124">124</a> +<a class="jxr_linenumber" name="L125" href="#L125">125</a> <em class="jxr_javadoccomment">/** {@inheritDoc} */</em> +<a class="jxr_linenumber" name="L126" href="#L126">126</a> @Override +<a class="jxr_linenumber" name="L127" href="#L127">127</a> <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">double</strong> logDensity(<strong class="jxr_keyword">double</strong> x) { +<a class="jxr_linenumber" name="L128" href="#L128">128</a> <strong class="jxr_keyword">if</strong> (x <= SUPPORT_LO || +<a class="jxr_linenumber" name="L129" href="#L129">129</a> x >= SUPPORT_HI) { +<a class="jxr_linenumber" name="L130" href="#L130">130</a> <strong class="jxr_keyword">return</strong> Double.NEGATIVE_INFINITY; +<a class="jxr_linenumber" name="L131" href="#L131">131</a> } +<a class="jxr_linenumber" name="L132" href="#L132">132</a> +<a class="jxr_linenumber" name="L133" href="#L133">133</a> <strong class="jxr_keyword">return</strong> logDensityPrefactor + Math.log(x) * (2 * mu - 1) - (mu * x * x / omega); +<a class="jxr_linenumber" name="L134" href="#L134">134</a> } +<a class="jxr_linenumber" name="L135" href="#L135">135</a> +<a class="jxr_linenumber" name="L136" href="#L136">136</a> <em class="jxr_javadoccomment">/** {@inheritDoc} */</em> +<a class="jxr_linenumber" name="L137" href="#L137">137</a> @Override +<a class="jxr_linenumber" name="L138" href="#L138">138</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="L139" href="#L139">139</a> <strong class="jxr_keyword">if</strong> (x <= SUPPORT_LO) { +<a class="jxr_linenumber" name="L140" href="#L140">140</a> <strong class="jxr_keyword">return</strong> 0; +<a class="jxr_linenumber" name="L141" href="#L141">141</a> } <strong class="jxr_keyword">else</strong> <strong class="jxr_keyword">if</strong> (x >= SUPPORT_HI) { +<a class="jxr_linenumber" name="L142" href="#L142">142</a> <strong class="jxr_keyword">return</strong> 1; +<a class="jxr_linenumber" name="L143" href="#L143">143</a> } +<a class="jxr_linenumber" name="L144" href="#L144">144</a> +<a class="jxr_linenumber" name="L145" href="#L145">145</a> <strong class="jxr_keyword">return</strong> RegularizedGamma.P.value(mu, mu * x * x / omega); +<a class="jxr_linenumber" name="L146" href="#L146">146</a> } +<a class="jxr_linenumber" name="L147" href="#L147">147</a> +<a class="jxr_linenumber" name="L148" href="#L148">148</a> <em class="jxr_javadoccomment">/** {@inheritDoc} */</em> +<a class="jxr_linenumber" name="L149" href="#L149">149</a> @Override +<a class="jxr_linenumber" name="L150" href="#L150">150</a> <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">double</strong> survivalProbability(<strong class="jxr_keyword">double</strong> x) { +<a class="jxr_linenumber" name="L151" href="#L151">151</a> <strong class="jxr_keyword">if</strong> (x <= SUPPORT_LO) { +<a class="jxr_linenumber" name="L152" href="#L152">152</a> <strong class="jxr_keyword">return</strong> 1; +<a class="jxr_linenumber" name="L153" href="#L153">153</a> } <strong class="jxr_keyword">else</strong> <strong class="jxr_keyword">if</strong> (x >= SUPPORT_HI) { +<a class="jxr_linenumber" name="L154" href="#L154">154</a> <strong class="jxr_keyword">return</strong> 0; +<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> <strong class="jxr_keyword">return</strong> RegularizedGamma.Q.value(mu, mu * x * x / omega); +<a class="jxr_linenumber" name="L158" href="#L158">158</a> } +<a class="jxr_linenumber" name="L159" href="#L159">159</a> +<a class="jxr_linenumber" name="L160" href="#L160">160</a> <em class="jxr_javadoccomment">/**</em> +<a class="jxr_linenumber" name="L161" href="#L161">161</a> <em class="jxr_javadoccomment"> * {@inheritDoc}</em> +<a class="jxr_linenumber" name="L162" href="#L162">162</a> <em class="jxr_javadoccomment"> *</em> +<a class="jxr_linenumber" name="L163" href="#L163">163</a> <em class="jxr_javadoccomment"> * <p>For shape parameter \( \mu \) and scale parameter \( \Omega \), the mean is:</em> +<a class="jxr_linenumber" name="L164" href="#L164">164</a> <em class="jxr_javadoccomment"> *</em> +<a class="jxr_linenumber" name="L165" href="#L165">165</a> <em class="jxr_javadoccomment"> * <p>\[ \frac{\Gamma(m+\frac{1}{2})}{\Gamma(m)}\left(\frac{\Omega}{m}\right)^{1/2} \]</em> +<a class="jxr_linenumber" name="L166" href="#L166">166</a> <em class="jxr_javadoccomment"> */</em> +<a class="jxr_linenumber" name="L167" href="#L167">167</a> @Override +<a class="jxr_linenumber" name="L168" href="#L168">168</a> <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">double</strong> getMean() { +<a class="jxr_linenumber" name="L169" href="#L169">169</a> <strong class="jxr_keyword">return</strong> mean; +<a class="jxr_linenumber" name="L170" href="#L170">170</a> } +<a class="jxr_linenumber" name="L171" href="#L171">171</a> +<a class="jxr_linenumber" name="L172" href="#L172">172</a> <em class="jxr_javadoccomment">/**</em> +<a class="jxr_linenumber" name="L173" href="#L173">173</a> <em class="jxr_javadoccomment"> * {@inheritDoc}</em> +<a class="jxr_linenumber" name="L174" href="#L174">174</a> <em class="jxr_javadoccomment"> *</em> +<a class="jxr_linenumber" name="L175" href="#L175">175</a> <em class="jxr_javadoccomment"> * <p>For shape parameter \( \mu \) and scale parameter \( \Omega \), the variance is:</em> +<a class="jxr_linenumber" name="L176" href="#L176">176</a> <em class="jxr_javadoccomment"> *</em> +<a class="jxr_linenumber" name="L177" href="#L177">177</a> <em class="jxr_javadoccomment"> * <p>\[ \Omega\left(1-\frac{1}{m}\left(\frac{\Gamma(m+\frac{1}{2})}{\Gamma(m)}\right)^2\right) \]</em> +<a class="jxr_linenumber" name="L178" href="#L178">178</a> <em class="jxr_javadoccomment"> */</em> +<a class="jxr_linenumber" name="L179" href="#L179">179</a> @Override +<a class="jxr_linenumber" name="L180" href="#L180">180</a> <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">double</strong> getVariance() { +<a class="jxr_linenumber" name="L181" href="#L181">181</a> <strong class="jxr_keyword">return</strong> variance; +<a class="jxr_linenumber" name="L182" href="#L182">182</a> } +<a class="jxr_linenumber" name="L183" href="#L183">183</a> +<a class="jxr_linenumber" name="L184" href="#L184">184</a> <em class="jxr_javadoccomment">/**</em> +<a class="jxr_linenumber" name="L185" href="#L185">185</a> <em class="jxr_javadoccomment"> * {@inheritDoc}</em> +<a class="jxr_linenumber" name="L186" href="#L186">186</a> <em class="jxr_javadoccomment"> *</em> +<a class="jxr_linenumber" name="L187" href="#L187">187</a> <em class="jxr_javadoccomment"> * <p>The lower bound of the support is always 0.</em> +<a class="jxr_linenumber" name="L188" href="#L188">188</a> <em class="jxr_javadoccomment"> *</em> +<a class="jxr_linenumber" name="L189" href="#L189">189</a> <em class="jxr_javadoccomment"> * @return 0.</em> +<a class="jxr_linenumber" name="L190" href="#L190">190</a> <em class="jxr_javadoccomment"> */</em> +<a class="jxr_linenumber" name="L191" href="#L191">191</a> @Override +<a class="jxr_linenumber" name="L192" href="#L192">192</a> <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">double</strong> getSupportLowerBound() { +<a class="jxr_linenumber" name="L193" href="#L193">193</a> <strong class="jxr_keyword">return</strong> SUPPORT_LO; +<a class="jxr_linenumber" name="L194" href="#L194">194</a> } +<a class="jxr_linenumber" name="L195" href="#L195">195</a> +<a class="jxr_linenumber" name="L196" href="#L196">196</a> <em class="jxr_javadoccomment">/**</em> +<a class="jxr_linenumber" name="L197" href="#L197">197</a> <em class="jxr_javadoccomment"> * {@inheritDoc}</em> +<a class="jxr_linenumber" name="L198" href="#L198">198</a> <em class="jxr_javadoccomment"> *</em> +<a class="jxr_linenumber" name="L199" href="#L199">199</a> <em class="jxr_javadoccomment"> * <p>The upper bound of the support is always positive infinity.</em> +<a class="jxr_linenumber" name="L200" href="#L200">200</a> <em class="jxr_javadoccomment"> *</em> +<a class="jxr_linenumber" name="L201" href="#L201">201</a> <em class="jxr_javadoccomment"> * @return {@link Double#POSITIVE_INFINITY positive infinity}.</em> +<a class="jxr_linenumber" name="L202" href="#L202">202</a> <em class="jxr_javadoccomment"> */</em> +<a class="jxr_linenumber" name="L203" href="#L203">203</a> @Override +<a class="jxr_linenumber" name="L204" href="#L204">204</a> <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">double</strong> getSupportUpperBound() { +<a class="jxr_linenumber" name="L205" href="#L205">205</a> <strong class="jxr_keyword">return</strong> SUPPORT_HI; +<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> @Override +<a class="jxr_linenumber" name="L209" href="#L209">209</a> <strong class="jxr_keyword">public</strong> Sampler createSampler(UniformRandomProvider rng) { +<a class="jxr_linenumber" name="L210" href="#L210">210</a> <em class="jxr_comment">// Generate using a related Gamma distribution</em> +<a class="jxr_linenumber" name="L211" href="#L211">211</a> <em class="jxr_comment">// See https://en.wikipedia.org/wiki/Nakagami_distribution#Generation</em> +<a class="jxr_linenumber" name="L212" href="#L212">212</a> <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> shape = mu; +<a class="jxr_linenumber" name="L213" href="#L213">213</a> <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> scale = omega / mu; +<a class="jxr_linenumber" name="L214" href="#L214">214</a> <strong class="jxr_keyword">final</strong> SharedStateContinuousSampler sampler = +<a class="jxr_linenumber" name="L215" href="#L215">215</a> AhrensDieterMarsagliaTsangGammaSampler.of(rng, shape, scale); +<a class="jxr_linenumber" name="L216" href="#L216">216</a> <strong class="jxr_keyword">return</strong> () -> Math.sqrt(sampler.sample()); +<a class="jxr_linenumber" name="L217" href="#L217">217</a> } +<a class="jxr_linenumber" name="L218" href="#L218">218</a> } +</pre> +<hr/> +<div id="footer">Copyright © 2018–2022 <a href="https://www.apache.org/";>The Apache Software Foundation</a>. All rights reserved.</div> +</body> +</html> Added: dev/commons/statistics/1.0-RC1/site/xref/org/apache/commons/statistics/distribution/NormalDistribution.html ============================================================================== --- dev/commons/statistics/1.0-RC1/site/xref/org/apache/commons/statistics/distribution/NormalDistribution.html (added) +++ dev/commons/statistics/1.0-RC1/site/xref/org/apache/commons/statistics/distribution/NormalDistribution.html Thu Dec 1 16:47:12 2022 @@ -0,0 +1,226 @@ +<!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>NormalDistribution xref</title> +<link type="text/css" rel="stylesheet" href="../../../../../stylesheet.css" /> +</head> +<body> +<div id="overview"><a href="../../../../../../apidocs/org/apache/commons/statistics/distribution/NormalDistribution.html">View Javadoc</a></div><pre> +<a class="jxr_linenumber" name="L1" href="#L1">1</a> <em class="jxr_comment">/*</em> +<a class="jxr_linenumber" name="L2" href="#L2">2</a> <em class="jxr_comment"> * Licensed to the Apache Software Foundation (ASF) under one or more</em> +<a class="jxr_linenumber" name="L3" href="#L3">3</a> <em class="jxr_comment"> * contributor license agreements. See the NOTICE file distributed with</em> +<a class="jxr_linenumber" name="L4" href="#L4">4</a> <em class="jxr_comment"> * this work for additional information regarding copyright ownership.</em> +<a class="jxr_linenumber" name="L5" href="#L5">5</a> <em class="jxr_comment"> * The ASF licenses this file to You under the Apache License, Version 2.0</em> +<a class="jxr_linenumber" name="L6" href="#L6">6</a> <em class="jxr_comment"> * (the "License"); you may not use this file except in compliance with</em> +<a class="jxr_linenumber" name="L7" href="#L7">7</a> <em class="jxr_comment"> * the License. You may obtain a copy of the License at</em> +<a class="jxr_linenumber" name="L8" href="#L8">8</a> <em class="jxr_comment"> *</em> +<a class="jxr_linenumber" name="L9" href="#L9">9</a> <em class="jxr_comment"> * <a href="http://www.apache.org/licenses/LICENSE-2.0"; target="alexandria_uri">http://www.apache.org/licenses/LICENSE-2.0</a></em> +<a class="jxr_linenumber" name="L10" href="#L10">10</a> <em class="jxr_comment"> *</em> +<a class="jxr_linenumber" name="L11" href="#L11">11</a> <em class="jxr_comment"> * Unless required by applicable law or agreed to in writing, software</em> +<a class="jxr_linenumber" name="L12" href="#L12">12</a> <em class="jxr_comment"> * distributed under the License is distributed on an "AS IS" BASIS,</em> +<a class="jxr_linenumber" name="L13" href="#L13">13</a> <em class="jxr_comment"> * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.</em> +<a class="jxr_linenumber" name="L14" href="#L14">14</a> <em class="jxr_comment"> * See the License for the specific language governing permissions and</em> +<a class="jxr_linenumber" name="L15" href="#L15">15</a> <em class="jxr_comment"> * limitations under the License.</em> +<a class="jxr_linenumber" name="L16" href="#L16">16</a> <em class="jxr_comment"> */</em> +<a class="jxr_linenumber" name="L17" href="#L17">17</a> +<a class="jxr_linenumber" name="L18" href="#L18">18</a> <strong class="jxr_keyword">package</strong> org.apache.commons.statistics.distribution; +<a class="jxr_linenumber" name="L19" href="#L19">19</a> +<a class="jxr_linenumber" name="L20" href="#L20">20</a> <strong class="jxr_keyword">import</strong> org.apache.commons.numbers.gamma.Erfc; +<a class="jxr_linenumber" name="L21" href="#L21">21</a> <strong class="jxr_keyword">import</strong> org.apache.commons.numbers.gamma.InverseErfc; +<a class="jxr_linenumber" name="L22" href="#L22">22</a> <strong class="jxr_keyword">import</strong> org.apache.commons.numbers.gamma.ErfDifference; +<a class="jxr_linenumber" name="L23" href="#L23">23</a> <strong class="jxr_keyword">import</strong> org.apache.commons.rng.UniformRandomProvider; +<a class="jxr_linenumber" name="L24" href="#L24">24</a> <strong class="jxr_keyword">import</strong> org.apache.commons.rng.sampling.distribution.GaussianSampler; +<a class="jxr_linenumber" name="L25" href="#L25">25</a> <strong class="jxr_keyword">import</strong> org.apache.commons.rng.sampling.distribution.ZigguratSampler; +<a class="jxr_linenumber" name="L26" href="#L26">26</a> +<a class="jxr_linenumber" name="L27" href="#L27">27</a> <em class="jxr_javadoccomment">/**</em> +<a class="jxr_linenumber" name="L28" href="#L28">28</a> <em class="jxr_javadoccomment"> * Implementation of the normal (Gaussian) 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>The probability density function of \( X \) is:</em> +<a class="jxr_linenumber" name="L31" href="#L31">31</a> <em class="jxr_javadoccomment"> *</em> +<a class="jxr_linenumber" name="L32" href="#L32">32</a> <em class="jxr_javadoccomment"> * <p>\[ f(x; \mu, \sigma) = \frac 1 {\sigma\sqrt{2\pi}} e^{-{\frac 1 2}\left( \frac{x-\mu}{\sigma} \right)^2 } \]</em> +<a class="jxr_linenumber" name="L33" href="#L33">33</a> <em class="jxr_javadoccomment"> *</em> +<a class="jxr_linenumber" name="L34" href="#L34">34</a> <em class="jxr_javadoccomment"> * <p>for \( \mu \) the mean,</em> +<a class="jxr_linenumber" name="L35" href="#L35">35</a> <em class="jxr_javadoccomment"> * \( \sigma &gt; 0 \) the standard deviation, and</em> +<a class="jxr_linenumber" name="L36" href="#L36">36</a> <em class="jxr_javadoccomment"> * \( x \in (-\infty, \infty) \).</em> +<a class="jxr_linenumber" name="L37" href="#L37">37</a> <em class="jxr_javadoccomment"> *</em> +<a class="jxr_linenumber" name="L38" href="#L38">38</a> <em class="jxr_javadoccomment"> * @see <a href="<a href="https://en.wikipedia.org/wiki/Normal_distribution"; target="alexandria_uri">https://en.wikipedia.org/wiki/Normal_distribution</a>">Normal distribution (Wikipedia)</a></em> +<a class="jxr_linenumber" name="L39" href="#L39">39</a> <em class="jxr_javadoccomment"> * @see <a href="<a href="https://mathworld.wolfram.com/NormalDistribution.html"; target="alexandria_uri">https://mathworld.wolfram.com/NormalDistribution.html</a>">Normal distribution (MathWorld)</a></em> +<a class="jxr_linenumber" name="L40" href="#L40">40</a> <em class="jxr_javadoccomment"> */</em> +<a class="jxr_linenumber" name="L41" href="#L41">41</a> <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">class</strong> <a name="NormalDistribution" href="../../../../../org/apache/commons/statistics/distribution/NormalDistribution.html#NormalDistribution">NormalDistribution</a> <strong class="jxr_keyword">extends</strong> <a name="AbstractContinuousDistribution" href="../../../../../org/apache/commons/statistics/distribution/AbstractContinuousDistribution.html#AbstractContinuousDistribution">AbstractContinuousDistribution</a> { +<a class="jxr_linenumber" name="L42" href="#L42">42</a> <em class="jxr_javadoccomment">/** 0.5 * ln(2 * pi). Computed to 25-digits precision. */</em> +<a class="jxr_linenumber" name="L43" href="#L43">43</a> <strong class="jxr_keyword">private</strong> <strong class="jxr_keyword">static</strong> <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> HALF_LOG_TWO_PI = 0.9189385332046727417803297; +<a class="jxr_linenumber" name="L44" href="#L44">44</a> +<a class="jxr_linenumber" name="L45" href="#L45">45</a> <em class="jxr_javadoccomment">/** Mean of this distribution. */</em> +<a class="jxr_linenumber" name="L46" href="#L46">46</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="L47" href="#L47">47</a> <em class="jxr_javadoccomment">/** Standard deviation of this distribution. */</em> +<a class="jxr_linenumber" name="L48" href="#L48">48</a> <strong class="jxr_keyword">private</strong> <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> standardDeviation; +<a class="jxr_linenumber" name="L49" href="#L49">49</a> <em class="jxr_javadoccomment">/** The value of {@code log(sd) + 0.5*log(2*pi)} stored for faster computation. */</em> +<a class="jxr_linenumber" name="L50" href="#L50">50</a> <strong class="jxr_keyword">private</strong> <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> logStandardDeviationPlusHalfLog2Pi; +<a class="jxr_linenumber" name="L51" href="#L51">51</a> <em class="jxr_javadoccomment">/**</em> +<a class="jxr_linenumber" name="L52" href="#L52">52</a> <em class="jxr_javadoccomment"> * Standard deviation multiplied by sqrt(2).</em> +<a class="jxr_linenumber" name="L53" href="#L53">53</a> <em class="jxr_javadoccomment"> * This is used to avoid a double division when computing the value passed to the</em> +<a class="jxr_linenumber" name="L54" href="#L54">54</a> <em class="jxr_javadoccomment"> * error function:</em> +<a class="jxr_linenumber" name="L55" href="#L55">55</a> <em class="jxr_javadoccomment"> * <pre></em> +<a class="jxr_linenumber" name="L56" href="#L56">56</a> <em class="jxr_javadoccomment"> * ((x - u) / sd) / sqrt(2) == (x - u) / (sd * sqrt(2)).</em> +<a class="jxr_linenumber" name="L57" href="#L57">57</a> <em class="jxr_javadoccomment"> * </pre></em> +<a class="jxr_linenumber" name="L58" href="#L58">58</a> <em class="jxr_javadoccomment"> * <p>Note: Implementations may first normalise x and then divide by sqrt(2) resulting</em> +<a class="jxr_linenumber" name="L59" href="#L59">59</a> <em class="jxr_javadoccomment"> * in differences due to rounding error that show increasingly large relative</em> +<a class="jxr_linenumber" name="L60" href="#L60">60</a> <em class="jxr_javadoccomment"> * differences as the error function computes close to 0 in the extreme tail.</em> +<a class="jxr_linenumber" name="L61" href="#L61">61</a> <em class="jxr_javadoccomment"> */</em> +<a class="jxr_linenumber" name="L62" href="#L62">62</a> <strong class="jxr_keyword">private</strong> <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> sdSqrt2; +<a class="jxr_linenumber" name="L63" href="#L63">63</a> <em class="jxr_javadoccomment">/**</em> +<a class="jxr_linenumber" name="L64" href="#L64">64</a> <em class="jxr_javadoccomment"> * Standard deviation multiplied by sqrt(2 pi). Computed to high precision.</em> +<a class="jxr_linenumber" name="L65" href="#L65">65</a> <em class="jxr_javadoccomment"> */</em> +<a class="jxr_linenumber" name="L66" href="#L66">66</a> <strong class="jxr_keyword">private</strong> <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> sdSqrt2pi; +<a class="jxr_linenumber" name="L67" href="#L67">67</a> +<a class="jxr_linenumber" name="L68" href="#L68">68</a> <em class="jxr_javadoccomment">/**</em> +<a class="jxr_linenumber" name="L69" href="#L69">69</a> <em class="jxr_javadoccomment"> * @param mean Mean for this distribution.</em> +<a class="jxr_linenumber" name="L70" href="#L70">70</a> <em class="jxr_javadoccomment"> * @param sd Standard deviation for this distribution.</em> +<a class="jxr_linenumber" name="L71" href="#L71">71</a> <em class="jxr_javadoccomment"> */</em> +<a class="jxr_linenumber" name="L72" href="#L72">72</a> <strong class="jxr_keyword">private</strong> <a name="NormalDistribution" href="../../../../../org/apache/commons/statistics/distribution/NormalDistribution.html#NormalDistribution">NormalDistribution</a>(<strong class="jxr_keyword">double</strong> mean, +<a class="jxr_linenumber" name="L73" href="#L73">73</a> <strong class="jxr_keyword">double</strong> sd) { +<a class="jxr_linenumber" name="L74" href="#L74">74</a> <strong class="jxr_keyword">this</strong>.mean = mean; +<a class="jxr_linenumber" name="L75" href="#L75">75</a> standardDeviation = sd; +<a class="jxr_linenumber" name="L76" href="#L76">76</a> logStandardDeviationPlusHalfLog2Pi = Math.log(sd) + HALF_LOG_TWO_PI; +<a class="jxr_linenumber" name="L77" href="#L77">77</a> <em class="jxr_comment">// Minimise rounding error by computing sqrt(2 * sd * sd) exactly.</em> +<a class="jxr_linenumber" name="L78" href="#L78">78</a> <em class="jxr_comment">// Compute using extended precision with care to avoid over/underflow.</em> +<a class="jxr_linenumber" name="L79" href="#L79">79</a> sdSqrt2 = ExtendedPrecision.sqrt2xx(sd); +<a class="jxr_linenumber" name="L80" href="#L80">80</a> <em class="jxr_comment">// Compute sd * sqrt(2 * pi)</em> +<a class="jxr_linenumber" name="L81" href="#L81">81</a> sdSqrt2pi = ExtendedPrecision.xsqrt2pi(sd); +<a class="jxr_linenumber" name="L82" href="#L82">82</a> } +<a class="jxr_linenumber" name="L83" href="#L83">83</a> +<a class="jxr_linenumber" name="L84" href="#L84">84</a> <em class="jxr_javadoccomment">/**</em> +<a class="jxr_linenumber" name="L85" href="#L85">85</a> <em class="jxr_javadoccomment"> * Creates a normal distribution.</em> +<a class="jxr_linenumber" name="L86" href="#L86">86</a> <em class="jxr_javadoccomment"> *</em> +<a class="jxr_linenumber" name="L87" href="#L87">87</a> <em class="jxr_javadoccomment"> * @param mean Mean for this distribution.</em> +<a class="jxr_linenumber" name="L88" href="#L88">88</a> <em class="jxr_javadoccomment"> * @param sd Standard deviation for this distribution.</em> +<a class="jxr_linenumber" name="L89" href="#L89">89</a> <em class="jxr_javadoccomment"> * @return the distribution</em> +<a class="jxr_linenumber" name="L90" href="#L90">90</a> <em class="jxr_javadoccomment"> * @throws IllegalArgumentException if {@code sd <= 0}.</em> +<a class="jxr_linenumber" name="L91" href="#L91">91</a> <em class="jxr_javadoccomment"> */</em> +<a class="jxr_linenumber" name="L92" href="#L92">92</a> <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">static</strong> <a name="NormalDistribution" href="../../../../../org/apache/commons/statistics/distribution/NormalDistribution.html#NormalDistribution">NormalDistribution</a> of(<strong class="jxr_keyword">double</strong> mean, +<a class="jxr_linenumber" name="L93" href="#L93">93</a> <strong class="jxr_keyword">double</strong> sd) { +<a class="jxr_linenumber" name="L94" href="#L94">94</a> <strong class="jxr_keyword">if</strong> (sd > 0) { +<a class="jxr_linenumber" name="L95" href="#L95">95</a> <strong class="jxr_keyword">return</strong> <strong class="jxr_keyword">new</strong> <a name="NormalDistribution" href="../../../../../org/apache/commons/statistics/distribution/NormalDistribution.html#NormalDistribution">NormalDistribution</a>(mean, sd); +<a class="jxr_linenumber" name="L96" href="#L96">96</a> } +<a class="jxr_linenumber" name="L97" href="#L97">97</a> <em class="jxr_comment">// zero, negative or nan</em> +<a class="jxr_linenumber" name="L98" href="#L98">98</a> <strong class="jxr_keyword">throw</strong> <strong class="jxr_keyword">new</strong> <a name="DistributionException" href="../../../../../org/apache/commons/statistics/distribution/DistributionException.html#DistributionException">DistributionException</a>(DistributionException.NOT_STRICTLY_POSITIVE, sd); +<a class="jxr_linenumber" name="L99" href="#L99">99</a> } +<a class="jxr_linenumber" name="L100" href="#L100">100</a> +<a class="jxr_linenumber" name="L101" href="#L101">101</a> <em class="jxr_javadoccomment">/**</em> +<a class="jxr_linenumber" name="L102" href="#L102">102</a> <em class="jxr_javadoccomment"> * Gets the standard deviation parameter of this distribution.</em> +<a class="jxr_linenumber" name="L103" href="#L103">103</a> <em class="jxr_javadoccomment"> *</em> +<a class="jxr_linenumber" name="L104" href="#L104">104</a> <em class="jxr_javadoccomment"> * @return the standard deviation.</em> +<a class="jxr_linenumber" name="L105" href="#L105">105</a> <em class="jxr_javadoccomment"> */</em> +<a class="jxr_linenumber" name="L106" href="#L106">106</a> <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">double</strong> getStandardDeviation() { +<a class="jxr_linenumber" name="L107" href="#L107">107</a> <strong class="jxr_keyword">return</strong> standardDeviation; +<a class="jxr_linenumber" name="L108" href="#L108">108</a> } +<a class="jxr_linenumber" name="L109" href="#L109">109</a> +<a class="jxr_linenumber" name="L110" href="#L110">110</a> <em class="jxr_javadoccomment">/** {@inheritDoc} */</em> +<a class="jxr_linenumber" name="L111" href="#L111">111</a> @Override +<a class="jxr_linenumber" name="L112" href="#L112">112</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="L113" href="#L113">113</a> <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> z = (x - mean) / standardDeviation; +<a class="jxr_linenumber" name="L114" href="#L114">114</a> <strong class="jxr_keyword">return</strong> ExtendedPrecision.expmhxx(z) / sdSqrt2pi; +<a class="jxr_linenumber" name="L115" href="#L115">115</a> } +<a class="jxr_linenumber" name="L116" href="#L116">116</a> +<a class="jxr_linenumber" name="L117" href="#L117">117</a> <em class="jxr_javadoccomment">/** {@inheritDoc} */</em> +<a class="jxr_linenumber" name="L118" href="#L118">118</a> @Override +<a class="jxr_linenumber" name="L119" href="#L119">119</a> <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">double</strong> probability(<strong class="jxr_keyword">double</strong> x0, +<a class="jxr_linenumber" name="L120" href="#L120">120</a> <strong class="jxr_keyword">double</strong> x1) { +<a class="jxr_linenumber" name="L121" href="#L121">121</a> <strong class="jxr_keyword">if</strong> (x0 > x1) { +<a class="jxr_linenumber" name="L122" href="#L122">122</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, +<a class="jxr_linenumber" name="L123" href="#L123">123</a> x0, x1); +<a class="jxr_linenumber" name="L124" href="#L124">124</a> } +<a class="jxr_linenumber" name="L125" href="#L125">125</a> <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> v0 = (x0 - mean) / sdSqrt2; +<a class="jxr_linenumber" name="L126" href="#L126">126</a> <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> v1 = (x1 - mean) / sdSqrt2; +<a class="jxr_linenumber" name="L127" href="#L127">127</a> <strong class="jxr_keyword">return</strong> 0.5 * ErfDifference.value(v0, v1); +<a class="jxr_linenumber" name="L128" href="#L128">128</a> } +<a class="jxr_linenumber" name="L129" href="#L129">129</a> +<a class="jxr_linenumber" name="L130" href="#L130">130</a> <em class="jxr_javadoccomment">/** {@inheritDoc} */</em> +<a class="jxr_linenumber" name="L131" href="#L131">131</a> @Override +<a class="jxr_linenumber" name="L132" href="#L132">132</a> <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">double</strong> logDensity(<strong class="jxr_keyword">double</strong> x) { +<a class="jxr_linenumber" name="L133" href="#L133">133</a> <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> z = (x - mean) / standardDeviation; +<a class="jxr_linenumber" name="L134" href="#L134">134</a> <strong class="jxr_keyword">return</strong> -0.5 * z * z - logStandardDeviationPlusHalfLog2Pi; +<a class="jxr_linenumber" name="L135" href="#L135">135</a> } +<a class="jxr_linenumber" name="L136" href="#L136">136</a> +<a class="jxr_linenumber" name="L137" href="#L137">137</a> <em class="jxr_javadoccomment">/** {@inheritDoc} */</em> +<a class="jxr_linenumber" name="L138" href="#L138">138</a> @Override +<a class="jxr_linenumber" name="L139" href="#L139">139</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="L140" href="#L140">140</a> <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> dev = x - mean; +<a class="jxr_linenumber" name="L141" href="#L141">141</a> <strong class="jxr_keyword">return</strong> 0.5 * Erfc.value(-dev / sdSqrt2); +<a class="jxr_linenumber" name="L142" href="#L142">142</a> } +<a class="jxr_linenumber" name="L143" href="#L143">143</a> +<a class="jxr_linenumber" name="L144" href="#L144">144</a> <em class="jxr_javadoccomment">/** {@inheritDoc} */</em> +<a class="jxr_linenumber" name="L145" href="#L145">145</a> @Override +<a class="jxr_linenumber" name="L146" href="#L146">146</a> <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">double</strong> survivalProbability(<strong class="jxr_keyword">double</strong> x) { +<a class="jxr_linenumber" name="L147" href="#L147">147</a> <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> dev = x - mean; +<a class="jxr_linenumber" name="L148" href="#L148">148</a> <strong class="jxr_keyword">return</strong> 0.5 * Erfc.value(dev / sdSqrt2); +<a class="jxr_linenumber" name="L149" href="#L149">149</a> } +<a class="jxr_linenumber" name="L150" href="#L150">150</a> +<a class="jxr_linenumber" name="L151" href="#L151">151</a> <em class="jxr_javadoccomment">/** {@inheritDoc} */</em> +<a class="jxr_linenumber" name="L152" href="#L152">152</a> @Override +<a class="jxr_linenumber" name="L153" href="#L153">153</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="L154" href="#L154">154</a> ArgumentUtils.checkProbability(p); +<a class="jxr_linenumber" name="L155" href="#L155">155</a> <strong class="jxr_keyword">return</strong> mean - sdSqrt2 * InverseErfc.value(2 * p); +<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> <em class="jxr_javadoccomment">/** {@inheritDoc} */</em> +<a class="jxr_linenumber" name="L159" href="#L159">159</a> @Override +<a class="jxr_linenumber" name="L160" href="#L160">160</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="L161" href="#L161">161</a> ArgumentUtils.checkProbability(p); +<a class="jxr_linenumber" name="L162" href="#L162">162</a> <strong class="jxr_keyword">return</strong> mean + sdSqrt2 * InverseErfc.value(2 * p); +<a class="jxr_linenumber" name="L163" href="#L163">163</a> } +<a class="jxr_linenumber" name="L164" href="#L164">164</a> +<a class="jxr_linenumber" name="L165" href="#L165">165</a> <em class="jxr_javadoccomment">/** {@inheritDoc} */</em> +<a class="jxr_linenumber" name="L166" href="#L166">166</a> @Override +<a class="jxr_linenumber" name="L167" href="#L167">167</a> <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">double</strong> getMean() { +<a class="jxr_linenumber" name="L168" href="#L168">168</a> <strong class="jxr_keyword">return</strong> mean; +<a class="jxr_linenumber" name="L169" href="#L169">169</a> } +<a class="jxr_linenumber" name="L170" href="#L170">170</a> +<a class="jxr_linenumber" name="L171" href="#L171">171</a> <em class="jxr_javadoccomment">/**</em> +<a class="jxr_linenumber" name="L172" href="#L172">172</a> <em class="jxr_javadoccomment"> * {@inheritDoc}</em> +<a class="jxr_linenumber" name="L173" href="#L173">173</a> <em class="jxr_javadoccomment"> *</em> +<a class="jxr_linenumber" name="L174" href="#L174">174</a> <em class="jxr_javadoccomment"> * <p>For standard deviation parameter \( \sigma \), the variance is \( \sigma^2 \).</em> +<a class="jxr_linenumber" name="L175" href="#L175">175</a> <em class="jxr_javadoccomment"> */</em> +<a class="jxr_linenumber" name="L176" href="#L176">176</a> @Override +<a class="jxr_linenumber" name="L177" href="#L177">177</a> <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">double</strong> getVariance() { +<a class="jxr_linenumber" name="L178" href="#L178">178</a> <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> s = getStandardDeviation(); +<a class="jxr_linenumber" name="L179" href="#L179">179</a> <strong class="jxr_keyword">return</strong> s * s; +<a class="jxr_linenumber" name="L180" href="#L180">180</a> } +<a class="jxr_linenumber" name="L181" href="#L181">181</a> +<a class="jxr_linenumber" name="L182" href="#L182">182</a> <em class="jxr_javadoccomment">/**</em> +<a class="jxr_linenumber" name="L183" href="#L183">183</a> <em class="jxr_javadoccomment"> * {@inheritDoc}</em> +<a class="jxr_linenumber" name="L184" href="#L184">184</a> <em class="jxr_javadoccomment"> *</em> +<a class="jxr_linenumber" name="L185" href="#L185">185</a> <em class="jxr_javadoccomment"> * <p>The lower bound of the support is always negative infinity.</em> +<a class="jxr_linenumber" name="L186" href="#L186">186</a> <em class="jxr_javadoccomment"> *</em> +<a class="jxr_linenumber" name="L187" href="#L187">187</a> <em class="jxr_javadoccomment"> * @return {@link Double#NEGATIVE_INFINITY negative infinity}.</em> +<a class="jxr_linenumber" name="L188" href="#L188">188</a> <em class="jxr_javadoccomment"> */</em> +<a class="jxr_linenumber" name="L189" href="#L189">189</a> @Override +<a class="jxr_linenumber" name="L190" href="#L190">190</a> <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">double</strong> getSupportLowerBound() { +<a class="jxr_linenumber" name="L191" href="#L191">191</a> <strong class="jxr_keyword">return</strong> Double.NEGATIVE_INFINITY; +<a class="jxr_linenumber" name="L192" href="#L192">192</a> } +<a class="jxr_linenumber" name="L193" href="#L193">193</a> +<a class="jxr_linenumber" name="L194" href="#L194">194</a> <em class="jxr_javadoccomment">/**</em> +<a class="jxr_linenumber" name="L195" href="#L195">195</a> <em class="jxr_javadoccomment"> * {@inheritDoc}</em> +<a class="jxr_linenumber" name="L196" href="#L196">196</a> <em class="jxr_javadoccomment"> *</em> +<a class="jxr_linenumber" name="L197" href="#L197">197</a> <em class="jxr_javadoccomment"> * <p>The upper bound of the support is always positive infinity.</em> +<a class="jxr_linenumber" name="L198" href="#L198">198</a> <em class="jxr_javadoccomment"> *</em> +<a class="jxr_linenumber" name="L199" href="#L199">199</a> <em class="jxr_javadoccomment"> * @return {@link Double#POSITIVE_INFINITY positive infinity}.</em> +<a class="jxr_linenumber" name="L200" href="#L200">200</a> <em class="jxr_javadoccomment"> */</em> +<a class="jxr_linenumber" name="L201" href="#L201">201</a> @Override +<a class="jxr_linenumber" name="L202" href="#L202">202</a> <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">double</strong> getSupportUpperBound() { +<a class="jxr_linenumber" name="L203" href="#L203">203</a> <strong class="jxr_keyword">return</strong> Double.POSITIVE_INFINITY; +<a class="jxr_linenumber" name="L204" href="#L204">204</a> } +<a class="jxr_linenumber" name="L205" href="#L205">205</a> +<a class="jxr_linenumber" name="L206" href="#L206">206</a> <em class="jxr_javadoccomment">/** {@inheritDoc} */</em> +<a class="jxr_linenumber" name="L207" href="#L207">207</a> @Override +<a class="jxr_linenumber" name="L208" href="#L208">208</a> <strong class="jxr_keyword">public</strong> ContinuousDistribution.Sampler createSampler(<strong class="jxr_keyword">final</strong> UniformRandomProvider rng) { +<a class="jxr_linenumber" name="L209" href="#L209">209</a> <em class="jxr_comment">// Gaussian distribution sampler.</em> +<a class="jxr_linenumber" name="L210" href="#L210">210</a> <strong class="jxr_keyword">return</strong> GaussianSampler.of(ZigguratSampler.NormalizedGaussian.of(rng), +<a class="jxr_linenumber" name="L211" href="#L211">211</a> mean, standardDeviation)::sample; +<a class="jxr_linenumber" name="L212" href="#L212">212</a> } +<a class="jxr_linenumber" name="L213" href="#L213">213</a> } +</pre> +<hr/> +<div id="footer">Copyright © 2018–2022 <a href="https://www.apache.org/";>The Apache Software Foundation</a>. All rights reserved.</div> +</body> +</html>
