commons-notifications mailing list archives

Site index · List index
Message view « Date » · « Thread »
Top « Date » · « Thread »
From l..@apache.org
Subject svn commit: r951633 [32/49] - 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/ZipfDistribution.html
==============================================================================
--- websites/production/commons/content/proper/commons-math/xref/org/apache/commons/math3/distribution/ZipfDistribution.html (original)
+++ websites/production/commons/content/proper/commons-math/xref/org/apache/commons/math3/distribution/ZipfDistribution.html Sun May 17 17:05:50 2015
@@ -51,223 +51,383 @@
 <a class="jxr_linenumber" name="L43" href="#L43">43</a>      <strong class="jxr_keyword">private</strong> <strong class="jxr_keyword">double</strong> numericalVariance = Double.NaN;
 <a class="jxr_linenumber" name="L44" href="#L44">44</a>      <em class="jxr_javadoccomment">/** Whether or not the numerical variance has been calculated */</em>
 <a class="jxr_linenumber" name="L45" href="#L45">45</a>      <strong class="jxr_keyword">private</strong> <strong class="jxr_keyword">boolean</strong> numericalVarianceIsCalculated = false;
-<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">     * Create a new Zipf distribution with the given number of elements and</em>
-<a class="jxr_linenumber" name="L49" href="#L49">49</a>  <em class="jxr_javadoccomment">     * exponent.</em>
-<a class="jxr_linenumber" name="L50" href="#L50">50</a>  <em class="jxr_javadoccomment">     * &lt;p&gt;</em>
-<a class="jxr_linenumber" name="L51" href="#L51">51</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="L52" href="#L52">52</a>  <em class="jxr_javadoccomment">     * {@link Well19937c} as random generator to be used for sampling only (see</em>
-<a class="jxr_linenumber" name="L53" href="#L53">53</a>  <em class="jxr_javadoccomment">     * {@link #sample()} and {@link #sample(int)}). In case no sampling is</em>
-<a class="jxr_linenumber" name="L54" href="#L54">54</a>  <em class="jxr_javadoccomment">     * needed for the created distribution, it is advised to pass {@code null}</em>
-<a class="jxr_linenumber" name="L55" href="#L55">55</a>  <em class="jxr_javadoccomment">     * as random generator via the appropriate constructors to avoid the</em>
-<a class="jxr_linenumber" name="L56" href="#L56">56</a>  <em class="jxr_javadoccomment">     * additional initialisation overhead.</em>
-<a class="jxr_linenumber" name="L57" href="#L57">57</a>  <em class="jxr_javadoccomment">     *</em>
-<a class="jxr_linenumber" name="L58" href="#L58">58</a>  <em class="jxr_javadoccomment">     * @param numberOfElements Number of elements.</em>
-<a class="jxr_linenumber" name="L59" href="#L59">59</a>  <em class="jxr_javadoccomment">     * @param exponent Exponent.</em>
-<a class="jxr_linenumber" name="L60" href="#L60">60</a>  <em class="jxr_javadoccomment">     * @exception NotStrictlyPositiveException if {@code numberOfElements &lt;= 0}</em>
-<a class="jxr_linenumber" name="L61" href="#L61">61</a>  <em class="jxr_javadoccomment">     * or {@code exponent &lt;= 0}.</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>      <strong class="jxr_keyword">public</strong> <a href="../../../../../org/apache/commons/math3/distribution/ZipfDistribution.html">ZipfDistribution</a>(<strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">int</strong> numberOfElements, <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> exponent) {
-<a class="jxr_linenumber" name="L64" href="#L64">64</a>          <strong class="jxr_keyword">this</strong>(<strong class="jxr_keyword">new</strong> <a href="../../../../../org/apache/commons/math3/random/Well19937c.html">Well19937c</a>(), numberOfElements, exponent);
-<a class="jxr_linenumber" name="L65" href="#L65">65</a>      }
-<a class="jxr_linenumber" name="L66" href="#L66">66</a>  
-<a class="jxr_linenumber" name="L67" href="#L67">67</a>      <em class="jxr_javadoccomment">/**</em>
-<a class="jxr_linenumber" name="L68" href="#L68">68</a>  <em class="jxr_javadoccomment">     * Creates a Zipf distribution.</em>
-<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">     * @param rng Random number generator.</em>
-<a class="jxr_linenumber" name="L71" href="#L71">71</a>  <em class="jxr_javadoccomment">     * @param numberOfElements Number of elements.</em>
-<a class="jxr_linenumber" name="L72" href="#L72">72</a>  <em class="jxr_javadoccomment">     * @param exponent Exponent.</em>
-<a class="jxr_linenumber" name="L73" href="#L73">73</a>  <em class="jxr_javadoccomment">     * @exception NotStrictlyPositiveException if {@code numberOfElements &lt;= 0}</em>
-<a class="jxr_linenumber" name="L74" href="#L74">74</a>  <em class="jxr_javadoccomment">     * or {@code exponent &lt;= 0}.</em>
-<a class="jxr_linenumber" name="L75" href="#L75">75</a>  <em class="jxr_javadoccomment">     * @since 3.1</em>
-<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>      <strong class="jxr_keyword">public</strong> <a href="../../../../../org/apache/commons/math3/distribution/ZipfDistribution.html">ZipfDistribution</a>(<a href="../../../../../org/apache/commons/math3/random/RandomGenerator.html">RandomGenerator</a> rng,
-<a class="jxr_linenumber" name="L78" href="#L78">78</a>                              <strong class="jxr_keyword">int</strong> numberOfElements,
-<a class="jxr_linenumber" name="L79" href="#L79">79</a>                              <strong class="jxr_keyword">double</strong> exponent)
-<a class="jxr_linenumber" name="L80" href="#L80">80</a>          <strong class="jxr_keyword">throws</strong> <a href="../../../../../org/apache/commons/math3/exception/NotStrictlyPositiveException.html">NotStrictlyPositiveException</a> {
-<a class="jxr_linenumber" name="L81" href="#L81">81</a>          <strong class="jxr_keyword">super</strong>(rng);
-<a class="jxr_linenumber" name="L82" href="#L82">82</a>  
-<a class="jxr_linenumber" name="L83" href="#L83">83</a>          <strong class="jxr_keyword">if</strong> (numberOfElements &lt;= 0) {
-<a class="jxr_linenumber" name="L84" href="#L84">84</a>              <strong class="jxr_keyword">throw</strong> <strong class="jxr_keyword">new</strong> <a href="../../../../../org/apache/commons/math3/exception/NotStrictlyPositiveException.html">NotStrictlyPositiveException</a>(LocalizedFormats.DIMENSION,
-<a class="jxr_linenumber" name="L85" href="#L85">85</a>                                                     numberOfElements);
-<a class="jxr_linenumber" name="L86" href="#L86">86</a>          }
-<a class="jxr_linenumber" name="L87" href="#L87">87</a>          <strong class="jxr_keyword">if</strong> (exponent &lt;= 0) {
-<a class="jxr_linenumber" name="L88" href="#L88">88</a>              <strong class="jxr_keyword">throw</strong> <strong class="jxr_keyword">new</strong> <a href="../../../../../org/apache/commons/math3/exception/NotStrictlyPositiveException.html">NotStrictlyPositiveException</a>(LocalizedFormats.EXPONENT,
-<a class="jxr_linenumber" name="L89" href="#L89">89</a>                                                     exponent);
-<a class="jxr_linenumber" name="L90" href="#L90">90</a>          }
-<a class="jxr_linenumber" name="L91" href="#L91">91</a>  
-<a class="jxr_linenumber" name="L92" href="#L92">92</a>          <strong class="jxr_keyword">this</strong>.numberOfElements = numberOfElements;
-<a class="jxr_linenumber" name="L93" href="#L93">93</a>          <strong class="jxr_keyword">this</strong>.exponent = exponent;
-<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">     * Get the number of elements (e.g. corpus size) for the 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 number of elements</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">int</strong> getNumberOfElements() {
-<a class="jxr_linenumber" name="L102" href="#L102">102</a>         <strong class="jxr_keyword">return</strong> numberOfElements;
-<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">     * Get the exponent characterizing the 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 exponent</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> getExponent() {
-<a class="jxr_linenumber" name="L111" href="#L111">111</a>         <strong class="jxr_keyword">return</strong> exponent;
-<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>     <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">double</strong> probability(<strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">int</strong> x) {
-<a class="jxr_linenumber" name="L116" href="#L116">116</a>         <strong class="jxr_keyword">if</strong> (x &lt;= 0 || x &gt; numberOfElements) {
-<a class="jxr_linenumber" name="L117" href="#L117">117</a>             <strong class="jxr_keyword">return</strong> 0.0;
-<a class="jxr_linenumber" name="L118" href="#L118">118</a>         }
-<a class="jxr_linenumber" name="L119" href="#L119">119</a> 
-<a class="jxr_linenumber" name="L120" href="#L120">120</a>         <strong class="jxr_keyword">return</strong> (1.0 / FastMath.pow(x, exponent)) / generalizedHarmonic(numberOfElements, exponent);
-<a class="jxr_linenumber" name="L121" href="#L121">121</a>     }
-<a class="jxr_linenumber" name="L122" href="#L122">122</a> 
-<a class="jxr_linenumber" name="L123" href="#L123">123</a>     <em class="jxr_javadoccomment">/** {@inheritDoc} */</em>
-<a class="jxr_linenumber" name="L124" href="#L124">124</a>     @Override
-<a class="jxr_linenumber" name="L125" href="#L125">125</a>     <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">double</strong> logProbability(<strong class="jxr_keyword">int</strong> x) {
-<a class="jxr_linenumber" name="L126" href="#L126">126</a>         <strong class="jxr_keyword">if</strong> (x &lt;= 0 || x &gt; numberOfElements) {
-<a class="jxr_linenumber" name="L127" href="#L127">127</a>             <strong class="jxr_keyword">return</strong> Double.NEGATIVE_INFINITY;
-<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>         <strong class="jxr_keyword">return</strong> -FastMath.log(x) * exponent - FastMath.log(generalizedHarmonic(numberOfElements, exponent));
-<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>     <em class="jxr_javadoccomment">/** {@inheritDoc} */</em>
-<a class="jxr_linenumber" name="L134" href="#L134">134</a>     <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">double</strong> cumulativeProbability(<strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">int</strong> x) {
-<a class="jxr_linenumber" name="L135" href="#L135">135</a>         <strong class="jxr_keyword">if</strong> (x &lt;= 0) {
-<a class="jxr_linenumber" name="L136" href="#L136">136</a>             <strong class="jxr_keyword">return</strong> 0.0;
-<a class="jxr_linenumber" name="L137" href="#L137">137</a>         } <strong class="jxr_keyword">else</strong> <strong class="jxr_keyword">if</strong> (x &gt;= numberOfElements) {
-<a class="jxr_linenumber" name="L138" href="#L138">138</a>             <strong class="jxr_keyword">return</strong> 1.0;
-<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>         <strong class="jxr_keyword">return</strong> generalizedHarmonic(x, exponent) / generalizedHarmonic(numberOfElements, exponent);
-<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">/**</em>
-<a class="jxr_linenumber" name="L145" href="#L145">145</a> <em class="jxr_javadoccomment">     * {@inheritDoc}</em>
-<a class="jxr_linenumber" name="L146" href="#L146">146</a> <em class="jxr_javadoccomment">     *</em>
-<a class="jxr_linenumber" name="L147" href="#L147">147</a> <em class="jxr_javadoccomment">     * For number of elements {@code N} and exponent {@code s}, the mean is</em>
-<a class="jxr_linenumber" name="L148" href="#L148">148</a> <em class="jxr_javadoccomment">     * {@code Hs1 / Hs}, where</em>
-<a class="jxr_linenumber" name="L149" href="#L149">149</a> <em class="jxr_javadoccomment">     * &lt;ul&gt;</em>
-<a class="jxr_linenumber" name="L150" href="#L150">150</a> <em class="jxr_javadoccomment">     *  &lt;li&gt;{@code Hs1 = generalizedHarmonic(N, s - 1)},&lt;/li&gt;</em>
-<a class="jxr_linenumber" name="L151" href="#L151">151</a> <em class="jxr_javadoccomment">     *  &lt;li&gt;{@code Hs = generalizedHarmonic(N, s)}.&lt;/li&gt;</em>
-<a class="jxr_linenumber" name="L152" href="#L152">152</a> <em class="jxr_javadoccomment">     * &lt;/ul&gt;</em>
-<a class="jxr_linenumber" name="L153" href="#L153">153</a> <em class="jxr_javadoccomment">     */</em>
-<a class="jxr_linenumber" name="L154" href="#L154">154</a>     <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">double</strong> getNumericalMean() {
-<a class="jxr_linenumber" name="L155" href="#L155">155</a>         <strong class="jxr_keyword">if</strong> (!numericalMeanIsCalculated) {
-<a class="jxr_linenumber" name="L156" href="#L156">156</a>             numericalMean = calculateNumericalMean();
-<a class="jxr_linenumber" name="L157" href="#L157">157</a>             numericalMeanIsCalculated = <strong class="jxr_keyword">true</strong>;
-<a class="jxr_linenumber" name="L158" href="#L158">158</a>         }
-<a class="jxr_linenumber" name="L159" href="#L159">159</a>         <strong class="jxr_keyword">return</strong> numericalMean;
-<a class="jxr_linenumber" name="L160" href="#L160">160</a>     }
-<a class="jxr_linenumber" name="L161" href="#L161">161</a> 
-<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">     * Used by {@link #getNumericalMean()}.</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">     * @return the mean of this distribution</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>     <strong class="jxr_keyword">protected</strong> <strong class="jxr_keyword">double</strong> calculateNumericalMean() {
-<a class="jxr_linenumber" name="L168" href="#L168">168</a>         <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">int</strong> N = getNumberOfElements();
-<a class="jxr_linenumber" name="L169" href="#L169">169</a>         <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> s = getExponent();
-<a class="jxr_linenumber" name="L170" href="#L170">170</a> 
-<a class="jxr_linenumber" name="L171" href="#L171">171</a>         <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> Hs1 = generalizedHarmonic(N, s - 1);
-<a class="jxr_linenumber" name="L172" href="#L172">172</a>         <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> Hs = generalizedHarmonic(N, s);
-<a class="jxr_linenumber" name="L173" href="#L173">173</a> 
-<a class="jxr_linenumber" name="L174" href="#L174">174</a>         <strong class="jxr_keyword">return</strong> Hs1 / Hs;
-<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">     * For number of elements {@code N} and exponent {@code s}, the mean is</em>
-<a class="jxr_linenumber" name="L181" href="#L181">181</a> <em class="jxr_javadoccomment">     * {@code (Hs2 / Hs) - (Hs1^2 / Hs^2)}, where</em>
-<a class="jxr_linenumber" name="L182" href="#L182">182</a> <em class="jxr_javadoccomment">     * &lt;ul&gt;</em>
-<a class="jxr_linenumber" name="L183" href="#L183">183</a> <em class="jxr_javadoccomment">     *  &lt;li&gt;{@code Hs2 = generalizedHarmonic(N, s - 2)},&lt;/li&gt;</em>
-<a class="jxr_linenumber" name="L184" href="#L184">184</a> <em class="jxr_javadoccomment">     *  &lt;li&gt;{@code Hs1 = generalizedHarmonic(N, s - 1)},&lt;/li&gt;</em>
-<a class="jxr_linenumber" name="L185" href="#L185">185</a> <em class="jxr_javadoccomment">     *  &lt;li&gt;{@code Hs = generalizedHarmonic(N, s)}.&lt;/li&gt;</em>
-<a class="jxr_linenumber" name="L186" href="#L186">186</a> <em class="jxr_javadoccomment">     * &lt;/ul&gt;</em>
-<a class="jxr_linenumber" name="L187" href="#L187">187</a> <em class="jxr_javadoccomment">     */</em>
-<a class="jxr_linenumber" name="L188" href="#L188">188</a>     <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">double</strong> getNumericalVariance() {
-<a class="jxr_linenumber" name="L189" href="#L189">189</a>         <strong class="jxr_keyword">if</strong> (!numericalVarianceIsCalculated) {
-<a class="jxr_linenumber" name="L190" href="#L190">190</a>             numericalVariance = calculateNumericalVariance();
-<a class="jxr_linenumber" name="L191" href="#L191">191</a>             numericalVarianceIsCalculated = <strong class="jxr_keyword">true</strong>;
-<a class="jxr_linenumber" name="L192" href="#L192">192</a>         }
-<a class="jxr_linenumber" name="L193" href="#L193">193</a>         <strong class="jxr_keyword">return</strong> numericalVariance;
-<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">     * Used by {@link #getNumericalVariance()}.</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 the variance of this distribution</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>     <strong class="jxr_keyword">protected</strong> <strong class="jxr_keyword">double</strong> calculateNumericalVariance() {
-<a class="jxr_linenumber" name="L202" href="#L202">202</a>         <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">int</strong> N = getNumberOfElements();
-<a class="jxr_linenumber" name="L203" href="#L203">203</a>         <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> s = getExponent();
-<a class="jxr_linenumber" name="L204" href="#L204">204</a> 
-<a class="jxr_linenumber" name="L205" href="#L205">205</a>         <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> Hs2 = generalizedHarmonic(N, s - 2);
-<a class="jxr_linenumber" name="L206" href="#L206">206</a>         <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> Hs1 = generalizedHarmonic(N, s - 1);
-<a class="jxr_linenumber" name="L207" href="#L207">207</a>         <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> Hs = generalizedHarmonic(N, s);
-<a class="jxr_linenumber" name="L208" href="#L208">208</a> 
-<a class="jxr_linenumber" name="L209" href="#L209">209</a>         <strong class="jxr_keyword">return</strong> (Hs2 / Hs) - ((Hs1 * Hs1) / (Hs * Hs));
-<a class="jxr_linenumber" name="L210" href="#L210">210</a>     }
-<a class="jxr_linenumber" name="L211" href="#L211">211</a> 
-<a class="jxr_linenumber" name="L212" href="#L212">212</a>     <em class="jxr_javadoccomment">/**</em>
-<a class="jxr_linenumber" name="L213" href="#L213">213</a> <em class="jxr_javadoccomment">     * Calculates the Nth generalized harmonic number. See</em>
-<a class="jxr_linenumber" name="L214" href="#L214">214</a> <em class="jxr_javadoccomment">     * &lt;a href="<a href="http://mathworld.wolfram.com/HarmonicSeries.html" target="alexandria_uri">http://mathworld.wolfram.com/HarmonicSeries.html</a>"&gt;Harmonic</em>
-<a class="jxr_linenumber" name="L215" href="#L215">215</a> <em class="jxr_javadoccomment">     * Series&lt;/a&gt;.</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">     * @param n Term in the series to calculate (must be larger than 1)</em>
-<a class="jxr_linenumber" name="L218" href="#L218">218</a> <em class="jxr_javadoccomment">     * @param m Exponent (special case {@code m = 1} is the harmonic series).</em>
-<a class="jxr_linenumber" name="L219" href="#L219">219</a> <em class="jxr_javadoccomment">     * @return the n&lt;sup&gt;th&lt;/sup&gt; generalized harmonic number.</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">private</strong> <strong class="jxr_keyword">double</strong> generalizedHarmonic(<strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">int</strong> n, <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> m) {
-<a class="jxr_linenumber" name="L222" href="#L222">222</a>         <strong class="jxr_keyword">double</strong> value = 0;
-<a class="jxr_linenumber" name="L223" href="#L223">223</a>         <strong class="jxr_keyword">for</strong> (<strong class="jxr_keyword">int</strong> k = n; k &gt; 0; --k) {
-<a class="jxr_linenumber" name="L224" href="#L224">224</a>             value += 1.0 / FastMath.pow(k, m);
-<a class="jxr_linenumber" name="L225" href="#L225">225</a>         }
-<a class="jxr_linenumber" name="L226" href="#L226">226</a>         <strong class="jxr_keyword">return</strong> value;
-<a class="jxr_linenumber" name="L227" href="#L227">227</a>     }
-<a class="jxr_linenumber" name="L228" href="#L228">228</a> 
-<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">     * {@inheritDoc}</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">     * The lower bound of the support is always 1 no matter the parameters.</em>
+<a class="jxr_linenumber" name="L46" href="#L46">46</a>      <em class="jxr_javadoccomment">/** The sampler to be used for the sample() method */</em>
+<a class="jxr_linenumber" name="L47" href="#L47">47</a>      <strong class="jxr_keyword">private</strong> <strong class="jxr_keyword">transient</strong> <a href="../../../../../org/apache/commons/math3/distribution/ZipfDistribution.html">ZipfRejectionSampler</a> sampler;
+<a class="jxr_linenumber" name="L48" href="#L48">48</a>  
+<a class="jxr_linenumber" name="L49" href="#L49">49</a>      <em class="jxr_javadoccomment">/**</em>
+<a class="jxr_linenumber" name="L50" href="#L50">50</a>  <em class="jxr_javadoccomment">     * Create a new Zipf distribution with the given number of elements and</em>
+<a class="jxr_linenumber" name="L51" href="#L51">51</a>  <em class="jxr_javadoccomment">     * exponent.</em>
+<a class="jxr_linenumber" name="L52" href="#L52">52</a>  <em class="jxr_javadoccomment">     * &lt;p&gt;</em>
+<a class="jxr_linenumber" name="L53" href="#L53">53</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="L54" href="#L54">54</a>  <em class="jxr_javadoccomment">     * {@link Well19937c} as random generator to be used for sampling only (see</em>
+<a class="jxr_linenumber" name="L55" href="#L55">55</a>  <em class="jxr_javadoccomment">     * {@link #sample()} and {@link #sample(int)}). In case no sampling is</em>
+<a class="jxr_linenumber" name="L56" href="#L56">56</a>  <em class="jxr_javadoccomment">     * needed for the created distribution, it is advised to pass {@code null}</em>
+<a class="jxr_linenumber" name="L57" href="#L57">57</a>  <em class="jxr_javadoccomment">     * as random generator via the appropriate constructors to avoid the</em>
+<a class="jxr_linenumber" name="L58" href="#L58">58</a>  <em class="jxr_javadoccomment">     * additional initialisation overhead.</em>
+<a class="jxr_linenumber" name="L59" href="#L59">59</a>  <em class="jxr_javadoccomment">     *</em>
+<a class="jxr_linenumber" name="L60" href="#L60">60</a>  <em class="jxr_javadoccomment">     * @param numberOfElements Number of elements.</em>
+<a class="jxr_linenumber" name="L61" href="#L61">61</a>  <em class="jxr_javadoccomment">     * @param exponent Exponent.</em>
+<a class="jxr_linenumber" name="L62" href="#L62">62</a>  <em class="jxr_javadoccomment">     * @exception NotStrictlyPositiveException if {@code numberOfElements &lt;= 0}</em>
+<a class="jxr_linenumber" name="L63" href="#L63">63</a>  <em class="jxr_javadoccomment">     * or {@code exponent &lt;= 0}.</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/ZipfDistribution.html">ZipfDistribution</a>(<strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">int</strong> numberOfElements, <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> exponent) {
+<a class="jxr_linenumber" name="L66" href="#L66">66</a>          <strong class="jxr_keyword">this</strong>(<strong class="jxr_keyword">new</strong> <a href="../../../../../org/apache/commons/math3/random/Well19937c.html">Well19937c</a>(), numberOfElements, exponent);
+<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">     * Creates a Zipf 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>  <em class="jxr_javadoccomment">     * @param rng Random number generator.</em>
+<a class="jxr_linenumber" name="L73" href="#L73">73</a>  <em class="jxr_javadoccomment">     * @param numberOfElements Number of elements.</em>
+<a class="jxr_linenumber" name="L74" href="#L74">74</a>  <em class="jxr_javadoccomment">     * @param exponent Exponent.</em>
+<a class="jxr_linenumber" name="L75" href="#L75">75</a>  <em class="jxr_javadoccomment">     * @exception NotStrictlyPositiveException if {@code numberOfElements &lt;= 0}</em>
+<a class="jxr_linenumber" name="L76" href="#L76">76</a>  <em class="jxr_javadoccomment">     * or {@code exponent &lt;= 0}.</em>
+<a class="jxr_linenumber" name="L77" href="#L77">77</a>  <em class="jxr_javadoccomment">     * @since 3.1</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>      <strong class="jxr_keyword">public</strong> <a href="../../../../../org/apache/commons/math3/distribution/ZipfDistribution.html">ZipfDistribution</a>(<a href="../../../../../org/apache/commons/math3/random/RandomGenerator.html">RandomGenerator</a> rng,
+<a class="jxr_linenumber" name="L80" href="#L80">80</a>                              <strong class="jxr_keyword">int</strong> numberOfElements,
+<a class="jxr_linenumber" name="L81" href="#L81">81</a>                              <strong class="jxr_keyword">double</strong> exponent)
+<a class="jxr_linenumber" name="L82" href="#L82">82</a>          <strong class="jxr_keyword">throws</strong> <a href="../../../../../org/apache/commons/math3/exception/NotStrictlyPositiveException.html">NotStrictlyPositiveException</a> {
+<a class="jxr_linenumber" name="L83" href="#L83">83</a>          <strong class="jxr_keyword">super</strong>(rng);
+<a class="jxr_linenumber" name="L84" href="#L84">84</a>  
+<a class="jxr_linenumber" name="L85" href="#L85">85</a>          <strong class="jxr_keyword">if</strong> (numberOfElements &lt;= 0) {
+<a class="jxr_linenumber" name="L86" href="#L86">86</a>              <strong class="jxr_keyword">throw</strong> <strong class="jxr_keyword">new</strong> <a href="../../../../../org/apache/commons/math3/exception/NotStrictlyPositiveException.html">NotStrictlyPositiveException</a>(LocalizedFormats.DIMENSION,
+<a class="jxr_linenumber" name="L87" href="#L87">87</a>                                                     numberOfElements);
+<a class="jxr_linenumber" name="L88" href="#L88">88</a>          }
+<a class="jxr_linenumber" name="L89" href="#L89">89</a>          <strong class="jxr_keyword">if</strong> (exponent &lt;= 0) {
+<a class="jxr_linenumber" name="L90" href="#L90">90</a>              <strong class="jxr_keyword">throw</strong> <strong class="jxr_keyword">new</strong> <a href="../../../../../org/apache/commons/math3/exception/NotStrictlyPositiveException.html">NotStrictlyPositiveException</a>(LocalizedFormats.EXPONENT,
+<a class="jxr_linenumber" name="L91" href="#L91">91</a>                                                     exponent);
+<a class="jxr_linenumber" name="L92" href="#L92">92</a>          }
+<a class="jxr_linenumber" name="L93" href="#L93">93</a>  
+<a class="jxr_linenumber" name="L94" href="#L94">94</a>          <strong class="jxr_keyword">this</strong>.numberOfElements = numberOfElements;
+<a class="jxr_linenumber" name="L95" href="#L95">95</a>          <strong class="jxr_keyword">this</strong>.exponent = exponent;
+<a class="jxr_linenumber" name="L96" href="#L96">96</a>      }
+<a class="jxr_linenumber" name="L97" href="#L97">97</a>  
+<a class="jxr_linenumber" name="L98" href="#L98">98</a>      <em class="jxr_javadoccomment">/**</em>
+<a class="jxr_linenumber" name="L99" href="#L99">99</a>  <em class="jxr_javadoccomment">     * Get the number of elements (e.g. corpus size) for the distribution.</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> <em class="jxr_javadoccomment">     * @return the number of elements</em>
+<a class="jxr_linenumber" name="L102" href="#L102">102</a> <em class="jxr_javadoccomment">     */</em>
+<a class="jxr_linenumber" name="L103" href="#L103">103</a>     <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">int</strong> getNumberOfElements() {
+<a class="jxr_linenumber" name="L104" href="#L104">104</a>         <strong class="jxr_keyword">return</strong> numberOfElements;
+<a class="jxr_linenumber" name="L105" href="#L105">105</a>     }
+<a class="jxr_linenumber" name="L106" href="#L106">106</a> 
+<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">     * Get the exponent characterizing the distribution.</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> <em class="jxr_javadoccomment">     * @return the exponent</em>
+<a class="jxr_linenumber" name="L111" href="#L111">111</a> <em class="jxr_javadoccomment">     */</em>
+<a class="jxr_linenumber" name="L112" href="#L112">112</a>     <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">double</strong> getExponent() {
+<a class="jxr_linenumber" name="L113" href="#L113">113</a>         <strong class="jxr_keyword">return</strong> exponent;
+<a class="jxr_linenumber" name="L114" href="#L114">114</a>     }
+<a class="jxr_linenumber" name="L115" href="#L115">115</a> 
+<a class="jxr_linenumber" name="L116" href="#L116">116</a>     <em class="jxr_javadoccomment">/** {@inheritDoc} */</em>
+<a class="jxr_linenumber" name="L117" href="#L117">117</a>     <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">double</strong> probability(<strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">int</strong> x) {
+<a class="jxr_linenumber" name="L118" href="#L118">118</a>         <strong class="jxr_keyword">if</strong> (x &lt;= 0 || x &gt; numberOfElements) {
+<a class="jxr_linenumber" name="L119" href="#L119">119</a>             <strong class="jxr_keyword">return</strong> 0.0;
+<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> (1.0 / FastMath.pow(x, exponent)) / generalizedHarmonic(numberOfElements, exponent);
+<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> logProbability(<strong class="jxr_keyword">int</strong> x) {
+<a class="jxr_linenumber" name="L128" href="#L128">128</a>         <strong class="jxr_keyword">if</strong> (x &lt;= 0 || x &gt; numberOfElements) {
+<a class="jxr_linenumber" name="L129" href="#L129">129</a>             <strong class="jxr_keyword">return</strong> Double.NEGATIVE_INFINITY;
+<a class="jxr_linenumber" name="L130" href="#L130">130</a>         }
+<a class="jxr_linenumber" name="L131" href="#L131">131</a> 
+<a class="jxr_linenumber" name="L132" href="#L132">132</a>         <strong class="jxr_keyword">return</strong> -FastMath.log(x) * exponent - FastMath.log(generalizedHarmonic(numberOfElements, exponent));
+<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">/** {@inheritDoc} */</em>
+<a class="jxr_linenumber" name="L136" href="#L136">136</a>     <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">double</strong> cumulativeProbability(<strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">int</strong> x) {
+<a class="jxr_linenumber" name="L137" href="#L137">137</a>         <strong class="jxr_keyword">if</strong> (x &lt;= 0) {
+<a class="jxr_linenumber" name="L138" href="#L138">138</a>             <strong class="jxr_keyword">return</strong> 0.0;
+<a class="jxr_linenumber" name="L139" href="#L139">139</a>         } <strong class="jxr_keyword">else</strong> <strong class="jxr_keyword">if</strong> (x &gt;= numberOfElements) {
+<a class="jxr_linenumber" name="L140" href="#L140">140</a>             <strong class="jxr_keyword">return</strong> 1.0;
+<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>         <strong class="jxr_keyword">return</strong> generalizedHarmonic(x, exponent) / generalizedHarmonic(numberOfElements, exponent);
+<a class="jxr_linenumber" name="L144" href="#L144">144</a>     }
+<a class="jxr_linenumber" name="L145" href="#L145">145</a> 
+<a class="jxr_linenumber" name="L146" href="#L146">146</a>     <em class="jxr_javadoccomment">/**</em>
+<a class="jxr_linenumber" name="L147" href="#L147">147</a> <em class="jxr_javadoccomment">     * {@inheritDoc}</em>
+<a class="jxr_linenumber" name="L148" href="#L148">148</a> <em class="jxr_javadoccomment">     *</em>
+<a class="jxr_linenumber" name="L149" href="#L149">149</a> <em class="jxr_javadoccomment">     * For number of elements {@code N} and exponent {@code s}, the mean is</em>
+<a class="jxr_linenumber" name="L150" href="#L150">150</a> <em class="jxr_javadoccomment">     * {@code Hs1 / Hs}, where</em>
+<a class="jxr_linenumber" name="L151" href="#L151">151</a> <em class="jxr_javadoccomment">     * &lt;ul&gt;</em>
+<a class="jxr_linenumber" name="L152" href="#L152">152</a> <em class="jxr_javadoccomment">     *  &lt;li&gt;{@code Hs1 = generalizedHarmonic(N, s - 1)},&lt;/li&gt;</em>
+<a class="jxr_linenumber" name="L153" href="#L153">153</a> <em class="jxr_javadoccomment">     *  &lt;li&gt;{@code Hs = generalizedHarmonic(N, s)}.&lt;/li&gt;</em>
+<a class="jxr_linenumber" name="L154" href="#L154">154</a> <em class="jxr_javadoccomment">     * &lt;/ul&gt;</em>
+<a class="jxr_linenumber" name="L155" href="#L155">155</a> <em class="jxr_javadoccomment">     */</em>
+<a class="jxr_linenumber" name="L156" href="#L156">156</a>     <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">double</strong> getNumericalMean() {
+<a class="jxr_linenumber" name="L157" href="#L157">157</a>         <strong class="jxr_keyword">if</strong> (!numericalMeanIsCalculated) {
+<a class="jxr_linenumber" name="L158" href="#L158">158</a>             numericalMean = calculateNumericalMean();
+<a class="jxr_linenumber" name="L159" href="#L159">159</a>             numericalMeanIsCalculated = <strong class="jxr_keyword">true</strong>;
+<a class="jxr_linenumber" name="L160" href="#L160">160</a>         }
+<a class="jxr_linenumber" name="L161" href="#L161">161</a>         <strong class="jxr_keyword">return</strong> numericalMean;
+<a class="jxr_linenumber" name="L162" href="#L162">162</a>     }
+<a class="jxr_linenumber" name="L163" href="#L163">163</a> 
+<a class="jxr_linenumber" name="L164" href="#L164">164</a>     <em class="jxr_javadoccomment">/**</em>
+<a class="jxr_linenumber" name="L165" href="#L165">165</a> <em class="jxr_javadoccomment">     * Used by {@link #getNumericalMean()}.</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> <em class="jxr_javadoccomment">     * @return the mean of this distribution</em>
+<a class="jxr_linenumber" name="L168" href="#L168">168</a> <em class="jxr_javadoccomment">     */</em>
+<a class="jxr_linenumber" name="L169" href="#L169">169</a>     <strong class="jxr_keyword">protected</strong> <strong class="jxr_keyword">double</strong> calculateNumericalMean() {
+<a class="jxr_linenumber" name="L170" href="#L170">170</a>         <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">int</strong> N = getNumberOfElements();
+<a class="jxr_linenumber" name="L171" href="#L171">171</a>         <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> s = getExponent();
+<a class="jxr_linenumber" name="L172" href="#L172">172</a> 
+<a class="jxr_linenumber" name="L173" href="#L173">173</a>         <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> Hs1 = generalizedHarmonic(N, s - 1);
+<a class="jxr_linenumber" name="L174" href="#L174">174</a>         <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> Hs = generalizedHarmonic(N, s);
+<a class="jxr_linenumber" name="L175" href="#L175">175</a> 
+<a class="jxr_linenumber" name="L176" href="#L176">176</a>         <strong class="jxr_keyword">return</strong> Hs1 / Hs;
+<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">/**</em>
+<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> <em class="jxr_javadoccomment">     *</em>
+<a class="jxr_linenumber" name="L182" href="#L182">182</a> <em class="jxr_javadoccomment">     * For number of elements {@code N} and exponent {@code s}, the mean is</em>
+<a class="jxr_linenumber" name="L183" href="#L183">183</a> <em class="jxr_javadoccomment">     * {@code (Hs2 / Hs) - (Hs1^2 / Hs^2)}, where</em>
+<a class="jxr_linenumber" name="L184" href="#L184">184</a> <em class="jxr_javadoccomment">     * &lt;ul&gt;</em>
+<a class="jxr_linenumber" name="L185" href="#L185">185</a> <em class="jxr_javadoccomment">     *  &lt;li&gt;{@code Hs2 = generalizedHarmonic(N, s - 2)},&lt;/li&gt;</em>
+<a class="jxr_linenumber" name="L186" href="#L186">186</a> <em class="jxr_javadoccomment">     *  &lt;li&gt;{@code Hs1 = generalizedHarmonic(N, s - 1)},&lt;/li&gt;</em>
+<a class="jxr_linenumber" name="L187" href="#L187">187</a> <em class="jxr_javadoccomment">     *  &lt;li&gt;{@code Hs = generalizedHarmonic(N, s)}.&lt;/li&gt;</em>
+<a class="jxr_linenumber" name="L188" href="#L188">188</a> <em class="jxr_javadoccomment">     * &lt;/ul&gt;</em>
+<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>     <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">double</strong> getNumericalVariance() {
+<a class="jxr_linenumber" name="L191" href="#L191">191</a>         <strong class="jxr_keyword">if</strong> (!numericalVarianceIsCalculated) {
+<a class="jxr_linenumber" name="L192" href="#L192">192</a>             numericalVariance = calculateNumericalVariance();
+<a class="jxr_linenumber" name="L193" href="#L193">193</a>             numericalVarianceIsCalculated = <strong class="jxr_keyword">true</strong>;
+<a class="jxr_linenumber" name="L194" href="#L194">194</a>         }
+<a class="jxr_linenumber" name="L195" href="#L195">195</a>         <strong class="jxr_keyword">return</strong> numericalVariance;
+<a class="jxr_linenumber" name="L196" href="#L196">196</a>     }
+<a class="jxr_linenumber" name="L197" href="#L197">197</a> 
+<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">     * Used by {@link #getNumericalVariance()}.</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 the variance of this distribution</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>     <strong class="jxr_keyword">protected</strong> <strong class="jxr_keyword">double</strong> calculateNumericalVariance() {
+<a class="jxr_linenumber" name="L204" href="#L204">204</a>         <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">int</strong> N = getNumberOfElements();
+<a class="jxr_linenumber" name="L205" href="#L205">205</a>         <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> s = getExponent();
+<a class="jxr_linenumber" name="L206" href="#L206">206</a> 
+<a class="jxr_linenumber" name="L207" href="#L207">207</a>         <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> Hs2 = generalizedHarmonic(N, s - 2);
+<a class="jxr_linenumber" name="L208" href="#L208">208</a>         <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> Hs1 = generalizedHarmonic(N, s - 1);
+<a class="jxr_linenumber" name="L209" href="#L209">209</a>         <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> Hs = generalizedHarmonic(N, s);
+<a class="jxr_linenumber" name="L210" href="#L210">210</a> 
+<a class="jxr_linenumber" name="L211" href="#L211">211</a>         <strong class="jxr_keyword">return</strong> (Hs2 / Hs) - ((Hs1 * Hs1) / (Hs * Hs));
+<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">     * Calculates the Nth generalized harmonic number. See</em>
+<a class="jxr_linenumber" name="L216" href="#L216">216</a> <em class="jxr_javadoccomment">     * &lt;a href="<a href="http://mathworld.wolfram.com/HarmonicSeries.html" target="alexandria_uri">http://mathworld.wolfram.com/HarmonicSeries.html</a>"&gt;Harmonic</em>
+<a class="jxr_linenumber" name="L217" href="#L217">217</a> <em class="jxr_javadoccomment">     * Series&lt;/a&gt;.</em>
+<a class="jxr_linenumber" name="L218" href="#L218">218</a> <em class="jxr_javadoccomment">     *</em>
+<a class="jxr_linenumber" name="L219" href="#L219">219</a> <em class="jxr_javadoccomment">     * @param n Term in the series to calculate (must be larger than 1)</em>
+<a class="jxr_linenumber" name="L220" href="#L220">220</a> <em class="jxr_javadoccomment">     * @param m Exponent (special case {@code m = 1} is the harmonic series).</em>
+<a class="jxr_linenumber" name="L221" href="#L221">221</a> <em class="jxr_javadoccomment">     * @return the n&lt;sup&gt;th&lt;/sup&gt; generalized harmonic number.</em>
+<a class="jxr_linenumber" name="L222" href="#L222">222</a> <em class="jxr_javadoccomment">     */</em>
+<a class="jxr_linenumber" name="L223" href="#L223">223</a>     <strong class="jxr_keyword">private</strong> <strong class="jxr_keyword">double</strong> generalizedHarmonic(<strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">int</strong> n, <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> m) {
+<a class="jxr_linenumber" name="L224" href="#L224">224</a>         <strong class="jxr_keyword">double</strong> value = 0;
+<a class="jxr_linenumber" name="L225" href="#L225">225</a>         <strong class="jxr_keyword">for</strong> (<strong class="jxr_keyword">int</strong> k = n; k &gt; 0; --k) {
+<a class="jxr_linenumber" name="L226" href="#L226">226</a>             value += 1.0 / FastMath.pow(k, m);
+<a class="jxr_linenumber" name="L227" href="#L227">227</a>         }
+<a class="jxr_linenumber" name="L228" href="#L228">228</a>         <strong class="jxr_keyword">return</strong> value;
+<a class="jxr_linenumber" name="L229" href="#L229">229</a>     }
+<a class="jxr_linenumber" name="L230" href="#L230">230</a> 
+<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">     * {@inheritDoc}</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> <em class="jxr_javadoccomment">     * @return lower bound of the support (always 1)</em>
-<a class="jxr_linenumber" name="L235" href="#L235">235</a> <em class="jxr_javadoccomment">     */</em>
-<a class="jxr_linenumber" name="L236" href="#L236">236</a>     <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">int</strong> getSupportLowerBound() {
-<a class="jxr_linenumber" name="L237" href="#L237">237</a>         <strong class="jxr_keyword">return</strong> 1;
-<a class="jxr_linenumber" name="L238" href="#L238">238</a>     }
-<a class="jxr_linenumber" name="L239" href="#L239">239</a> 
-<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">     * {@inheritDoc}</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">     * The upper bound of the support is the number of elements.</em>
+<a class="jxr_linenumber" name="L234" href="#L234">234</a> <em class="jxr_javadoccomment">     * The lower bound of the support is always 1 no matter the parameters.</em>
+<a class="jxr_linenumber" name="L235" href="#L235">235</a> <em class="jxr_javadoccomment">     *</em>
+<a class="jxr_linenumber" name="L236" href="#L236">236</a> <em class="jxr_javadoccomment">     * @return lower bound of the support (always 1)</em>
+<a class="jxr_linenumber" name="L237" href="#L237">237</a> <em class="jxr_javadoccomment">     */</em>
+<a class="jxr_linenumber" name="L238" href="#L238">238</a>     <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">int</strong> getSupportLowerBound() {
+<a class="jxr_linenumber" name="L239" href="#L239">239</a>         <strong class="jxr_keyword">return</strong> 1;
+<a class="jxr_linenumber" name="L240" href="#L240">240</a>     }
+<a class="jxr_linenumber" name="L241" href="#L241">241</a> 
+<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">     * {@inheritDoc}</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> <em class="jxr_javadoccomment">     * @return upper bound of the support</em>
-<a class="jxr_linenumber" name="L246" href="#L246">246</a> <em class="jxr_javadoccomment">     */</em>
-<a class="jxr_linenumber" name="L247" href="#L247">247</a>     <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">int</strong> getSupportUpperBound() {
-<a class="jxr_linenumber" name="L248" href="#L248">248</a>         <strong class="jxr_keyword">return</strong> getNumberOfElements();
-<a class="jxr_linenumber" name="L249" href="#L249">249</a>     }
-<a class="jxr_linenumber" name="L250" href="#L250">250</a> 
-<a class="jxr_linenumber" name="L251" href="#L251">251</a>     <em class="jxr_javadoccomment">/**</em>
-<a class="jxr_linenumber" name="L252" href="#L252">252</a> <em class="jxr_javadoccomment">     * {@inheritDoc}</em>
-<a class="jxr_linenumber" name="L253" href="#L253">253</a> <em class="jxr_javadoccomment">     *</em>
-<a class="jxr_linenumber" name="L254" href="#L254">254</a> <em class="jxr_javadoccomment">     * The support of this distribution is connected.</em>
+<a class="jxr_linenumber" name="L245" href="#L245">245</a> <em class="jxr_javadoccomment">     * The upper bound of the support is the number of elements.</em>
+<a class="jxr_linenumber" name="L246" href="#L246">246</a> <em class="jxr_javadoccomment">     *</em>
+<a class="jxr_linenumber" name="L247" href="#L247">247</a> <em class="jxr_javadoccomment">     * @return upper bound of the support</em>
+<a class="jxr_linenumber" name="L248" href="#L248">248</a> <em class="jxr_javadoccomment">     */</em>
+<a class="jxr_linenumber" name="L249" href="#L249">249</a>     <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">int</strong> getSupportUpperBound() {
+<a class="jxr_linenumber" name="L250" href="#L250">250</a>         <strong class="jxr_keyword">return</strong> getNumberOfElements();
+<a class="jxr_linenumber" name="L251" href="#L251">251</a>     }
+<a class="jxr_linenumber" name="L252" href="#L252">252</a> 
+<a class="jxr_linenumber" name="L253" href="#L253">253</a>     <em class="jxr_javadoccomment">/**</em>
+<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> <em class="jxr_javadoccomment">     *</em>
-<a class="jxr_linenumber" name="L256" href="#L256">256</a> <em class="jxr_javadoccomment">     * @return {@code true}</em>
-<a class="jxr_linenumber" name="L257" href="#L257">257</a> <em class="jxr_javadoccomment">     */</em>
-<a class="jxr_linenumber" name="L258" href="#L258">258</a>     <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">boolean</strong> isSupportConnected() {
-<a class="jxr_linenumber" name="L259" href="#L259">259</a>         <strong class="jxr_keyword">return</strong> <strong class="jxr_keyword">true</strong>;
-<a class="jxr_linenumber" name="L260" href="#L260">260</a>     }
-<a class="jxr_linenumber" name="L261" href="#L261">261</a> }
-<a class="jxr_linenumber" name="L262" href="#L262">262</a> 
+<a class="jxr_linenumber" name="L256" href="#L256">256</a> <em class="jxr_javadoccomment">     * The support of this distribution is connected.</em>
+<a class="jxr_linenumber" name="L257" href="#L257">257</a> <em class="jxr_javadoccomment">     *</em>
+<a class="jxr_linenumber" name="L258" href="#L258">258</a> <em class="jxr_javadoccomment">     * @return {@code true}</em>
+<a class="jxr_linenumber" name="L259" href="#L259">259</a> <em class="jxr_javadoccomment">     */</em>
+<a class="jxr_linenumber" name="L260" href="#L260">260</a>     <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">boolean</strong> isSupportConnected() {
+<a class="jxr_linenumber" name="L261" href="#L261">261</a>         <strong class="jxr_keyword">return</strong> <strong class="jxr_keyword">true</strong>;
+<a class="jxr_linenumber" name="L262" href="#L262">262</a>     }
+<a class="jxr_linenumber" name="L263" href="#L263">263</a> 
+<a class="jxr_linenumber" name="L264" href="#L264">264</a>     <em class="jxr_javadoccomment">/**</em>
+<a class="jxr_linenumber" name="L265" href="#L265">265</a> <em class="jxr_javadoccomment">     * {@inheritDoc}</em>
+<a class="jxr_linenumber" name="L266" href="#L266">266</a> <em class="jxr_javadoccomment">     * &lt;p&gt;</em>
+<a class="jxr_linenumber" name="L267" href="#L267">267</a> <em class="jxr_javadoccomment">     * An instrumental distribution g(k) is used to generate random values by</em>
+<a class="jxr_linenumber" name="L268" href="#L268">268</a> <em class="jxr_javadoccomment">     * rejection sampling. g(k) is defined as g(1):= 1 and g(k) := I(-s,k-1/2,k+1/2)</em>
+<a class="jxr_linenumber" name="L269" href="#L269">269</a> <em class="jxr_javadoccomment">     * for k larger than 1, where s denotes the exponent of the Zipf distribution</em>
+<a class="jxr_linenumber" name="L270" href="#L270">270</a> <em class="jxr_javadoccomment">     * and I(r,a,b) is the integral of x^r for x from a to b.</em>
+<a class="jxr_linenumber" name="L271" href="#L271">271</a> <em class="jxr_javadoccomment">     * &lt;p&gt;</em>
+<a class="jxr_linenumber" name="L272" href="#L272">272</a> <em class="jxr_javadoccomment">     * Since 1^x^s is a convex function, Jensens's inequality gives</em>
+<a class="jxr_linenumber" name="L273" href="#L273">273</a> <em class="jxr_javadoccomment">     * I(-s,k-1/2,k+1/2) &gt;= 1/k^s for all positive k and non-negative s.</em>
+<a class="jxr_linenumber" name="L274" href="#L274">274</a> <em class="jxr_javadoccomment">     * In order to limit the rejection rate for large exponents s,</em>
+<a class="jxr_linenumber" name="L275" href="#L275">275</a> <em class="jxr_javadoccomment">     * the instrumental distribution weight is differently defined for value 1.</em>
+<a class="jxr_linenumber" name="L276" href="#L276">276</a> <em class="jxr_javadoccomment">     */</em>
+<a class="jxr_linenumber" name="L277" href="#L277">277</a>     @Override
+<a class="jxr_linenumber" name="L278" href="#L278">278</a>     <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">int</strong> sample() {
+<a class="jxr_linenumber" name="L279" href="#L279">279</a>         <strong class="jxr_keyword">if</strong> (sampler == <strong class="jxr_keyword">null</strong>) {
+<a class="jxr_linenumber" name="L280" href="#L280">280</a>             sampler = <strong class="jxr_keyword">new</strong> <a href="../../../../../org/apache/commons/math3/distribution/ZipfDistribution.html">ZipfRejectionSampler</a>(numberOfElements, exponent);
+<a class="jxr_linenumber" name="L281" href="#L281">281</a>         }
+<a class="jxr_linenumber" name="L282" href="#L282">282</a>         <strong class="jxr_keyword">return</strong> sampler.sample(random);
+<a class="jxr_linenumber" name="L283" href="#L283">283</a>     }
+<a class="jxr_linenumber" name="L284" href="#L284">284</a> 
+<a class="jxr_linenumber" name="L285" href="#L285">285</a>     <em class="jxr_javadoccomment">/**</em>
+<a class="jxr_linenumber" name="L286" href="#L286">286</a> <em class="jxr_javadoccomment">     * Utility class implementing a rejection sampling method for a discrete,</em>
+<a class="jxr_linenumber" name="L287" href="#L287">287</a> <em class="jxr_javadoccomment">     * bounded Zipf distribution.</em>
+<a class="jxr_linenumber" name="L288" href="#L288">288</a> <em class="jxr_javadoccomment">     *</em>
+<a class="jxr_linenumber" name="L289" href="#L289">289</a> <em class="jxr_javadoccomment">     * @since 3.6</em>
+<a class="jxr_linenumber" name="L290" href="#L290">290</a> <em class="jxr_javadoccomment">     */</em>
+<a class="jxr_linenumber" name="L291" href="#L291">291</a>     <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/ZipfDistribution.html">ZipfRejectionSampler</a> {
+<a class="jxr_linenumber" name="L292" href="#L292">292</a> 
+<a class="jxr_linenumber" name="L293" href="#L293">293</a>         <em class="jxr_javadoccomment">/** Number of elements. */</em>
+<a class="jxr_linenumber" name="L294" href="#L294">294</a>         <strong class="jxr_keyword">private</strong> <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">int</strong> numberOfElements;
+<a class="jxr_linenumber" name="L295" href="#L295">295</a>         <em class="jxr_javadoccomment">/** Exponent parameter of the distribution. */</em>
+<a class="jxr_linenumber" name="L296" href="#L296">296</a>         <strong class="jxr_keyword">private</strong> <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> exponent;
+<a class="jxr_linenumber" name="L297" href="#L297">297</a>         <em class="jxr_javadoccomment">/** Cached tail weight of instrumental distribution used for rejection sampling */</em>
+<a class="jxr_linenumber" name="L298" href="#L298">298</a>         <strong class="jxr_keyword">private</strong> <strong class="jxr_keyword">double</strong> instrumentalDistributionTailWeight = Double.NaN;
+<a class="jxr_linenumber" name="L299" href="#L299">299</a> 
+<a class="jxr_linenumber" name="L300" href="#L300">300</a>         <em class="jxr_javadoccomment">/**</em>
+<a class="jxr_linenumber" name="L301" href="#L301">301</a> <em class="jxr_javadoccomment">         * Simple constructor.</em>
+<a class="jxr_linenumber" name="L302" href="#L302">302</a> <em class="jxr_javadoccomment">         * @param numberOfElements number of elements</em>
+<a class="jxr_linenumber" name="L303" href="#L303">303</a> <em class="jxr_javadoccomment">         * @param exponent exponent parameter of the distribution</em>
+<a class="jxr_linenumber" name="L304" href="#L304">304</a> <em class="jxr_javadoccomment">         */</em>
+<a class="jxr_linenumber" name="L305" href="#L305">305</a>         <a href="../../../../../org/apache/commons/math3/distribution/ZipfDistribution.html">ZipfRejectionSampler</a>(<strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">int</strong> numberOfElements, <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> exponent) {
+<a class="jxr_linenumber" name="L306" href="#L306">306</a>             <strong class="jxr_keyword">this</strong>.numberOfElements = numberOfElements;
+<a class="jxr_linenumber" name="L307" href="#L307">307</a>             <strong class="jxr_keyword">this</strong>.exponent = exponent;
+<a class="jxr_linenumber" name="L308" href="#L308">308</a>         }
+<a class="jxr_linenumber" name="L309" href="#L309">309</a> 
+<a class="jxr_linenumber" name="L310" href="#L310">310</a>         <em class="jxr_javadoccomment">/** Generate a random value sampled from this distribution.</em>
+<a class="jxr_linenumber" name="L311" href="#L311">311</a> <em class="jxr_javadoccomment">         * @param random random generator to use</em>
+<a class="jxr_linenumber" name="L312" href="#L312">312</a> <em class="jxr_javadoccomment">         * @return random value sampled from this distribution</em>
+<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>         <strong class="jxr_keyword">int</strong> sample(<strong class="jxr_keyword">final</strong> <a href="../../../../../org/apache/commons/math3/random/RandomGenerator.html">RandomGenerator</a> random) {
+<a class="jxr_linenumber" name="L315" href="#L315">315</a>             <strong class="jxr_keyword">if</strong> (Double.isNaN(instrumentalDistributionTailWeight)) {
+<a class="jxr_linenumber" name="L316" href="#L316">316</a>                 instrumentalDistributionTailWeight = integratePowerFunction(-exponent, 1.5, numberOfElements+0.5);
+<a class="jxr_linenumber" name="L317" href="#L317">317</a>             }
+<a class="jxr_linenumber" name="L318" href="#L318">318</a> 
+<a class="jxr_linenumber" name="L319" href="#L319">319</a>             <strong class="jxr_keyword">while</strong>(<strong class="jxr_keyword">true</strong>) {
+<a class="jxr_linenumber" name="L320" href="#L320">320</a>                 <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> randomValue = random.nextDouble()*(instrumentalDistributionTailWeight + 1.);
+<a class="jxr_linenumber" name="L321" href="#L321">321</a>                 <strong class="jxr_keyword">if</strong> (randomValue &lt; instrumentalDistributionTailWeight) {
+<a class="jxr_linenumber" name="L322" href="#L322">322</a>                     <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> q = randomValue / instrumentalDistributionTailWeight;
+<a class="jxr_linenumber" name="L323" href="#L323">323</a>                     <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">int</strong> sample = sampleFromInstrumentalDistributionTail(q);
+<a class="jxr_linenumber" name="L324" href="#L324">324</a>                     <strong class="jxr_keyword">if</strong> (random.nextDouble() &lt; acceptanceRateForTailSample(sample)) {
+<a class="jxr_linenumber" name="L325" href="#L325">325</a>                         <strong class="jxr_keyword">return</strong> sample;
+<a class="jxr_linenumber" name="L326" href="#L326">326</a>                     }
+<a class="jxr_linenumber" name="L327" href="#L327">327</a>                 }
+<a class="jxr_linenumber" name="L328" href="#L328">328</a>                 <strong class="jxr_keyword">else</strong> {
+<a class="jxr_linenumber" name="L329" href="#L329">329</a>                     <strong class="jxr_keyword">return</strong> 1;
+<a class="jxr_linenumber" name="L330" href="#L330">330</a>                 }
+<a class="jxr_linenumber" name="L331" href="#L331">331</a>             }
+<a class="jxr_linenumber" name="L332" href="#L332">332</a>         }
+<a class="jxr_linenumber" name="L333" href="#L333">333</a> 
+<a class="jxr_linenumber" name="L334" href="#L334">334</a>         <em class="jxr_javadoccomment">/**</em>
+<a class="jxr_linenumber" name="L335" href="#L335">335</a> <em class="jxr_javadoccomment">         * Returns a sample from the instrumental distribution tail for a given</em>
+<a class="jxr_linenumber" name="L336" href="#L336">336</a> <em class="jxr_javadoccomment">         * uniformly distributed random value.</em>
+<a class="jxr_linenumber" name="L337" href="#L337">337</a> <em class="jxr_javadoccomment">         *</em>
+<a class="jxr_linenumber" name="L338" href="#L338">338</a> <em class="jxr_javadoccomment">         * @param q a uniformly distributed random value taken from [0,1]</em>
+<a class="jxr_linenumber" name="L339" href="#L339">339</a> <em class="jxr_javadoccomment">         * @return a sample in the range [2, {@link #numberOfElements}]</em>
+<a class="jxr_linenumber" name="L340" href="#L340">340</a> <em class="jxr_javadoccomment">         */</em>
+<a class="jxr_linenumber" name="L341" href="#L341">341</a>         <strong class="jxr_keyword">int</strong> sampleFromInstrumentalDistributionTail(<strong class="jxr_keyword">double</strong> q) {
+<a class="jxr_linenumber" name="L342" href="#L342">342</a>             <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> a = 1.5;
+<a class="jxr_linenumber" name="L343" href="#L343">343</a>             <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> b = numberOfElements + 0.5;
+<a class="jxr_linenumber" name="L344" href="#L344">344</a>             <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> logBdviA = FastMath.log(b / a);
+<a class="jxr_linenumber" name="L345" href="#L345">345</a> 
+<a class="jxr_linenumber" name="L346" href="#L346">346</a>             <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">int</strong> result  = (<strong class="jxr_keyword">int</strong>) (a * FastMath.exp(logBdviA * helper1(q, logBdviA * (1. - exponent))) + 0.5);
+<a class="jxr_linenumber" name="L347" href="#L347">347</a>             <strong class="jxr_keyword">if</strong> (result &lt; 2) {
+<a class="jxr_linenumber" name="L348" href="#L348">348</a>                 <strong class="jxr_keyword">return</strong> 2;
+<a class="jxr_linenumber" name="L349" href="#L349">349</a>             }
+<a class="jxr_linenumber" name="L350" href="#L350">350</a>             <strong class="jxr_keyword">if</strong> (result &gt; numberOfElements) {
+<a class="jxr_linenumber" name="L351" href="#L351">351</a>                 <strong class="jxr_keyword">return</strong> numberOfElements;
+<a class="jxr_linenumber" name="L352" href="#L352">352</a>             }
+<a class="jxr_linenumber" name="L353" href="#L353">353</a>             <strong class="jxr_keyword">return</strong> result;
+<a class="jxr_linenumber" name="L354" href="#L354">354</a>         }
+<a class="jxr_linenumber" name="L355" href="#L355">355</a> 
+<a class="jxr_linenumber" name="L356" href="#L356">356</a>         <em class="jxr_javadoccomment">/**</em>
+<a class="jxr_linenumber" name="L357" href="#L357">357</a> <em class="jxr_javadoccomment">         * Helper function that calculates log((1-q)+q*exp(x))/x.</em>
+<a class="jxr_linenumber" name="L358" href="#L358">358</a> <em class="jxr_javadoccomment">         * &lt;p&gt;</em>
+<a class="jxr_linenumber" name="L359" href="#L359">359</a> <em class="jxr_javadoccomment">         * A Taylor series expansion is used, if x is close to 0.</em>
+<a class="jxr_linenumber" name="L360" href="#L360">360</a> <em class="jxr_javadoccomment">         *</em>
+<a class="jxr_linenumber" name="L361" href="#L361">361</a> <em class="jxr_javadoccomment">         * @param q a value in the range [0,1]</em>
+<a class="jxr_linenumber" name="L362" href="#L362">362</a> <em class="jxr_javadoccomment">         * @param x free parameter</em>
+<a class="jxr_linenumber" name="L363" href="#L363">363</a> <em class="jxr_javadoccomment">         * @return log((1-q)+q*exp(x))/x</em>
+<a class="jxr_linenumber" name="L364" href="#L364">364</a> <em class="jxr_javadoccomment">         */</em>
+<a class="jxr_linenumber" name="L365" href="#L365">365</a>         <strong class="jxr_keyword">static</strong> <strong class="jxr_keyword">double</strong> helper1(<strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> q, <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> x) {
+<a class="jxr_linenumber" name="L366" href="#L366">366</a>             <strong class="jxr_keyword">if</strong> (Math.abs(x) &gt; 1e-8) {
+<a class="jxr_linenumber" name="L367" href="#L367">367</a>                 <strong class="jxr_keyword">return</strong> FastMath.log((1.-q)+q*FastMath.exp(x))/x;
+<a class="jxr_linenumber" name="L368" href="#L368">368</a>             }
+<a class="jxr_linenumber" name="L369" href="#L369">369</a>             <strong class="jxr_keyword">else</strong> {
+<a class="jxr_linenumber" name="L370" href="#L370">370</a>                 <strong class="jxr_keyword">return</strong> q*(1.+(1./2.)*x*(1.-q)*(1+(1./3.)*x*((1.-2.*q) + (1./4.)*x*(6*q*q*(q-1)+1))));
+<a class="jxr_linenumber" name="L371" href="#L371">371</a>             }
+<a class="jxr_linenumber" name="L372" href="#L372">372</a>         }
+<a class="jxr_linenumber" name="L373" href="#L373">373</a> 
+<a class="jxr_linenumber" name="L374" href="#L374">374</a>         <em class="jxr_javadoccomment">/**</em>
+<a class="jxr_linenumber" name="L375" href="#L375">375</a> <em class="jxr_javadoccomment">         * Helper function to calculate (exp(x)-1)/x.</em>
+<a class="jxr_linenumber" name="L376" href="#L376">376</a> <em class="jxr_javadoccomment">         * &lt;p&gt;</em>
+<a class="jxr_linenumber" name="L377" href="#L377">377</a> <em class="jxr_javadoccomment">         * A Taylor series expansion is used, if x is close to 0.</em>
+<a class="jxr_linenumber" name="L378" href="#L378">378</a> <em class="jxr_javadoccomment">         *</em>
+<a class="jxr_linenumber" name="L379" href="#L379">379</a> <em class="jxr_javadoccomment">         * @param x free parameter</em>
+<a class="jxr_linenumber" name="L380" href="#L380">380</a> <em class="jxr_javadoccomment">         * @return (exp(x)-1)/x if x is non-zero, 1 if x=0</em>
+<a class="jxr_linenumber" name="L381" href="#L381">381</a> <em class="jxr_javadoccomment">         */</em>
+<a class="jxr_linenumber" name="L382" href="#L382">382</a>         <strong class="jxr_keyword">static</strong> <strong class="jxr_keyword">double</strong> helper2(<strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> x) {
+<a class="jxr_linenumber" name="L383" href="#L383">383</a>             <strong class="jxr_keyword">if</strong> (FastMath.abs(x)&gt;1e-8) {
+<a class="jxr_linenumber" name="L384" href="#L384">384</a>                 <strong class="jxr_keyword">return</strong> FastMath.expm1(x)/x;
+<a class="jxr_linenumber" name="L385" href="#L385">385</a>             }
+<a class="jxr_linenumber" name="L386" href="#L386">386</a>             <strong class="jxr_keyword">else</strong> {
+<a class="jxr_linenumber" name="L387" href="#L387">387</a>                 <strong class="jxr_keyword">return</strong> 1.+x*(1./2.)*(1.+x*(1./3.)*(1.+x*(1./4.)));
+<a class="jxr_linenumber" name="L388" href="#L388">388</a>             }
+<a class="jxr_linenumber" name="L389" href="#L389">389</a>         }
+<a class="jxr_linenumber" name="L390" href="#L390">390</a> 
+<a class="jxr_linenumber" name="L391" href="#L391">391</a>         <em class="jxr_javadoccomment">/**</em>
+<a class="jxr_linenumber" name="L392" href="#L392">392</a> <em class="jxr_javadoccomment">         * Integrates the power function x^r from x=a to b.</em>
+<a class="jxr_linenumber" name="L393" href="#L393">393</a> <em class="jxr_javadoccomment">         *</em>
+<a class="jxr_linenumber" name="L394" href="#L394">394</a> <em class="jxr_javadoccomment">         * @param r the exponent</em>
+<a class="jxr_linenumber" name="L395" href="#L395">395</a> <em class="jxr_javadoccomment">         * @param a the integral lower bound</em>
+<a class="jxr_linenumber" name="L396" href="#L396">396</a> <em class="jxr_javadoccomment">         * @param b the integral upper bound</em>
+<a class="jxr_linenumber" name="L397" href="#L397">397</a> <em class="jxr_javadoccomment">         * @return the calculated integral value</em>
+<a class="jxr_linenumber" name="L398" href="#L398">398</a> <em class="jxr_javadoccomment">         */</em>
+<a class="jxr_linenumber" name="L399" href="#L399">399</a>         <strong class="jxr_keyword">static</strong> <strong class="jxr_keyword">double</strong> integratePowerFunction(<strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> r, <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> a, <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> b) {
+<a class="jxr_linenumber" name="L400" href="#L400">400</a>             <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> logA = FastMath.log(a);
+<a class="jxr_linenumber" name="L401" href="#L401">401</a>             <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> logBdivA = FastMath.log(b/a);
+<a class="jxr_linenumber" name="L402" href="#L402">402</a>             <strong class="jxr_keyword">return</strong> FastMath.exp((1.+r)*logA)*helper2((1.+r)*logBdivA)*logBdivA;
+<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>         <em class="jxr_javadoccomment">/**</em>
+<a class="jxr_linenumber" name="L407" href="#L407">407</a> <em class="jxr_javadoccomment">         * Calculates the acceptance rate for a sample taken from the tail of the instrumental distribution.</em>
+<a class="jxr_linenumber" name="L408" href="#L408">408</a> <em class="jxr_javadoccomment">         * &lt;p&gt;</em>
+<a class="jxr_linenumber" name="L409" href="#L409">409</a> <em class="jxr_javadoccomment">         * The acceptance rate is given by the ratio k^(-s)/I(-s,k-0.5, k+0.5)</em>
+<a class="jxr_linenumber" name="L410" href="#L410">410</a> <em class="jxr_javadoccomment">         * where I(r,a,b) is the integral of x^r for x from a to b.</em>
+<a class="jxr_linenumber" name="L411" href="#L411">411</a> <em class="jxr_javadoccomment">         *</em>
+<a class="jxr_linenumber" name="L412" href="#L412">412</a> <em class="jxr_javadoccomment">         * @param k the value which has been sampled using the instrumental distribution</em>
+<a class="jxr_linenumber" name="L413" href="#L413">413</a> <em class="jxr_javadoccomment">         * @return the acceptance rate</em>
+<a class="jxr_linenumber" name="L414" href="#L414">414</a> <em class="jxr_javadoccomment">         */</em>
+<a class="jxr_linenumber" name="L415" href="#L415">415</a>         <strong class="jxr_keyword">double</strong> acceptanceRateForTailSample(<strong class="jxr_keyword">int</strong> k) {
+<a class="jxr_linenumber" name="L416" href="#L416">416</a>             <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> a = FastMath.log1p(1./(2.*k-1.));
+<a class="jxr_linenumber" name="L417" href="#L417">417</a>             <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> b = FastMath.log1p(2./(2.*k-1.));
+<a class="jxr_linenumber" name="L418" href="#L418">418</a>             <strong class="jxr_keyword">return</strong> FastMath.exp((1.-exponent)*a)/(k*b*helper2((1.-exponent)*b));
+<a class="jxr_linenumber" name="L419" href="#L419">419</a>         }
+<a class="jxr_linenumber" name="L420" href="#L420">420</a>     }
+<a class="jxr_linenumber" name="L421" href="#L421">421</a> 
+<a class="jxr_linenumber" name="L422" href="#L422">422</a> }
 </pre>
 <hr/>
 <div id="footer">Copyright &#169; 2003&#x2013;2015 <a href="http://www.apache.org/">The Apache Software Foundation</a>. All rights reserved.</div>

Modified: websites/production/commons/content/proper/commons-math/xref/org/apache/commons/math3/distribution/fitting/package-frame.html
==============================================================================
--- websites/production/commons/content/proper/commons-math/xref/org/apache/commons/math3/distribution/fitting/package-frame.html (original)
+++ websites/production/commons/content/proper/commons-math/xref/org/apache/commons/math3/distribution/fitting/package-frame.html Sun May 17 17:05:50 2015
@@ -3,7 +3,7 @@
 <html xml:lang="en" lang="en">
 	<head>
 		<meta http-equiv="content-type" content="text/html; charset=UTF-8" />
-		<title>Apache Commons Math 3.5 Reference Package org.apache.commons.math3.distribution.fitting</title>
+		<title>Apache Commons Math 3.6-SNAPSHOT Reference Package org.apache.commons.math3.distribution.fitting</title>
 		<link rel="stylesheet" type="text/css" href="../../../../../../stylesheet.css" title="style" />
 	</head>
 	<body>

Modified: websites/production/commons/content/proper/commons-math/xref/org/apache/commons/math3/distribution/fitting/package-summary.html
==============================================================================
--- websites/production/commons/content/proper/commons-math/xref/org/apache/commons/math3/distribution/fitting/package-summary.html (original)
+++ websites/production/commons/content/proper/commons-math/xref/org/apache/commons/math3/distribution/fitting/package-summary.html Sun May 17 17:05:50 2015
@@ -3,7 +3,7 @@
 <html xml:lang="en" lang="en">
 	<head>
 		<meta http-equiv="content-type" content="text/html; charset=UTF-8" />
-		<title>Apache Commons Math 3.5 Reference Package org.apache.commons.math3.distribution.fitting</title>
+		<title>Apache Commons Math 3.6-SNAPSHOT Reference Package org.apache.commons.math3.distribution.fitting</title>
 		<link rel="stylesheet" type="text/css" href="../../../../../../stylesheet.css" title="style" />
 	</head>
 	<body>



Mime
View raw message