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From l..@apache.org
Subject svn commit: r951633 [31/49] - in /websites/production/commons/content/proper/commons-math: xref-test/ xref-test/org/apache/commons/math3/ xref-test/org/apache/commons/math3/analysis/ xref-test/org/apache/commons/math3/analysis/differentiation/ xref-tes...
Date Sun, 17 May 2015 17:05:54 GMT
Modified: websites/production/commons/content/proper/commons-math/xref/org/apache/commons/math3/distribution/BetaDistribution.html
==============================================================================
--- websites/production/commons/content/proper/commons-math/xref/org/apache/commons/math3/distribution/BetaDistribution.html (original)
+++ websites/production/commons/content/proper/commons-math/xref/org/apache/commons/math3/distribution/BetaDistribution.html Sun May 17 17:05:50 2015
@@ -31,250 +31,387 @@
 <a class="jxr_linenumber" name="L23" href="#L23">23</a>  <strong class="jxr_keyword">import</strong> org.apache.commons.math3.special.Beta;
 <a class="jxr_linenumber" name="L24" href="#L24">24</a>  <strong class="jxr_keyword">import</strong> org.apache.commons.math3.special.Gamma;
 <a class="jxr_linenumber" name="L25" href="#L25">25</a>  <strong class="jxr_keyword">import</strong> org.apache.commons.math3.util.FastMath;
-<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"> * Implements the Beta 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"> * @see &lt;a href="<a href="http://en.wikipedia.org/wiki/Beta_distribution" target="alexandria_uri">http://en.wikipedia.org/wiki/Beta_distribution</a>"&gt;Beta distribution&lt;/a&gt;</em>
-<a class="jxr_linenumber" name="L31" href="#L31">31</a>  <em class="jxr_javadoccomment"> * @since 2.0 (changed to concrete class in 3.0)</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">class</strong> <a href="../../../../../org/apache/commons/math3/distribution/BetaDistribution.html">BetaDistribution</a> <strong class="jxr_keyword">extends</strong> <a href="../../../../../org/apache/commons/math3/distribution/AbstractRealDistribution.html">AbstractRealDistribution</a> {
-<a class="jxr_linenumber" name="L34" href="#L34">34</a>      <em class="jxr_javadoccomment">/**</em>
-<a class="jxr_linenumber" name="L35" href="#L35">35</a>  <em class="jxr_javadoccomment">     * Default inverse cumulative probability accuracy.</em>
-<a class="jxr_linenumber" name="L36" href="#L36">36</a>  <em class="jxr_javadoccomment">     * @since 2.1</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>      <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">static</strong> <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> DEFAULT_INVERSE_ABSOLUTE_ACCURACY = 1e-9;
-<a class="jxr_linenumber" name="L39" href="#L39">39</a>      <em class="jxr_javadoccomment">/** Serializable version identifier. */</em>
-<a class="jxr_linenumber" name="L40" href="#L40">40</a>      <strong class="jxr_keyword">private</strong> <strong class="jxr_keyword">static</strong> <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">long</strong> serialVersionUID = -1221965979403477668L;
-<a class="jxr_linenumber" name="L41" href="#L41">41</a>      <em class="jxr_javadoccomment">/** First shape parameter. */</em>
-<a class="jxr_linenumber" name="L42" href="#L42">42</a>      <strong class="jxr_keyword">private</strong> <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> alpha;
-<a class="jxr_linenumber" name="L43" href="#L43">43</a>      <em class="jxr_javadoccomment">/** Second shape parameter. */</em>
-<a class="jxr_linenumber" name="L44" href="#L44">44</a>      <strong class="jxr_keyword">private</strong> <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> beta;
-<a class="jxr_linenumber" name="L45" href="#L45">45</a>      <em class="jxr_javadoccomment">/** Normalizing factor used in density computations.</em>
-<a class="jxr_linenumber" name="L46" href="#L46">46</a>  <em class="jxr_javadoccomment">     * updated whenever alpha or beta are changed.</em>
-<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>      <strong class="jxr_keyword">private</strong> <strong class="jxr_keyword">double</strong> z;
-<a class="jxr_linenumber" name="L49" href="#L49">49</a>      <em class="jxr_javadoccomment">/** Inverse cumulative probability accuracy. */</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> solverAbsoluteAccuracy;
-<a class="jxr_linenumber" name="L51" href="#L51">51</a>  
-<a class="jxr_linenumber" name="L52" href="#L52">52</a>      <em class="jxr_javadoccomment">/**</em>
-<a class="jxr_linenumber" name="L53" href="#L53">53</a>  <em class="jxr_javadoccomment">     * Build a new instance.</em>
-<a class="jxr_linenumber" name="L54" href="#L54">54</a>  <em class="jxr_javadoccomment">     * &lt;p&gt;</em>
-<a class="jxr_linenumber" name="L55" href="#L55">55</a>  <em class="jxr_javadoccomment">     * &lt;b&gt;Note:&lt;/b&gt; this constructor will implicitly create an instance of</em>
-<a class="jxr_linenumber" name="L56" href="#L56">56</a>  <em class="jxr_javadoccomment">     * {@link Well19937c} as random generator to be used for sampling only (see</em>
-<a class="jxr_linenumber" name="L57" href="#L57">57</a>  <em class="jxr_javadoccomment">     * {@link #sample()} and {@link #sample(int)}). In case no sampling is</em>
-<a class="jxr_linenumber" name="L58" href="#L58">58</a>  <em class="jxr_javadoccomment">     * needed for the created distribution, it is advised to pass {@code null}</em>
-<a class="jxr_linenumber" name="L59" href="#L59">59</a>  <em class="jxr_javadoccomment">     * as random generator via the appropriate constructors to avoid the</em>
-<a class="jxr_linenumber" name="L60" href="#L60">60</a>  <em class="jxr_javadoccomment">     * additional initialisation overhead.</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>  <em class="jxr_javadoccomment">     * @param alpha First shape parameter (must be positive).</em>
-<a class="jxr_linenumber" name="L63" href="#L63">63</a>  <em class="jxr_javadoccomment">     * @param beta Second shape parameter (must be positive).</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">public</strong> <a href="../../../../../org/apache/commons/math3/distribution/BetaDistribution.html">BetaDistribution</a>(<strong class="jxr_keyword">double</strong> alpha, <strong class="jxr_keyword">double</strong> beta) {
-<a class="jxr_linenumber" name="L66" href="#L66">66</a>          <strong class="jxr_keyword">this</strong>(alpha, beta, DEFAULT_INVERSE_ABSOLUTE_ACCURACY);
-<a class="jxr_linenumber" name="L67" href="#L67">67</a>      }
-<a class="jxr_linenumber" name="L68" href="#L68">68</a>  
-<a class="jxr_linenumber" name="L69" href="#L69">69</a>      <em class="jxr_javadoccomment">/**</em>
-<a class="jxr_linenumber" name="L70" href="#L70">70</a>  <em class="jxr_javadoccomment">     * Build a new instance.</em>
-<a class="jxr_linenumber" name="L71" href="#L71">71</a>  <em class="jxr_javadoccomment">     * &lt;p&gt;</em>
-<a class="jxr_linenumber" name="L72" href="#L72">72</a>  <em class="jxr_javadoccomment">     * &lt;b&gt;Note:&lt;/b&gt; this constructor will implicitly create an instance of</em>
-<a class="jxr_linenumber" name="L73" href="#L73">73</a>  <em class="jxr_javadoccomment">     * {@link Well19937c} as random generator to be used for sampling only (see</em>
-<a class="jxr_linenumber" name="L74" href="#L74">74</a>  <em class="jxr_javadoccomment">     * {@link #sample()} and {@link #sample(int)}). In case no sampling is</em>
-<a class="jxr_linenumber" name="L75" href="#L75">75</a>  <em class="jxr_javadoccomment">     * needed for the created distribution, it is advised to pass {@code null}</em>
-<a class="jxr_linenumber" name="L76" href="#L76">76</a>  <em class="jxr_javadoccomment">     * as random generator via the appropriate constructors to avoid the</em>
-<a class="jxr_linenumber" name="L77" href="#L77">77</a>  <em class="jxr_javadoccomment">     * additional initialisation overhead.</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 alpha First shape parameter (must be positive).</em>
-<a class="jxr_linenumber" name="L80" href="#L80">80</a>  <em class="jxr_javadoccomment">     * @param beta Second shape parameter (must be positive).</em>
-<a class="jxr_linenumber" name="L81" href="#L81">81</a>  <em class="jxr_javadoccomment">     * @param inverseCumAccuracy Maximum absolute error in inverse</em>
-<a class="jxr_linenumber" name="L82" href="#L82">82</a>  <em class="jxr_javadoccomment">     * cumulative probability estimates (defaults to</em>
-<a class="jxr_linenumber" name="L83" href="#L83">83</a>  <em class="jxr_javadoccomment">     * {@link #DEFAULT_INVERSE_ABSOLUTE_ACCURACY}).</em>
-<a class="jxr_linenumber" name="L84" href="#L84">84</a>  <em class="jxr_javadoccomment">     * @since 2.1</em>
-<a class="jxr_linenumber" name="L85" href="#L85">85</a>  <em class="jxr_javadoccomment">     */</em>
-<a class="jxr_linenumber" name="L86" href="#L86">86</a>      <strong class="jxr_keyword">public</strong> <a href="../../../../../org/apache/commons/math3/distribution/BetaDistribution.html">BetaDistribution</a>(<strong class="jxr_keyword">double</strong> alpha, <strong class="jxr_keyword">double</strong> beta, <strong class="jxr_keyword">double</strong> inverseCumAccuracy) {
-<a class="jxr_linenumber" name="L87" href="#L87">87</a>          <strong class="jxr_keyword">this</strong>(<strong class="jxr_keyword">new</strong> <a href="../../../../../org/apache/commons/math3/random/Well19937c.html">Well19937c</a>(), alpha, beta, inverseCumAccuracy);
-<a class="jxr_linenumber" name="L88" href="#L88">88</a>      }
-<a class="jxr_linenumber" name="L89" href="#L89">89</a>  
-<a class="jxr_linenumber" name="L90" href="#L90">90</a>      <em class="jxr_javadoccomment">/**</em>
-<a class="jxr_linenumber" name="L91" href="#L91">91</a>  <em class="jxr_javadoccomment">     * Creates a &amp;beta; distribution.</em>
-<a class="jxr_linenumber" name="L92" href="#L92">92</a>  <em class="jxr_javadoccomment">     *</em>
-<a class="jxr_linenumber" name="L93" href="#L93">93</a>  <em class="jxr_javadoccomment">     * @param rng Random number generator.</em>
-<a class="jxr_linenumber" name="L94" href="#L94">94</a>  <em class="jxr_javadoccomment">     * @param alpha First shape parameter (must be positive).</em>
-<a class="jxr_linenumber" name="L95" href="#L95">95</a>  <em class="jxr_javadoccomment">     * @param beta Second shape parameter (must be positive).</em>
-<a class="jxr_linenumber" name="L96" href="#L96">96</a>  <em class="jxr_javadoccomment">     * @since 3.3</em>
-<a class="jxr_linenumber" name="L97" href="#L97">97</a>  <em class="jxr_javadoccomment">     */</em>
-<a class="jxr_linenumber" name="L98" href="#L98">98</a>      <strong class="jxr_keyword">public</strong> <a href="../../../../../org/apache/commons/math3/distribution/BetaDistribution.html">BetaDistribution</a>(<a href="../../../../../org/apache/commons/math3/random/RandomGenerator.html">RandomGenerator</a> rng, <strong class="jxr_keyword">double</strong> alpha, <strong class="jxr_keyword">double</strong> beta) {
-<a class="jxr_linenumber" name="L99" href="#L99">99</a>          <strong class="jxr_keyword">this</strong>(rng, alpha, beta, DEFAULT_INVERSE_ABSOLUTE_ACCURACY);
-<a class="jxr_linenumber" name="L100" href="#L100">100</a>     }
-<a class="jxr_linenumber" name="L101" href="#L101">101</a> 
-<a class="jxr_linenumber" name="L102" href="#L102">102</a>     <em class="jxr_javadoccomment">/**</em>
-<a class="jxr_linenumber" name="L103" href="#L103">103</a> <em class="jxr_javadoccomment">     * Creates a &amp;beta; distribution.</em>
-<a class="jxr_linenumber" name="L104" href="#L104">104</a> <em class="jxr_javadoccomment">     *</em>
-<a class="jxr_linenumber" name="L105" href="#L105">105</a> <em class="jxr_javadoccomment">     * @param rng Random number generator.</em>
-<a class="jxr_linenumber" name="L106" href="#L106">106</a> <em class="jxr_javadoccomment">     * @param alpha First shape parameter (must be positive).</em>
-<a class="jxr_linenumber" name="L107" href="#L107">107</a> <em class="jxr_javadoccomment">     * @param beta Second shape parameter (must be positive).</em>
-<a class="jxr_linenumber" name="L108" href="#L108">108</a> <em class="jxr_javadoccomment">     * @param inverseCumAccuracy Maximum absolute error in inverse</em>
-<a class="jxr_linenumber" name="L109" href="#L109">109</a> <em class="jxr_javadoccomment">     * cumulative probability estimates (defaults to</em>
-<a class="jxr_linenumber" name="L110" href="#L110">110</a> <em class="jxr_javadoccomment">     * {@link #DEFAULT_INVERSE_ABSOLUTE_ACCURACY}).</em>
-<a class="jxr_linenumber" name="L111" href="#L111">111</a> <em class="jxr_javadoccomment">     * @since 3.1</em>
-<a class="jxr_linenumber" name="L112" href="#L112">112</a> <em class="jxr_javadoccomment">     */</em>
-<a class="jxr_linenumber" name="L113" href="#L113">113</a>     <strong class="jxr_keyword">public</strong> <a href="../../../../../org/apache/commons/math3/distribution/BetaDistribution.html">BetaDistribution</a>(<a href="../../../../../org/apache/commons/math3/random/RandomGenerator.html">RandomGenerator</a> rng,
-<a class="jxr_linenumber" name="L114" href="#L114">114</a>                             <strong class="jxr_keyword">double</strong> alpha,
-<a class="jxr_linenumber" name="L115" href="#L115">115</a>                             <strong class="jxr_keyword">double</strong> beta,
-<a class="jxr_linenumber" name="L116" href="#L116">116</a>                             <strong class="jxr_keyword">double</strong> inverseCumAccuracy) {
-<a class="jxr_linenumber" name="L117" href="#L117">117</a>         <strong class="jxr_keyword">super</strong>(rng);
-<a class="jxr_linenumber" name="L118" href="#L118">118</a> 
-<a class="jxr_linenumber" name="L119" href="#L119">119</a>         <strong class="jxr_keyword">this</strong>.alpha = alpha;
-<a class="jxr_linenumber" name="L120" href="#L120">120</a>         <strong class="jxr_keyword">this</strong>.beta = beta;
-<a class="jxr_linenumber" name="L121" href="#L121">121</a>         z = Double.NaN;
-<a class="jxr_linenumber" name="L122" href="#L122">122</a>         solverAbsoluteAccuracy = inverseCumAccuracy;
-<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">/**</em>
-<a class="jxr_linenumber" name="L126" href="#L126">126</a> <em class="jxr_javadoccomment">     * Access the first shape parameter, {@code alpha}.</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> <em class="jxr_javadoccomment">     * @return the first shape parameter.</em>
-<a class="jxr_linenumber" name="L129" href="#L129">129</a> <em class="jxr_javadoccomment">     */</em>
-<a class="jxr_linenumber" name="L130" href="#L130">130</a>     <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">double</strong> getAlpha() {
-<a class="jxr_linenumber" name="L131" href="#L131">131</a>         <strong class="jxr_keyword">return</strong> alpha;
-<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">     * Access the second shape parameter, {@code beta}.</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">     * @return the second shape parameter.</em>
-<a class="jxr_linenumber" name="L138" href="#L138">138</a> <em class="jxr_javadoccomment">     */</em>
-<a class="jxr_linenumber" name="L139" href="#L139">139</a>     <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">double</strong> getBeta() {
-<a class="jxr_linenumber" name="L140" href="#L140">140</a>         <strong class="jxr_keyword">return</strong> beta;
-<a class="jxr_linenumber" name="L141" href="#L141">141</a>     }
-<a class="jxr_linenumber" name="L142" href="#L142">142</a> 
-<a class="jxr_linenumber" name="L143" href="#L143">143</a>     <em class="jxr_javadoccomment">/** Recompute the normalization factor. */</em>
-<a class="jxr_linenumber" name="L144" href="#L144">144</a>     <strong class="jxr_keyword">private</strong> <strong class="jxr_keyword">void</strong> recomputeZ() {
-<a class="jxr_linenumber" name="L145" href="#L145">145</a>         <strong class="jxr_keyword">if</strong> (Double.isNaN(z)) {
-<a class="jxr_linenumber" name="L146" href="#L146">146</a>             z = Gamma.logGamma(alpha) + Gamma.logGamma(beta) - Gamma.logGamma(alpha + beta);
-<a class="jxr_linenumber" name="L147" href="#L147">147</a>         }
-<a class="jxr_linenumber" name="L148" href="#L148">148</a>     }
-<a class="jxr_linenumber" name="L149" href="#L149">149</a> 
-<a class="jxr_linenumber" name="L150" href="#L150">150</a>     <em class="jxr_javadoccomment">/** {@inheritDoc} */</em>
-<a class="jxr_linenumber" name="L151" href="#L151">151</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="L152" href="#L152">152</a>         <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> logDensity = logDensity(x);
-<a class="jxr_linenumber" name="L153" href="#L153">153</a>         <strong class="jxr_keyword">return</strong> logDensity == Double.NEGATIVE_INFINITY ? 0 : FastMath.exp(logDensity);
-<a class="jxr_linenumber" name="L154" href="#L154">154</a>     }
-<a class="jxr_linenumber" name="L155" href="#L155">155</a> 
-<a class="jxr_linenumber" name="L156" href="#L156">156</a>     <em class="jxr_javadoccomment">/** {@inheritDoc} **/</em>
-<a class="jxr_linenumber" name="L157" href="#L157">157</a>     @Override
-<a class="jxr_linenumber" name="L158" href="#L158">158</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="L159" href="#L159">159</a>         recomputeZ();
-<a class="jxr_linenumber" name="L160" href="#L160">160</a>         <strong class="jxr_keyword">if</strong> (x &lt; 0 || x &gt; 1) {
-<a class="jxr_linenumber" name="L161" href="#L161">161</a>             <strong class="jxr_keyword">return</strong> Double.NEGATIVE_INFINITY;
-<a class="jxr_linenumber" name="L162" href="#L162">162</a>         } <strong class="jxr_keyword">else</strong> <strong class="jxr_keyword">if</strong> (x == 0) {
-<a class="jxr_linenumber" name="L163" href="#L163">163</a>             <strong class="jxr_keyword">if</strong> (alpha &lt; 1) {
-<a class="jxr_linenumber" name="L164" href="#L164">164</a>                 <strong class="jxr_keyword">throw</strong> <strong class="jxr_keyword">new</strong> <a href="../../../../../org/apache/commons/math3/exception/NumberIsTooSmallException.html">NumberIsTooSmallException</a>(LocalizedFormats.CANNOT_COMPUTE_BETA_DENSITY_AT_0_FOR_SOME_ALPHA, alpha, 1, false);
-<a class="jxr_linenumber" name="L165" href="#L165">165</a>             }
-<a class="jxr_linenumber" name="L166" href="#L166">166</a>             <strong class="jxr_keyword">return</strong> Double.NEGATIVE_INFINITY;
-<a class="jxr_linenumber" name="L167" href="#L167">167</a>         } <strong class="jxr_keyword">else</strong> <strong class="jxr_keyword">if</strong> (x == 1) {
-<a class="jxr_linenumber" name="L168" href="#L168">168</a>             <strong class="jxr_keyword">if</strong> (beta &lt; 1) {
-<a class="jxr_linenumber" name="L169" href="#L169">169</a>                 <strong class="jxr_keyword">throw</strong> <strong class="jxr_keyword">new</strong> <a href="../../../../../org/apache/commons/math3/exception/NumberIsTooSmallException.html">NumberIsTooSmallException</a>(LocalizedFormats.CANNOT_COMPUTE_BETA_DENSITY_AT_1_FOR_SOME_BETA, beta, 1, false);
-<a class="jxr_linenumber" name="L170" href="#L170">170</a>             }
-<a class="jxr_linenumber" name="L171" href="#L171">171</a>             <strong class="jxr_keyword">return</strong> Double.NEGATIVE_INFINITY;
-<a class="jxr_linenumber" name="L172" href="#L172">172</a>         } <strong class="jxr_keyword">else</strong> {
-<a class="jxr_linenumber" name="L173" href="#L173">173</a>             <strong class="jxr_keyword">double</strong> logX = FastMath.log(x);
-<a class="jxr_linenumber" name="L174" href="#L174">174</a>             <strong class="jxr_keyword">double</strong> log1mX = FastMath.log1p(-x);
-<a class="jxr_linenumber" name="L175" href="#L175">175</a>             <strong class="jxr_keyword">return</strong> (alpha - 1) * logX + (beta - 1) * log1mX - z;
-<a class="jxr_linenumber" name="L176" href="#L176">176</a>         }
-<a class="jxr_linenumber" name="L177" href="#L177">177</a>     }
-<a class="jxr_linenumber" name="L178" href="#L178">178</a> 
-<a class="jxr_linenumber" name="L179" href="#L179">179</a>     <em class="jxr_javadoccomment">/** {@inheritDoc} */</em>
-<a class="jxr_linenumber" name="L180" href="#L180">180</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="L181" href="#L181">181</a>         <strong class="jxr_keyword">if</strong> (x &lt;= 0) {
-<a class="jxr_linenumber" name="L182" href="#L182">182</a>             <strong class="jxr_keyword">return</strong> 0;
-<a class="jxr_linenumber" name="L183" href="#L183">183</a>         } <strong class="jxr_keyword">else</strong> <strong class="jxr_keyword">if</strong> (x &gt;= 1) {
-<a class="jxr_linenumber" name="L184" href="#L184">184</a>             <strong class="jxr_keyword">return</strong> 1;
-<a class="jxr_linenumber" name="L185" href="#L185">185</a>         } <strong class="jxr_keyword">else</strong> {
-<a class="jxr_linenumber" name="L186" href="#L186">186</a>             <strong class="jxr_keyword">return</strong> Beta.regularizedBeta(x, alpha, beta);
-<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> 
-<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> <em class="jxr_javadoccomment">     * Return the absolute accuracy setting of the solver used to estimate</em>
-<a class="jxr_linenumber" name="L192" href="#L192">192</a> <em class="jxr_javadoccomment">     * inverse cumulative probabilities.</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 the solver absolute accuracy.</em>
-<a class="jxr_linenumber" name="L195" href="#L195">195</a> <em class="jxr_javadoccomment">     * @since 2.1</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>     @Override
-<a class="jxr_linenumber" name="L198" href="#L198">198</a>     <strong class="jxr_keyword">protected</strong> <strong class="jxr_keyword">double</strong> getSolverAbsoluteAccuracy() {
-<a class="jxr_linenumber" name="L199" href="#L199">199</a>         <strong class="jxr_keyword">return</strong> solverAbsoluteAccuracy;
-<a class="jxr_linenumber" name="L200" href="#L200">200</a>     }
-<a class="jxr_linenumber" name="L201" href="#L201">201</a> 
-<a class="jxr_linenumber" name="L202" href="#L202">202</a>     <em class="jxr_javadoccomment">/**</em>
-<a class="jxr_linenumber" name="L203" href="#L203">203</a> <em class="jxr_javadoccomment">     * {@inheritDoc}</em>
-<a class="jxr_linenumber" name="L204" href="#L204">204</a> <em class="jxr_javadoccomment">     *</em>
-<a class="jxr_linenumber" name="L205" href="#L205">205</a> <em class="jxr_javadoccomment">     * For first shape parameter {@code alpha} and second shape parameter</em>
-<a class="jxr_linenumber" name="L206" href="#L206">206</a> <em class="jxr_javadoccomment">     * {@code beta}, the mean is {@code alpha / (alpha + beta)}.</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>     <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">double</strong> getNumericalMean() {
-<a class="jxr_linenumber" name="L209" href="#L209">209</a>         <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> a = getAlpha();
-<a class="jxr_linenumber" name="L210" href="#L210">210</a>         <strong class="jxr_keyword">return</strong> a / (a + getBeta());
-<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">/**</em>
-<a class="jxr_linenumber" name="L214" href="#L214">214</a> <em class="jxr_javadoccomment">     * {@inheritDoc}</em>
-<a class="jxr_linenumber" name="L215" href="#L215">215</a> <em class="jxr_javadoccomment">     *</em>
-<a class="jxr_linenumber" name="L216" href="#L216">216</a> <em class="jxr_javadoccomment">     * For first shape parameter {@code alpha} and second shape parameter</em>
-<a class="jxr_linenumber" name="L217" href="#L217">217</a> <em class="jxr_javadoccomment">     * {@code beta}, the variance is</em>
-<a class="jxr_linenumber" name="L218" href="#L218">218</a> <em class="jxr_javadoccomment">     * {@code (alpha * beta) / [(alpha + beta)^2 * (alpha + beta + 1)]}.</em>
-<a class="jxr_linenumber" name="L219" href="#L219">219</a> <em class="jxr_javadoccomment">     */</em>
-<a class="jxr_linenumber" name="L220" href="#L220">220</a>     <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">double</strong> getNumericalVariance() {
-<a class="jxr_linenumber" name="L221" href="#L221">221</a>         <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> a = getAlpha();
-<a class="jxr_linenumber" name="L222" href="#L222">222</a>         <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> b = getBeta();
-<a class="jxr_linenumber" name="L223" href="#L223">223</a>         <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> alphabetasum = a + b;
-<a class="jxr_linenumber" name="L224" href="#L224">224</a>         <strong class="jxr_keyword">return</strong> (a * b) / ((alphabetasum * alphabetasum) * (alphabetasum + 1));
-<a class="jxr_linenumber" name="L225" href="#L225">225</a>     }
-<a class="jxr_linenumber" name="L226" href="#L226">226</a> 
-<a class="jxr_linenumber" name="L227" href="#L227">227</a>     <em class="jxr_javadoccomment">/**</em>
-<a class="jxr_linenumber" name="L228" href="#L228">228</a> <em class="jxr_javadoccomment">     * {@inheritDoc}</em>
-<a class="jxr_linenumber" name="L229" href="#L229">229</a> <em class="jxr_javadoccomment">     *</em>
-<a class="jxr_linenumber" name="L230" href="#L230">230</a> <em class="jxr_javadoccomment">     * The lower bound of the support is always 0 no matter the parameters.</em>
-<a class="jxr_linenumber" name="L231" href="#L231">231</a> <em class="jxr_javadoccomment">     *</em>
-<a class="jxr_linenumber" name="L232" href="#L232">232</a> <em class="jxr_javadoccomment">     * @return lower bound of the support (always 0)</em>
-<a class="jxr_linenumber" name="L233" href="#L233">233</a> <em class="jxr_javadoccomment">     */</em>
-<a class="jxr_linenumber" name="L234" href="#L234">234</a>     <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">double</strong> getSupportLowerBound() {
-<a class="jxr_linenumber" name="L235" href="#L235">235</a>         <strong class="jxr_keyword">return</strong> 0;
-<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>     <em class="jxr_javadoccomment">/**</em>
-<a class="jxr_linenumber" name="L239" href="#L239">239</a> <em class="jxr_javadoccomment">     * {@inheritDoc}</em>
-<a class="jxr_linenumber" name="L240" href="#L240">240</a> <em class="jxr_javadoccomment">     *</em>
-<a class="jxr_linenumber" name="L241" href="#L241">241</a> <em class="jxr_javadoccomment">     * The upper bound of the support is always 1 no matter the parameters.</em>
-<a class="jxr_linenumber" name="L242" href="#L242">242</a> <em class="jxr_javadoccomment">     *</em>
-<a class="jxr_linenumber" name="L243" href="#L243">243</a> <em class="jxr_javadoccomment">     * @return upper bound of the support (always 1)</em>
-<a class="jxr_linenumber" name="L244" href="#L244">244</a> <em class="jxr_javadoccomment">     */</em>
-<a class="jxr_linenumber" name="L245" href="#L245">245</a>     <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">double</strong> getSupportUpperBound() {
-<a class="jxr_linenumber" name="L246" href="#L246">246</a>         <strong class="jxr_keyword">return</strong> 1;
-<a class="jxr_linenumber" name="L247" href="#L247">247</a>     }
-<a class="jxr_linenumber" name="L248" href="#L248">248</a> 
-<a class="jxr_linenumber" name="L249" href="#L249">249</a>     <em class="jxr_javadoccomment">/** {@inheritDoc} */</em>
-<a class="jxr_linenumber" name="L250" href="#L250">250</a>     <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">boolean</strong> isSupportLowerBoundInclusive() {
-<a class="jxr_linenumber" name="L251" href="#L251">251</a>         <strong class="jxr_keyword">return</strong> false;
-<a class="jxr_linenumber" name="L252" href="#L252">252</a>     }
-<a class="jxr_linenumber" name="L253" href="#L253">253</a> 
-<a class="jxr_linenumber" name="L254" href="#L254">254</a>     <em class="jxr_javadoccomment">/** {@inheritDoc} */</em>
-<a class="jxr_linenumber" name="L255" href="#L255">255</a>     <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">boolean</strong> isSupportUpperBoundInclusive() {
-<a class="jxr_linenumber" name="L256" href="#L256">256</a>         <strong class="jxr_keyword">return</strong> false;
-<a class="jxr_linenumber" name="L257" href="#L257">257</a>     }
-<a class="jxr_linenumber" name="L258" href="#L258">258</a> 
-<a class="jxr_linenumber" name="L259" href="#L259">259</a>     <em class="jxr_javadoccomment">/**</em>
-<a class="jxr_linenumber" name="L260" href="#L260">260</a> <em class="jxr_javadoccomment">     * {@inheritDoc}</em>
-<a class="jxr_linenumber" name="L261" href="#L261">261</a> <em class="jxr_javadoccomment">     *</em>
-<a class="jxr_linenumber" name="L262" href="#L262">262</a> <em class="jxr_javadoccomment">     * The support of this distribution is connected.</em>
-<a class="jxr_linenumber" name="L263" href="#L263">263</a> <em class="jxr_javadoccomment">     *</em>
-<a class="jxr_linenumber" name="L264" href="#L264">264</a> <em class="jxr_javadoccomment">     * @return {@code true}</em>
-<a class="jxr_linenumber" name="L265" href="#L265">265</a> <em class="jxr_javadoccomment">     */</em>
-<a class="jxr_linenumber" name="L266" href="#L266">266</a>     <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">boolean</strong> isSupportConnected() {
-<a class="jxr_linenumber" name="L267" href="#L267">267</a>         <strong class="jxr_keyword">return</strong> <strong class="jxr_keyword">true</strong>;
-<a class="jxr_linenumber" name="L268" href="#L268">268</a>     }
-<a class="jxr_linenumber" name="L269" href="#L269">269</a> }
+<a class="jxr_linenumber" name="L26" href="#L26">26</a>  <strong class="jxr_keyword">import</strong> org.apache.commons.math3.util.Precision;
+<a class="jxr_linenumber" name="L27" href="#L27">27</a>  
+<a class="jxr_linenumber" name="L28" href="#L28">28</a>  <em class="jxr_javadoccomment">/**</em>
+<a class="jxr_linenumber" name="L29" href="#L29">29</a>  <em class="jxr_javadoccomment"> * Implements the Beta distribution.</em>
+<a class="jxr_linenumber" name="L30" href="#L30">30</a>  <em class="jxr_javadoccomment"> *</em>
+<a class="jxr_linenumber" name="L31" href="#L31">31</a>  <em class="jxr_javadoccomment"> * @see &lt;a href="<a href="http://en.wikipedia.org/wiki/Beta_distribution" target="alexandria_uri">http://en.wikipedia.org/wiki/Beta_distribution</a>"&gt;Beta distribution&lt;/a&gt;</em>
+<a class="jxr_linenumber" name="L32" href="#L32">32</a>  <em class="jxr_javadoccomment"> * @since 2.0 (changed to concrete class in 3.0)</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>  <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">class</strong> <a href="../../../../../org/apache/commons/math3/distribution/BetaDistribution.html">BetaDistribution</a> <strong class="jxr_keyword">extends</strong> <a href="../../../../../org/apache/commons/math3/distribution/AbstractRealDistribution.html">AbstractRealDistribution</a> {
+<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">     * Default inverse cumulative probability accuracy.</em>
+<a class="jxr_linenumber" name="L37" href="#L37">37</a>  <em class="jxr_javadoccomment">     * @since 2.1</em>
+<a class="jxr_linenumber" name="L38" href="#L38">38</a>  <em class="jxr_javadoccomment">     */</em>
+<a class="jxr_linenumber" name="L39" href="#L39">39</a>      <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">static</strong> <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> DEFAULT_INVERSE_ABSOLUTE_ACCURACY = 1e-9;
+<a class="jxr_linenumber" name="L40" href="#L40">40</a>      <em class="jxr_javadoccomment">/** Serializable version identifier. */</em>
+<a class="jxr_linenumber" name="L41" href="#L41">41</a>      <strong class="jxr_keyword">private</strong> <strong class="jxr_keyword">static</strong> <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">long</strong> serialVersionUID = -1221965979403477668L;
+<a class="jxr_linenumber" name="L42" href="#L42">42</a>      <em class="jxr_javadoccomment">/** First shape 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> alpha;
+<a class="jxr_linenumber" name="L44" href="#L44">44</a>      <em class="jxr_javadoccomment">/** Second shape parameter. */</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> beta;
+<a class="jxr_linenumber" name="L46" href="#L46">46</a>      <em class="jxr_javadoccomment">/** Normalizing factor used in density computations.</em>
+<a class="jxr_linenumber" name="L47" href="#L47">47</a>  <em class="jxr_javadoccomment">     * updated whenever alpha or beta are changed.</em>
+<a class="jxr_linenumber" name="L48" href="#L48">48</a>  <em class="jxr_javadoccomment">     */</em>
+<a class="jxr_linenumber" name="L49" href="#L49">49</a>      <strong class="jxr_keyword">private</strong> <strong class="jxr_keyword">double</strong> z;
+<a class="jxr_linenumber" name="L50" href="#L50">50</a>      <em class="jxr_javadoccomment">/** Inverse cumulative probability accuracy. */</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> solverAbsoluteAccuracy;
+<a class="jxr_linenumber" name="L52" href="#L52">52</a>  
+<a class="jxr_linenumber" name="L53" href="#L53">53</a>      <em class="jxr_javadoccomment">/**</em>
+<a class="jxr_linenumber" name="L54" href="#L54">54</a>  <em class="jxr_javadoccomment">     * Build a new instance.</em>
+<a class="jxr_linenumber" name="L55" href="#L55">55</a>  <em class="jxr_javadoccomment">     * &lt;p&gt;</em>
+<a class="jxr_linenumber" name="L56" href="#L56">56</a>  <em class="jxr_javadoccomment">     * &lt;b&gt;Note:&lt;/b&gt; this constructor will implicitly create an instance of</em>
+<a class="jxr_linenumber" name="L57" href="#L57">57</a>  <em class="jxr_javadoccomment">     * {@link Well19937c} as random generator to be used for sampling only (see</em>
+<a class="jxr_linenumber" name="L58" href="#L58">58</a>  <em class="jxr_javadoccomment">     * {@link #sample()} and {@link #sample(int)}). In case no sampling is</em>
+<a class="jxr_linenumber" name="L59" href="#L59">59</a>  <em class="jxr_javadoccomment">     * needed for the created distribution, it is advised to pass {@code null}</em>
+<a class="jxr_linenumber" name="L60" href="#L60">60</a>  <em class="jxr_javadoccomment">     * as random generator via the appropriate constructors to avoid the</em>
+<a class="jxr_linenumber" name="L61" href="#L61">61</a>  <em class="jxr_javadoccomment">     * additional initialisation overhead.</em>
+<a class="jxr_linenumber" name="L62" href="#L62">62</a>  <em class="jxr_javadoccomment">     *</em>
+<a class="jxr_linenumber" name="L63" href="#L63">63</a>  <em class="jxr_javadoccomment">     * @param alpha First shape parameter (must be positive).</em>
+<a class="jxr_linenumber" name="L64" href="#L64">64</a>  <em class="jxr_javadoccomment">     * @param beta Second shape parameter (must be positive).</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> <a href="../../../../../org/apache/commons/math3/distribution/BetaDistribution.html">BetaDistribution</a>(<strong class="jxr_keyword">double</strong> alpha, <strong class="jxr_keyword">double</strong> beta) {
+<a class="jxr_linenumber" name="L67" href="#L67">67</a>          <strong class="jxr_keyword">this</strong>(alpha, beta, DEFAULT_INVERSE_ABSOLUTE_ACCURACY);
+<a class="jxr_linenumber" name="L68" href="#L68">68</a>      }
+<a class="jxr_linenumber" name="L69" href="#L69">69</a>  
+<a class="jxr_linenumber" name="L70" href="#L70">70</a>      <em class="jxr_javadoccomment">/**</em>
+<a class="jxr_linenumber" name="L71" href="#L71">71</a>  <em class="jxr_javadoccomment">     * Build a new instance.</em>
+<a class="jxr_linenumber" name="L72" href="#L72">72</a>  <em class="jxr_javadoccomment">     * &lt;p&gt;</em>
+<a class="jxr_linenumber" name="L73" href="#L73">73</a>  <em class="jxr_javadoccomment">     * &lt;b&gt;Note:&lt;/b&gt; this constructor will implicitly create an instance of</em>
+<a class="jxr_linenumber" name="L74" href="#L74">74</a>  <em class="jxr_javadoccomment">     * {@link Well19937c} as random generator to be used for sampling only (see</em>
+<a class="jxr_linenumber" name="L75" href="#L75">75</a>  <em class="jxr_javadoccomment">     * {@link #sample()} and {@link #sample(int)}). In case no sampling is</em>
+<a class="jxr_linenumber" name="L76" href="#L76">76</a>  <em class="jxr_javadoccomment">     * needed for the created distribution, it is advised to pass {@code null}</em>
+<a class="jxr_linenumber" name="L77" href="#L77">77</a>  <em class="jxr_javadoccomment">     * as random generator via the appropriate constructors to avoid the</em>
+<a class="jxr_linenumber" name="L78" href="#L78">78</a>  <em class="jxr_javadoccomment">     * additional initialisation overhead.</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>  <em class="jxr_javadoccomment">     * @param alpha First shape parameter (must be positive).</em>
+<a class="jxr_linenumber" name="L81" href="#L81">81</a>  <em class="jxr_javadoccomment">     * @param beta Second shape parameter (must be positive).</em>
+<a class="jxr_linenumber" name="L82" href="#L82">82</a>  <em class="jxr_javadoccomment">     * @param inverseCumAccuracy Maximum absolute error in inverse</em>
+<a class="jxr_linenumber" name="L83" href="#L83">83</a>  <em class="jxr_javadoccomment">     * cumulative probability estimates (defaults to</em>
+<a class="jxr_linenumber" name="L84" href="#L84">84</a>  <em class="jxr_javadoccomment">     * {@link #DEFAULT_INVERSE_ABSOLUTE_ACCURACY}).</em>
+<a class="jxr_linenumber" name="L85" href="#L85">85</a>  <em class="jxr_javadoccomment">     * @since 2.1</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>      <strong class="jxr_keyword">public</strong> <a href="../../../../../org/apache/commons/math3/distribution/BetaDistribution.html">BetaDistribution</a>(<strong class="jxr_keyword">double</strong> alpha, <strong class="jxr_keyword">double</strong> beta, <strong class="jxr_keyword">double</strong> inverseCumAccuracy) {
+<a class="jxr_linenumber" name="L88" href="#L88">88</a>          <strong class="jxr_keyword">this</strong>(<strong class="jxr_keyword">new</strong> <a href="../../../../../org/apache/commons/math3/random/Well19937c.html">Well19937c</a>(), alpha, beta, inverseCumAccuracy);
+<a class="jxr_linenumber" name="L89" href="#L89">89</a>      }
+<a class="jxr_linenumber" name="L90" href="#L90">90</a>  
+<a class="jxr_linenumber" name="L91" href="#L91">91</a>      <em class="jxr_javadoccomment">/**</em>
+<a class="jxr_linenumber" name="L92" href="#L92">92</a>  <em class="jxr_javadoccomment">     * Creates a &amp;beta; distribution.</em>
+<a class="jxr_linenumber" name="L93" href="#L93">93</a>  <em class="jxr_javadoccomment">     *</em>
+<a class="jxr_linenumber" name="L94" href="#L94">94</a>  <em class="jxr_javadoccomment">     * @param rng Random number generator.</em>
+<a class="jxr_linenumber" name="L95" href="#L95">95</a>  <em class="jxr_javadoccomment">     * @param alpha First shape parameter (must be positive).</em>
+<a class="jxr_linenumber" name="L96" href="#L96">96</a>  <em class="jxr_javadoccomment">     * @param beta Second shape parameter (must be positive).</em>
+<a class="jxr_linenumber" name="L97" href="#L97">97</a>  <em class="jxr_javadoccomment">     * @since 3.3</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>      <strong class="jxr_keyword">public</strong> <a href="../../../../../org/apache/commons/math3/distribution/BetaDistribution.html">BetaDistribution</a>(<a href="../../../../../org/apache/commons/math3/random/RandomGenerator.html">RandomGenerator</a> rng, <strong class="jxr_keyword">double</strong> alpha, <strong class="jxr_keyword">double</strong> beta) {
+<a class="jxr_linenumber" name="L100" href="#L100">100</a>         <strong class="jxr_keyword">this</strong>(rng, alpha, beta, DEFAULT_INVERSE_ABSOLUTE_ACCURACY);
+<a class="jxr_linenumber" name="L101" href="#L101">101</a>     }
+<a class="jxr_linenumber" name="L102" href="#L102">102</a> 
+<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">     * Creates a &amp;beta; distribution.</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> <em class="jxr_javadoccomment">     * @param rng Random number generator.</em>
+<a class="jxr_linenumber" name="L107" href="#L107">107</a> <em class="jxr_javadoccomment">     * @param alpha First shape parameter (must be positive).</em>
+<a class="jxr_linenumber" name="L108" href="#L108">108</a> <em class="jxr_javadoccomment">     * @param beta Second shape parameter (must be positive).</em>
+<a class="jxr_linenumber" name="L109" href="#L109">109</a> <em class="jxr_javadoccomment">     * @param inverseCumAccuracy Maximum absolute error in inverse</em>
+<a class="jxr_linenumber" name="L110" href="#L110">110</a> <em class="jxr_javadoccomment">     * cumulative probability estimates (defaults to</em>
+<a class="jxr_linenumber" name="L111" href="#L111">111</a> <em class="jxr_javadoccomment">     * {@link #DEFAULT_INVERSE_ABSOLUTE_ACCURACY}).</em>
+<a class="jxr_linenumber" name="L112" href="#L112">112</a> <em class="jxr_javadoccomment">     * @since 3.1</em>
+<a class="jxr_linenumber" name="L113" href="#L113">113</a> <em class="jxr_javadoccomment">     */</em>
+<a class="jxr_linenumber" name="L114" href="#L114">114</a>     <strong class="jxr_keyword">public</strong> <a href="../../../../../org/apache/commons/math3/distribution/BetaDistribution.html">BetaDistribution</a>(<a href="../../../../../org/apache/commons/math3/random/RandomGenerator.html">RandomGenerator</a> rng,
+<a class="jxr_linenumber" name="L115" href="#L115">115</a>                             <strong class="jxr_keyword">double</strong> alpha,
+<a class="jxr_linenumber" name="L116" href="#L116">116</a>                             <strong class="jxr_keyword">double</strong> beta,
+<a class="jxr_linenumber" name="L117" href="#L117">117</a>                             <strong class="jxr_keyword">double</strong> inverseCumAccuracy) {
+<a class="jxr_linenumber" name="L118" href="#L118">118</a>         <strong class="jxr_keyword">super</strong>(rng);
+<a class="jxr_linenumber" name="L119" href="#L119">119</a> 
+<a class="jxr_linenumber" name="L120" href="#L120">120</a>         <strong class="jxr_keyword">this</strong>.alpha = alpha;
+<a class="jxr_linenumber" name="L121" href="#L121">121</a>         <strong class="jxr_keyword">this</strong>.beta = beta;
+<a class="jxr_linenumber" name="L122" href="#L122">122</a>         z = Double.NaN;
+<a class="jxr_linenumber" name="L123" href="#L123">123</a>         solverAbsoluteAccuracy = inverseCumAccuracy;
+<a class="jxr_linenumber" name="L124" href="#L124">124</a>     }
+<a class="jxr_linenumber" name="L125" href="#L125">125</a> 
+<a class="jxr_linenumber" name="L126" href="#L126">126</a>     <em class="jxr_javadoccomment">/**</em>
+<a class="jxr_linenumber" name="L127" href="#L127">127</a> <em class="jxr_javadoccomment">     * Access the first shape parameter, {@code alpha}.</em>
+<a class="jxr_linenumber" name="L128" href="#L128">128</a> <em class="jxr_javadoccomment">     *</em>
+<a class="jxr_linenumber" name="L129" href="#L129">129</a> <em class="jxr_javadoccomment">     * @return the first shape parameter.</em>
+<a class="jxr_linenumber" name="L130" href="#L130">130</a> <em class="jxr_javadoccomment">     */</em>
+<a class="jxr_linenumber" name="L131" href="#L131">131</a>     <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">double</strong> getAlpha() {
+<a class="jxr_linenumber" name="L132" href="#L132">132</a>         <strong class="jxr_keyword">return</strong> alpha;
+<a class="jxr_linenumber" name="L133" href="#L133">133</a>     }
+<a class="jxr_linenumber" name="L134" href="#L134">134</a> 
+<a class="jxr_linenumber" name="L135" href="#L135">135</a>     <em class="jxr_javadoccomment">/**</em>
+<a class="jxr_linenumber" name="L136" href="#L136">136</a> <em class="jxr_javadoccomment">     * Access the second shape parameter, {@code beta}.</em>
+<a class="jxr_linenumber" name="L137" href="#L137">137</a> <em class="jxr_javadoccomment">     *</em>
+<a class="jxr_linenumber" name="L138" href="#L138">138</a> <em class="jxr_javadoccomment">     * @return the second shape parameter.</em>
+<a class="jxr_linenumber" name="L139" href="#L139">139</a> <em class="jxr_javadoccomment">     */</em>
+<a class="jxr_linenumber" name="L140" href="#L140">140</a>     <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">double</strong> getBeta() {
+<a class="jxr_linenumber" name="L141" href="#L141">141</a>         <strong class="jxr_keyword">return</strong> beta;
+<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">/** Recompute the normalization factor. */</em>
+<a class="jxr_linenumber" name="L145" href="#L145">145</a>     <strong class="jxr_keyword">private</strong> <strong class="jxr_keyword">void</strong> recomputeZ() {
+<a class="jxr_linenumber" name="L146" href="#L146">146</a>         <strong class="jxr_keyword">if</strong> (Double.isNaN(z)) {
+<a class="jxr_linenumber" name="L147" href="#L147">147</a>             z = Gamma.logGamma(alpha) + Gamma.logGamma(beta) - Gamma.logGamma(alpha + beta);
+<a class="jxr_linenumber" name="L148" href="#L148">148</a>         }
+<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>     <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="L153" href="#L153">153</a>         <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> logDensity = logDensity(x);
+<a class="jxr_linenumber" name="L154" href="#L154">154</a>         <strong class="jxr_keyword">return</strong> logDensity == Double.NEGATIVE_INFINITY ? 0 : FastMath.exp(logDensity);
+<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>     <em class="jxr_javadoccomment">/** {@inheritDoc} **/</em>
+<a class="jxr_linenumber" name="L158" href="#L158">158</a>     @Override
+<a class="jxr_linenumber" name="L159" href="#L159">159</a>     <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">double</strong> logDensity(<strong class="jxr_keyword">double</strong> x) {
+<a class="jxr_linenumber" name="L160" href="#L160">160</a>         recomputeZ();
+<a class="jxr_linenumber" name="L161" href="#L161">161</a>         <strong class="jxr_keyword">if</strong> (x &lt; 0 || x &gt; 1) {
+<a class="jxr_linenumber" name="L162" href="#L162">162</a>             <strong class="jxr_keyword">return</strong> Double.NEGATIVE_INFINITY;
+<a class="jxr_linenumber" name="L163" href="#L163">163</a>         } <strong class="jxr_keyword">else</strong> <strong class="jxr_keyword">if</strong> (x == 0) {
+<a class="jxr_linenumber" name="L164" href="#L164">164</a>             <strong class="jxr_keyword">if</strong> (alpha &lt; 1) {
+<a class="jxr_linenumber" name="L165" href="#L165">165</a>                 <strong class="jxr_keyword">throw</strong> <strong class="jxr_keyword">new</strong> <a href="../../../../../org/apache/commons/math3/exception/NumberIsTooSmallException.html">NumberIsTooSmallException</a>(LocalizedFormats.CANNOT_COMPUTE_BETA_DENSITY_AT_0_FOR_SOME_ALPHA, alpha, 1, false);
+<a class="jxr_linenumber" name="L166" href="#L166">166</a>             }
+<a class="jxr_linenumber" name="L167" href="#L167">167</a>             <strong class="jxr_keyword">return</strong> Double.NEGATIVE_INFINITY;
+<a class="jxr_linenumber" name="L168" href="#L168">168</a>         } <strong class="jxr_keyword">else</strong> <strong class="jxr_keyword">if</strong> (x == 1) {
+<a class="jxr_linenumber" name="L169" href="#L169">169</a>             <strong class="jxr_keyword">if</strong> (beta &lt; 1) {
+<a class="jxr_linenumber" name="L170" href="#L170">170</a>                 <strong class="jxr_keyword">throw</strong> <strong class="jxr_keyword">new</strong> <a href="../../../../../org/apache/commons/math3/exception/NumberIsTooSmallException.html">NumberIsTooSmallException</a>(LocalizedFormats.CANNOT_COMPUTE_BETA_DENSITY_AT_1_FOR_SOME_BETA, beta, 1, false);
+<a class="jxr_linenumber" name="L171" href="#L171">171</a>             }
+<a class="jxr_linenumber" name="L172" href="#L172">172</a>             <strong class="jxr_keyword">return</strong> Double.NEGATIVE_INFINITY;
+<a class="jxr_linenumber" name="L173" href="#L173">173</a>         } <strong class="jxr_keyword">else</strong> {
+<a class="jxr_linenumber" name="L174" href="#L174">174</a>             <strong class="jxr_keyword">double</strong> logX = FastMath.log(x);
+<a class="jxr_linenumber" name="L175" href="#L175">175</a>             <strong class="jxr_keyword">double</strong> log1mX = FastMath.log1p(-x);
+<a class="jxr_linenumber" name="L176" href="#L176">176</a>             <strong class="jxr_keyword">return</strong> (alpha - 1) * logX + (beta - 1) * log1mX - z;
+<a class="jxr_linenumber" name="L177" href="#L177">177</a>         }
+<a class="jxr_linenumber" name="L178" href="#L178">178</a>     }
+<a class="jxr_linenumber" name="L179" href="#L179">179</a> 
+<a class="jxr_linenumber" name="L180" href="#L180">180</a>     <em class="jxr_javadoccomment">/** {@inheritDoc} */</em>
+<a class="jxr_linenumber" name="L181" href="#L181">181</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="L182" href="#L182">182</a>         <strong class="jxr_keyword">if</strong> (x &lt;= 0) {
+<a class="jxr_linenumber" name="L183" href="#L183">183</a>             <strong class="jxr_keyword">return</strong> 0;
+<a class="jxr_linenumber" name="L184" href="#L184">184</a>         } <strong class="jxr_keyword">else</strong> <strong class="jxr_keyword">if</strong> (x &gt;= 1) {
+<a class="jxr_linenumber" name="L185" href="#L185">185</a>             <strong class="jxr_keyword">return</strong> 1;
+<a class="jxr_linenumber" name="L186" href="#L186">186</a>         } <strong class="jxr_keyword">else</strong> {
+<a class="jxr_linenumber" name="L187" href="#L187">187</a>             <strong class="jxr_keyword">return</strong> Beta.regularizedBeta(x, alpha, beta);
+<a class="jxr_linenumber" name="L188" href="#L188">188</a>         }
+<a class="jxr_linenumber" name="L189" href="#L189">189</a>     }
+<a class="jxr_linenumber" name="L190" href="#L190">190</a> 
+<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">     * Return the absolute accuracy setting of the solver used to estimate</em>
+<a class="jxr_linenumber" name="L193" href="#L193">193</a> <em class="jxr_javadoccomment">     * inverse cumulative probabilities.</em>
+<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">     * @return the solver absolute accuracy.</em>
+<a class="jxr_linenumber" name="L196" href="#L196">196</a> <em class="jxr_javadoccomment">     * @since 2.1</em>
+<a class="jxr_linenumber" name="L197" href="#L197">197</a> <em class="jxr_javadoccomment">     */</em>
+<a class="jxr_linenumber" name="L198" href="#L198">198</a>     @Override
+<a class="jxr_linenumber" name="L199" href="#L199">199</a>     <strong class="jxr_keyword">protected</strong> <strong class="jxr_keyword">double</strong> getSolverAbsoluteAccuracy() {
+<a class="jxr_linenumber" name="L200" href="#L200">200</a>         <strong class="jxr_keyword">return</strong> solverAbsoluteAccuracy;
+<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>     <em class="jxr_javadoccomment">/**</em>
+<a class="jxr_linenumber" name="L204" href="#L204">204</a> <em class="jxr_javadoccomment">     * {@inheritDoc}</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">     * For first shape parameter {@code alpha} and second shape parameter</em>
+<a class="jxr_linenumber" name="L207" href="#L207">207</a> <em class="jxr_javadoccomment">     * {@code beta}, the mean is {@code alpha / (alpha + beta)}.</em>
+<a class="jxr_linenumber" name="L208" href="#L208">208</a> <em class="jxr_javadoccomment">     */</em>
+<a class="jxr_linenumber" name="L209" href="#L209">209</a>     <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">double</strong> getNumericalMean() {
+<a class="jxr_linenumber" name="L210" href="#L210">210</a>         <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> a = getAlpha();
+<a class="jxr_linenumber" name="L211" href="#L211">211</a>         <strong class="jxr_keyword">return</strong> a / (a + getBeta());
+<a class="jxr_linenumber" name="L212" href="#L212">212</a>     }
+<a class="jxr_linenumber" name="L213" href="#L213">213</a> 
+<a class="jxr_linenumber" name="L214" href="#L214">214</a>     <em class="jxr_javadoccomment">/**</em>
+<a class="jxr_linenumber" name="L215" href="#L215">215</a> <em class="jxr_javadoccomment">     * {@inheritDoc}</em>
+<a class="jxr_linenumber" name="L216" href="#L216">216</a> <em class="jxr_javadoccomment">     *</em>
+<a class="jxr_linenumber" name="L217" href="#L217">217</a> <em class="jxr_javadoccomment">     * For first shape parameter {@code alpha} and second shape parameter</em>
+<a class="jxr_linenumber" name="L218" href="#L218">218</a> <em class="jxr_javadoccomment">     * {@code beta}, the variance is</em>
+<a class="jxr_linenumber" name="L219" href="#L219">219</a> <em class="jxr_javadoccomment">     * {@code (alpha * beta) / [(alpha + beta)^2 * (alpha + beta + 1)]}.</em>
+<a class="jxr_linenumber" name="L220" href="#L220">220</a> <em class="jxr_javadoccomment">     */</em>
+<a class="jxr_linenumber" name="L221" href="#L221">221</a>     <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">double</strong> getNumericalVariance() {
+<a class="jxr_linenumber" name="L222" href="#L222">222</a>         <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> a = getAlpha();
+<a class="jxr_linenumber" name="L223" href="#L223">223</a>         <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> b = getBeta();
+<a class="jxr_linenumber" name="L224" href="#L224">224</a>         <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> alphabetasum = a + b;
+<a class="jxr_linenumber" name="L225" href="#L225">225</a>         <strong class="jxr_keyword">return</strong> (a * b) / ((alphabetasum * alphabetasum) * (alphabetasum + 1));
+<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>     <em class="jxr_javadoccomment">/**</em>
+<a class="jxr_linenumber" name="L229" href="#L229">229</a> <em class="jxr_javadoccomment">     * {@inheritDoc}</em>
+<a class="jxr_linenumber" name="L230" href="#L230">230</a> <em class="jxr_javadoccomment">     *</em>
+<a class="jxr_linenumber" name="L231" href="#L231">231</a> <em class="jxr_javadoccomment">     * The lower bound of the support is always 0 no matter the parameters.</em>
+<a class="jxr_linenumber" name="L232" href="#L232">232</a> <em class="jxr_javadoccomment">     *</em>
+<a class="jxr_linenumber" name="L233" href="#L233">233</a> <em class="jxr_javadoccomment">     * @return lower bound of the support (always 0)</em>
+<a class="jxr_linenumber" name="L234" href="#L234">234</a> <em class="jxr_javadoccomment">     */</em>
+<a class="jxr_linenumber" name="L235" href="#L235">235</a>     <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">double</strong> getSupportLowerBound() {
+<a class="jxr_linenumber" name="L236" href="#L236">236</a>         <strong class="jxr_keyword">return</strong> 0;
+<a class="jxr_linenumber" name="L237" href="#L237">237</a>     }
+<a class="jxr_linenumber" name="L238" href="#L238">238</a> 
+<a class="jxr_linenumber" name="L239" href="#L239">239</a>     <em class="jxr_javadoccomment">/**</em>
+<a class="jxr_linenumber" name="L240" href="#L240">240</a> <em class="jxr_javadoccomment">     * {@inheritDoc}</em>
+<a class="jxr_linenumber" name="L241" href="#L241">241</a> <em class="jxr_javadoccomment">     *</em>
+<a class="jxr_linenumber" name="L242" href="#L242">242</a> <em class="jxr_javadoccomment">     * The upper bound of the support is always 1 no matter the parameters.</em>
+<a class="jxr_linenumber" name="L243" href="#L243">243</a> <em class="jxr_javadoccomment">     *</em>
+<a class="jxr_linenumber" name="L244" href="#L244">244</a> <em class="jxr_javadoccomment">     * @return upper bound of the support (always 1)</em>
+<a class="jxr_linenumber" name="L245" href="#L245">245</a> <em class="jxr_javadoccomment">     */</em>
+<a class="jxr_linenumber" name="L246" href="#L246">246</a>     <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">double</strong> getSupportUpperBound() {
+<a class="jxr_linenumber" name="L247" href="#L247">247</a>         <strong class="jxr_keyword">return</strong> 1;
+<a class="jxr_linenumber" name="L248" href="#L248">248</a>     }
+<a class="jxr_linenumber" name="L249" href="#L249">249</a> 
+<a class="jxr_linenumber" name="L250" href="#L250">250</a>     <em class="jxr_javadoccomment">/** {@inheritDoc} */</em>
+<a class="jxr_linenumber" name="L251" href="#L251">251</a>     <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">boolean</strong> isSupportLowerBoundInclusive() {
+<a class="jxr_linenumber" name="L252" href="#L252">252</a>         <strong class="jxr_keyword">return</strong> false;
+<a class="jxr_linenumber" name="L253" href="#L253">253</a>     }
+<a class="jxr_linenumber" name="L254" href="#L254">254</a> 
+<a class="jxr_linenumber" name="L255" href="#L255">255</a>     <em class="jxr_javadoccomment">/** {@inheritDoc} */</em>
+<a class="jxr_linenumber" name="L256" href="#L256">256</a>     <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">boolean</strong> isSupportUpperBoundInclusive() {
+<a class="jxr_linenumber" name="L257" href="#L257">257</a>         <strong class="jxr_keyword">return</strong> false;
+<a class="jxr_linenumber" name="L258" href="#L258">258</a>     }
+<a class="jxr_linenumber" name="L259" href="#L259">259</a> 
+<a class="jxr_linenumber" name="L260" href="#L260">260</a>     <em class="jxr_javadoccomment">/**</em>
+<a class="jxr_linenumber" name="L261" href="#L261">261</a> <em class="jxr_javadoccomment">     * {@inheritDoc}</em>
+<a class="jxr_linenumber" name="L262" href="#L262">262</a> <em class="jxr_javadoccomment">     *</em>
+<a class="jxr_linenumber" name="L263" href="#L263">263</a> <em class="jxr_javadoccomment">     * The support of this distribution is connected.</em>
+<a class="jxr_linenumber" name="L264" href="#L264">264</a> <em class="jxr_javadoccomment">     *</em>
+<a class="jxr_linenumber" name="L265" href="#L265">265</a> <em class="jxr_javadoccomment">     * @return {@code true}</em>
+<a class="jxr_linenumber" name="L266" href="#L266">266</a> <em class="jxr_javadoccomment">     */</em>
+<a class="jxr_linenumber" name="L267" href="#L267">267</a>     <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">boolean</strong> isSupportConnected() {
+<a class="jxr_linenumber" name="L268" href="#L268">268</a>         <strong class="jxr_keyword">return</strong> <strong class="jxr_keyword">true</strong>;
+<a class="jxr_linenumber" name="L269" href="#L269">269</a>     }
+<a class="jxr_linenumber" name="L270" href="#L270">270</a> 
+<a class="jxr_linenumber" name="L271" href="#L271">271</a> 
+<a class="jxr_linenumber" name="L272" href="#L272">272</a>     <em class="jxr_javadoccomment">/** {@inheritDoc}</em>
+<a class="jxr_linenumber" name="L273" href="#L273">273</a> <em class="jxr_javadoccomment">    * &lt;p&gt;</em>
+<a class="jxr_linenumber" name="L274" href="#L274">274</a> <em class="jxr_javadoccomment">    * Sampling is performed using Cheng algorithms:</em>
+<a class="jxr_linenumber" name="L275" href="#L275">275</a> <em class="jxr_javadoccomment">    * &lt;/p&gt;</em>
+<a class="jxr_linenumber" name="L276" href="#L276">276</a> <em class="jxr_javadoccomment">    * &lt;p&gt;</em>
+<a class="jxr_linenumber" name="L277" href="#L277">277</a> <em class="jxr_javadoccomment">    * R. C. H. Cheng, "Generating beta variates with nonintegral shape parameters.".</em>
+<a class="jxr_linenumber" name="L278" href="#L278">278</a> <em class="jxr_javadoccomment">    *                 Communications of the ACM, 21, 317–322, 1978.</em>
+<a class="jxr_linenumber" name="L279" href="#L279">279</a> <em class="jxr_javadoccomment">    * &lt;/p&gt;</em>
+<a class="jxr_linenumber" name="L280" href="#L280">280</a> <em class="jxr_javadoccomment">    */</em>
+<a class="jxr_linenumber" name="L281" href="#L281">281</a>     @Override
+<a class="jxr_linenumber" name="L282" href="#L282">282</a>     <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">double</strong> sample() {
+<a class="jxr_linenumber" name="L283" href="#L283">283</a>         <strong class="jxr_keyword">return</strong> ChengBetaSampler.sample(random, alpha, beta);
+<a class="jxr_linenumber" name="L284" href="#L284">284</a>     }
+<a class="jxr_linenumber" name="L285" href="#L285">285</a> 
+<a class="jxr_linenumber" name="L286" href="#L286">286</a>     <em class="jxr_javadoccomment">/** Utility class implementing Cheng's algorithms for beta distribution sampling.</em>
+<a class="jxr_linenumber" name="L287" href="#L287">287</a> <em class="jxr_javadoccomment">     * &lt;p&gt;</em>
+<a class="jxr_linenumber" name="L288" href="#L288">288</a> <em class="jxr_javadoccomment">     * R. C. H. Cheng, "Generating beta variates with nonintegral shape parameters.".</em>
+<a class="jxr_linenumber" name="L289" href="#L289">289</a> <em class="jxr_javadoccomment">     *                 Communications of the ACM, 21, 317–322, 1978.</em>
+<a class="jxr_linenumber" name="L290" href="#L290">290</a> <em class="jxr_javadoccomment">     * &lt;/p&gt;</em>
+<a class="jxr_linenumber" name="L291" href="#L291">291</a> <em class="jxr_javadoccomment">     * @since 3.6</em>
+<a class="jxr_linenumber" name="L292" href="#L292">292</a> <em class="jxr_javadoccomment">     */</em>
+<a class="jxr_linenumber" name="L293" href="#L293">293</a>     <strong class="jxr_keyword">private</strong> <strong class="jxr_keyword">static</strong> <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">class</strong> <a href="../../../../../org/apache/commons/math3/distribution/BetaDistribution.html">ChengBetaSampler</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">         * Returns one sample using Cheng's sampling algorithm.</em>
+<a class="jxr_linenumber" name="L297" href="#L297">297</a> <em class="jxr_javadoccomment">         * @param random random generator to use</em>
+<a class="jxr_linenumber" name="L298" href="#L298">298</a> <em class="jxr_javadoccomment">         * @param alpha distribution first shape parameter</em>
+<a class="jxr_linenumber" name="L299" href="#L299">299</a> <em class="jxr_javadoccomment">         * @param beta distribution second shape parameter</em>
+<a class="jxr_linenumber" name="L300" href="#L300">300</a> <em class="jxr_javadoccomment">         * @return sampled value</em>
+<a class="jxr_linenumber" name="L301" href="#L301">301</a> <em class="jxr_javadoccomment">         */</em>
+<a class="jxr_linenumber" name="L302" href="#L302">302</a>         <strong class="jxr_keyword">static</strong> <strong class="jxr_keyword">double</strong> sample(<a href="../../../../../org/apache/commons/math3/random/RandomGenerator.html">RandomGenerator</a> random, <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> alpha, <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> beta) {
+<a class="jxr_linenumber" name="L303" href="#L303">303</a>             <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> a = FastMath.min(alpha, beta);
+<a class="jxr_linenumber" name="L304" href="#L304">304</a>             <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> b = FastMath.max(alpha, beta);
+<a class="jxr_linenumber" name="L305" href="#L305">305</a> 
+<a class="jxr_linenumber" name="L306" href="#L306">306</a>             <strong class="jxr_keyword">if</strong> (a &gt; 1) {
+<a class="jxr_linenumber" name="L307" href="#L307">307</a>                 <strong class="jxr_keyword">return</strong> algorithmBB(random, alpha, a, b);
+<a class="jxr_linenumber" name="L308" href="#L308">308</a>             } <strong class="jxr_keyword">else</strong> {
+<a class="jxr_linenumber" name="L309" href="#L309">309</a>                 <strong class="jxr_keyword">return</strong> algorithmBC(random, alpha, b, a);
+<a class="jxr_linenumber" name="L310" href="#L310">310</a>             }
+<a class="jxr_linenumber" name="L311" href="#L311">311</a>         }
+<a class="jxr_linenumber" name="L312" href="#L312">312</a> 
+<a class="jxr_linenumber" name="L313" href="#L313">313</a>         <em class="jxr_javadoccomment">/**</em>
+<a class="jxr_linenumber" name="L314" href="#L314">314</a> <em class="jxr_javadoccomment">         * Returns one sample using Cheng's BB algorithm, when both &amp;alpha; and &amp;beta; are greater than 1.</em>
+<a class="jxr_linenumber" name="L315" href="#L315">315</a> <em class="jxr_javadoccomment">         * @param random random generator to use</em>
+<a class="jxr_linenumber" name="L316" href="#L316">316</a> <em class="jxr_javadoccomment">         * @param a0 distribution first shape parameter (&amp;alpha;)</em>
+<a class="jxr_linenumber" name="L317" href="#L317">317</a> <em class="jxr_javadoccomment">         * @param a min(&amp;alpha;, &amp;beta;) where &amp;alpha;, &amp;beta; are the two distribution shape parameters</em>
+<a class="jxr_linenumber" name="L318" href="#L318">318</a> <em class="jxr_javadoccomment">         * @param b max(&amp;alpha;, &amp;beta;) where &amp;alpha;, &amp;beta; are the two distribution shape parameters</em>
+<a class="jxr_linenumber" name="L319" href="#L319">319</a> <em class="jxr_javadoccomment">         * @return sampled value</em>
+<a class="jxr_linenumber" name="L320" href="#L320">320</a> <em class="jxr_javadoccomment">         */</em>
+<a class="jxr_linenumber" name="L321" href="#L321">321</a>         <strong class="jxr_keyword">private</strong> <strong class="jxr_keyword">static</strong> <strong class="jxr_keyword">double</strong> algorithmBB(<a href="../../../../../org/apache/commons/math3/random/RandomGenerator.html">RandomGenerator</a> random,
+<a class="jxr_linenumber" name="L322" href="#L322">322</a>                                           <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> a0,
+<a class="jxr_linenumber" name="L323" href="#L323">323</a>                                           <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> a,
+<a class="jxr_linenumber" name="L324" href="#L324">324</a>                                           <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> b) {
+<a class="jxr_linenumber" name="L325" href="#L325">325</a>             <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> alpha = a + b;
+<a class="jxr_linenumber" name="L326" href="#L326">326</a>             <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> beta = FastMath.sqrt((alpha - 2.) / (2. * a * b - alpha));
+<a class="jxr_linenumber" name="L327" href="#L327">327</a>             <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> gamma = a + 1. / beta;
+<a class="jxr_linenumber" name="L328" href="#L328">328</a> 
+<a class="jxr_linenumber" name="L329" href="#L329">329</a>             <strong class="jxr_keyword">double</strong> r;
+<a class="jxr_linenumber" name="L330" href="#L330">330</a>             <strong class="jxr_keyword">double</strong> w;
+<a class="jxr_linenumber" name="L331" href="#L331">331</a>             <strong class="jxr_keyword">double</strong> t;
+<a class="jxr_linenumber" name="L332" href="#L332">332</a>             <strong class="jxr_keyword">do</strong> {
+<a class="jxr_linenumber" name="L333" href="#L333">333</a>                 <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> u1 = random.nextDouble();
+<a class="jxr_linenumber" name="L334" href="#L334">334</a>                 <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> u2 = random.nextDouble();
+<a class="jxr_linenumber" name="L335" href="#L335">335</a>                 <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> v = beta * (FastMath.log(u1) - FastMath.log1p(-u1));
+<a class="jxr_linenumber" name="L336" href="#L336">336</a>                 w = a * FastMath.exp(v);
+<a class="jxr_linenumber" name="L337" href="#L337">337</a>                 <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> z = u1 * u1 * u2;
+<a class="jxr_linenumber" name="L338" href="#L338">338</a>                 r = gamma * v - 1.3862944;
+<a class="jxr_linenumber" name="L339" href="#L339">339</a>                 <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> s = a + r - w;
+<a class="jxr_linenumber" name="L340" href="#L340">340</a>                 <strong class="jxr_keyword">if</strong> (s + 2.609438 &gt;= 5 * z) {
+<a class="jxr_linenumber" name="L341" href="#L341">341</a>                     <strong class="jxr_keyword">break</strong>;
+<a class="jxr_linenumber" name="L342" href="#L342">342</a>                 }
+<a class="jxr_linenumber" name="L343" href="#L343">343</a> 
+<a class="jxr_linenumber" name="L344" href="#L344">344</a>                 t = FastMath.log(z);
+<a class="jxr_linenumber" name="L345" href="#L345">345</a>                 <strong class="jxr_keyword">if</strong> (s &gt;= t) {
+<a class="jxr_linenumber" name="L346" href="#L346">346</a>                     <strong class="jxr_keyword">break</strong>;
+<a class="jxr_linenumber" name="L347" href="#L347">347</a>                 }
+<a class="jxr_linenumber" name="L348" href="#L348">348</a>             } <strong class="jxr_keyword">while</strong> (r + alpha * (FastMath.log(alpha) - FastMath.log(b + w)) &lt; t);
+<a class="jxr_linenumber" name="L349" href="#L349">349</a> 
+<a class="jxr_linenumber" name="L350" href="#L350">350</a>             w = FastMath.min(w, Double.MAX_VALUE);
+<a class="jxr_linenumber" name="L351" href="#L351">351</a>             <strong class="jxr_keyword">return</strong> Precision.equals(a, a0) ? w / (b + w) : b / (b + w);
+<a class="jxr_linenumber" name="L352" href="#L352">352</a>         }
+<a class="jxr_linenumber" name="L353" href="#L353">353</a> 
+<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">         * Returns one sample using Cheng's BC algorithm, when at least one of &amp;alpha; and &amp;beta; is smaller than 1.</em>
+<a class="jxr_linenumber" name="L356" href="#L356">356</a> <em class="jxr_javadoccomment">         * @param random random generator to use</em>
+<a class="jxr_linenumber" name="L357" href="#L357">357</a> <em class="jxr_javadoccomment">         * @param a0 distribution first shape parameter (&amp;alpha;)</em>
+<a class="jxr_linenumber" name="L358" href="#L358">358</a> <em class="jxr_javadoccomment">         * @param a max(&amp;alpha;, &amp;beta;) where &amp;alpha;, &amp;beta; are the two distribution shape parameters</em>
+<a class="jxr_linenumber" name="L359" href="#L359">359</a> <em class="jxr_javadoccomment">         * @param b min(&amp;alpha;, &amp;beta;) where &amp;alpha;, &amp;beta; are the two distribution shape parameters</em>
+<a class="jxr_linenumber" name="L360" href="#L360">360</a> <em class="jxr_javadoccomment">         * @return sampled value</em>
+<a class="jxr_linenumber" name="L361" href="#L361">361</a> <em class="jxr_javadoccomment">         */</em>
+<a class="jxr_linenumber" name="L362" href="#L362">362</a>         <strong class="jxr_keyword">private</strong> <strong class="jxr_keyword">static</strong> <strong class="jxr_keyword">double</strong> algorithmBC(<a href="../../../../../org/apache/commons/math3/random/RandomGenerator.html">RandomGenerator</a> random,
+<a class="jxr_linenumber" name="L363" href="#L363">363</a>                                           <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> a0,
+<a class="jxr_linenumber" name="L364" href="#L364">364</a>                                           <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> a,
+<a class="jxr_linenumber" name="L365" href="#L365">365</a>                                           <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> b) {
+<a class="jxr_linenumber" name="L366" href="#L366">366</a>             <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> alpha = a + b;
+<a class="jxr_linenumber" name="L367" href="#L367">367</a>             <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> beta = 1. / b;
+<a class="jxr_linenumber" name="L368" href="#L368">368</a>             <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> delta = 1. + a - b;
+<a class="jxr_linenumber" name="L369" href="#L369">369</a>             <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> k1 = delta * (0.0138889 + 0.0416667 * b) / (a * beta - 0.777778);
+<a class="jxr_linenumber" name="L370" href="#L370">370</a>             <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> k2 = 0.25 + (0.5 + 0.25 / delta) * b;
+<a class="jxr_linenumber" name="L371" href="#L371">371</a> 
+<a class="jxr_linenumber" name="L372" href="#L372">372</a>             <strong class="jxr_keyword">double</strong> w;
+<a class="jxr_linenumber" name="L373" href="#L373">373</a>             <strong class="jxr_keyword">for</strong> (;;) {
+<a class="jxr_linenumber" name="L374" href="#L374">374</a>                 <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> u1 = random.nextDouble();
+<a class="jxr_linenumber" name="L375" href="#L375">375</a>                 <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> u2 = random.nextDouble();
+<a class="jxr_linenumber" name="L376" href="#L376">376</a>                 <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> y = u1 * u2;
+<a class="jxr_linenumber" name="L377" href="#L377">377</a>                 <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> z = u1 * y;
+<a class="jxr_linenumber" name="L378" href="#L378">378</a>                 <strong class="jxr_keyword">if</strong> (u1 &lt; 0.5) {
+<a class="jxr_linenumber" name="L379" href="#L379">379</a>                     <strong class="jxr_keyword">if</strong> (0.25 * u2 + z - y &gt;= k1) {
+<a class="jxr_linenumber" name="L380" href="#L380">380</a>                         <strong class="jxr_keyword">continue</strong>;
+<a class="jxr_linenumber" name="L381" href="#L381">381</a>                     }
+<a class="jxr_linenumber" name="L382" href="#L382">382</a>                 } <strong class="jxr_keyword">else</strong> {
+<a class="jxr_linenumber" name="L383" href="#L383">383</a>                     <strong class="jxr_keyword">if</strong> (z &lt;= 0.25) {
+<a class="jxr_linenumber" name="L384" href="#L384">384</a>                         <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> v = beta * (FastMath.log(u1) - FastMath.log1p(-u1));
+<a class="jxr_linenumber" name="L385" href="#L385">385</a>                         w = a * FastMath.exp(v);
+<a class="jxr_linenumber" name="L386" href="#L386">386</a>                         <strong class="jxr_keyword">break</strong>;
+<a class="jxr_linenumber" name="L387" href="#L387">387</a>                     }
+<a class="jxr_linenumber" name="L388" href="#L388">388</a> 
+<a class="jxr_linenumber" name="L389" href="#L389">389</a>                     <strong class="jxr_keyword">if</strong> (z &gt;= k2) {
+<a class="jxr_linenumber" name="L390" href="#L390">390</a>                         <strong class="jxr_keyword">continue</strong>;
+<a class="jxr_linenumber" name="L391" href="#L391">391</a>                     }
+<a class="jxr_linenumber" name="L392" href="#L392">392</a>                 }
+<a class="jxr_linenumber" name="L393" href="#L393">393</a> 
+<a class="jxr_linenumber" name="L394" href="#L394">394</a>                 <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> v = beta * (FastMath.log(u1) - FastMath.log1p(-u1));
+<a class="jxr_linenumber" name="L395" href="#L395">395</a>                 w = a * FastMath.exp(v);
+<a class="jxr_linenumber" name="L396" href="#L396">396</a>                 <strong class="jxr_keyword">if</strong> (alpha * (FastMath.log(alpha) - FastMath.log(b + w) + v) - 1.3862944 &gt;= FastMath.log(z)) {
+<a class="jxr_linenumber" name="L397" href="#L397">397</a>                     <strong class="jxr_keyword">break</strong>;
+<a class="jxr_linenumber" name="L398" href="#L398">398</a>                 }
+<a class="jxr_linenumber" name="L399" href="#L399">399</a>             }
+<a class="jxr_linenumber" name="L400" href="#L400">400</a> 
+<a class="jxr_linenumber" name="L401" href="#L401">401</a>             w = FastMath.min(w, Double.MAX_VALUE);
+<a class="jxr_linenumber" name="L402" href="#L402">402</a>             <strong class="jxr_keyword">return</strong> Precision.equals(a, a0) ? w / (b + w) : b / (b + w);
+<a class="jxr_linenumber" name="L403" href="#L403">403</a>         }
+<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> }
 </pre>
 <hr/>
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