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From l..@apache.org
Subject svn commit: r926176 [14/31] - in /websites/production/commons/content/proper/commons-math: apidocs/org/apache/commons/math3/analysis/interpolation/ apidocs/org/apache/commons/math3/analysis/interpolation/class-use/ apidocs/org/apache/commons/math3/dist...
Date Sat, 18 Oct 2014 20:10:40 GMT
Added: websites/production/commons/content/proper/commons-math/apidocs/src-html/org/apache/commons/math3/stat/descriptive/rank/Percentile.EstimationType.html
==============================================================================
--- websites/production/commons/content/proper/commons-math/apidocs/src-html/org/apache/commons/math3/stat/descriptive/rank/Percentile.EstimationType.html (added)
+++ websites/production/commons/content/proper/commons-math/apidocs/src-html/org/apache/commons/math3/stat/descriptive/rank/Percentile.EstimationType.html Sat Oct 18 20:10:38 2014
@@ -0,0 +1,1144 @@
+<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN" "http://www.w3.org/TR/html4/loose.dtd">
+<html lang="fr">
+<head>
+<title>Source code</title>
+<link rel="stylesheet" type="text/css" href="../../../../../../../../stylesheet.css" title="Style">
+</head>
+<body>
+<div class="sourceContainer">
+<pre><span class="sourceLineNo">001</span>/*<a name="line.1"></a>
+<span class="sourceLineNo">002</span> * Licensed to the Apache Software Foundation (ASF) under one or more<a name="line.2"></a>
+<span class="sourceLineNo">003</span> * contributor license agreements.  See the NOTICE file distributed with<a name="line.3"></a>
+<span class="sourceLineNo">004</span> * this work for additional information regarding copyright ownership.<a name="line.4"></a>
+<span class="sourceLineNo">005</span> * The ASF licenses this file to You under the Apache License, Version 2.0<a name="line.5"></a>
+<span class="sourceLineNo">006</span> * (the "License"); you may not use this file except in compliance with<a name="line.6"></a>
+<span class="sourceLineNo">007</span> * the License.  You may obtain a copy of the License at<a name="line.7"></a>
+<span class="sourceLineNo">008</span> *<a name="line.8"></a>
+<span class="sourceLineNo">009</span> *      http://www.apache.org/licenses/LICENSE-2.0<a name="line.9"></a>
+<span class="sourceLineNo">010</span> *<a name="line.10"></a>
+<span class="sourceLineNo">011</span> * Unless required by applicable law or agreed to in writing, software<a name="line.11"></a>
+<span class="sourceLineNo">012</span> * distributed under the License is distributed on an "AS IS" BASIS,<a name="line.12"></a>
+<span class="sourceLineNo">013</span> * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.<a name="line.13"></a>
+<span class="sourceLineNo">014</span> * See the License for the specific language governing permissions and<a name="line.14"></a>
+<span class="sourceLineNo">015</span> * limitations under the License.<a name="line.15"></a>
+<span class="sourceLineNo">016</span> */<a name="line.16"></a>
+<span class="sourceLineNo">017</span>package org.apache.commons.math3.stat.descriptive.rank;<a name="line.17"></a>
+<span class="sourceLineNo">018</span><a name="line.18"></a>
+<span class="sourceLineNo">019</span>import java.io.Serializable;<a name="line.19"></a>
+<span class="sourceLineNo">020</span>import java.util.Arrays;<a name="line.20"></a>
+<span class="sourceLineNo">021</span>import java.util.BitSet;<a name="line.21"></a>
+<span class="sourceLineNo">022</span><a name="line.22"></a>
+<span class="sourceLineNo">023</span>import org.apache.commons.math3.exception.MathIllegalArgumentException;<a name="line.23"></a>
+<span class="sourceLineNo">024</span>import org.apache.commons.math3.exception.MathUnsupportedOperationException;<a name="line.24"></a>
+<span class="sourceLineNo">025</span>import org.apache.commons.math3.exception.NullArgumentException;<a name="line.25"></a>
+<span class="sourceLineNo">026</span>import org.apache.commons.math3.exception.OutOfRangeException;<a name="line.26"></a>
+<span class="sourceLineNo">027</span>import org.apache.commons.math3.exception.util.LocalizedFormats;<a name="line.27"></a>
+<span class="sourceLineNo">028</span>import org.apache.commons.math3.stat.descriptive.AbstractUnivariateStatistic;<a name="line.28"></a>
+<span class="sourceLineNo">029</span>import org.apache.commons.math3.stat.ranking.NaNStrategy;<a name="line.29"></a>
+<span class="sourceLineNo">030</span>import org.apache.commons.math3.util.FastMath;<a name="line.30"></a>
+<span class="sourceLineNo">031</span>import org.apache.commons.math3.util.KthSelector;<a name="line.31"></a>
+<span class="sourceLineNo">032</span>import org.apache.commons.math3.util.MathArrays;<a name="line.32"></a>
+<span class="sourceLineNo">033</span>import org.apache.commons.math3.util.MathUtils;<a name="line.33"></a>
+<span class="sourceLineNo">034</span>import org.apache.commons.math3.util.MedianOf3PivotingStrategy;<a name="line.34"></a>
+<span class="sourceLineNo">035</span>import org.apache.commons.math3.util.PivotingStrategyInterface;<a name="line.35"></a>
+<span class="sourceLineNo">036</span>import org.apache.commons.math3.util.Precision;<a name="line.36"></a>
+<span class="sourceLineNo">037</span><a name="line.37"></a>
+<span class="sourceLineNo">038</span>/**<a name="line.38"></a>
+<span class="sourceLineNo">039</span> * Provides percentile computation.<a name="line.39"></a>
+<span class="sourceLineNo">040</span> * &lt;p&gt;<a name="line.40"></a>
+<span class="sourceLineNo">041</span> * There are several commonly used methods for estimating percentiles (a.k.a.<a name="line.41"></a>
+<span class="sourceLineNo">042</span> * quantiles) based on sample data.  For large samples, the different methods<a name="line.42"></a>
+<span class="sourceLineNo">043</span> * agree closely, but when sample sizes are small, different methods will give<a name="line.43"></a>
+<span class="sourceLineNo">044</span> * significantly different results.  The algorithm implemented here works as follows:<a name="line.44"></a>
+<span class="sourceLineNo">045</span> * &lt;ol&gt;<a name="line.45"></a>
+<span class="sourceLineNo">046</span> * &lt;li&gt;Let &lt;code&gt;n&lt;/code&gt; be the length of the (sorted) array and<a name="line.46"></a>
+<span class="sourceLineNo">047</span> * &lt;code&gt;0 &lt; p &lt;= 100&lt;/code&gt; be the desired percentile.&lt;/li&gt;<a name="line.47"></a>
+<span class="sourceLineNo">048</span> * &lt;li&gt;If &lt;code&gt; n = 1 &lt;/code&gt; return the unique array element (regardless of<a name="line.48"></a>
+<span class="sourceLineNo">049</span> * the value of &lt;code&gt;p&lt;/code&gt;); otherwise &lt;/li&gt;<a name="line.49"></a>
+<span class="sourceLineNo">050</span> * &lt;li&gt;Compute the estimated percentile position<a name="line.50"></a>
+<span class="sourceLineNo">051</span> * &lt;code&gt; pos = p * (n + 1) / 100&lt;/code&gt; and the difference, &lt;code&gt;d&lt;/code&gt;<a name="line.51"></a>
+<span class="sourceLineNo">052</span> * between &lt;code&gt;pos&lt;/code&gt; and &lt;code&gt;floor(pos)&lt;/code&gt; (i.e. the fractional<a name="line.52"></a>
+<span class="sourceLineNo">053</span> * part of &lt;code&gt;pos&lt;/code&gt;).&lt;/li&gt;<a name="line.53"></a>
+<span class="sourceLineNo">054</span> * &lt;li&gt; If &lt;code&gt;pos &lt; 1&lt;/code&gt; return the smallest element in the array.&lt;/li&gt;<a name="line.54"></a>
+<span class="sourceLineNo">055</span> * &lt;li&gt; Else if &lt;code&gt;pos &gt;= n&lt;/code&gt; return the largest element in the array.&lt;/li&gt;<a name="line.55"></a>
+<span class="sourceLineNo">056</span> * &lt;li&gt; Else let &lt;code&gt;lower&lt;/code&gt; be the element in position<a name="line.56"></a>
+<span class="sourceLineNo">057</span> * &lt;code&gt;floor(pos)&lt;/code&gt; in the array and let &lt;code&gt;upper&lt;/code&gt; be the<a name="line.57"></a>
+<span class="sourceLineNo">058</span> * next element in the array.  Return &lt;code&gt;lower + d * (upper - lower)&lt;/code&gt;<a name="line.58"></a>
+<span class="sourceLineNo">059</span> * &lt;/li&gt;<a name="line.59"></a>
+<span class="sourceLineNo">060</span> * &lt;/ol&gt;&lt;/p&gt;<a name="line.60"></a>
+<span class="sourceLineNo">061</span> * &lt;p&gt;<a name="line.61"></a>
+<span class="sourceLineNo">062</span> * To compute percentiles, the data must be at least partially ordered.  Input<a name="line.62"></a>
+<span class="sourceLineNo">063</span> * arrays are copied and recursively partitioned using an ordering definition.<a name="line.63"></a>
+<span class="sourceLineNo">064</span> * The ordering used by &lt;code&gt;Arrays.sort(double[])&lt;/code&gt; is the one determined<a name="line.64"></a>
+<span class="sourceLineNo">065</span> * by {@link java.lang.Double#compareTo(Double)}.  This ordering makes<a name="line.65"></a>
+<span class="sourceLineNo">066</span> * &lt;code&gt;Double.NaN&lt;/code&gt; larger than any other value (including<a name="line.66"></a>
+<span class="sourceLineNo">067</span> * &lt;code&gt;Double.POSITIVE_INFINITY&lt;/code&gt;).  Therefore, for example, the median<a name="line.67"></a>
+<span class="sourceLineNo">068</span> * (50th percentile) of<a name="line.68"></a>
+<span class="sourceLineNo">069</span> * &lt;code&gt;{0, 1, 2, 3, 4, Double.NaN}&lt;/code&gt; evaluates to &lt;code&gt;2.5.&lt;/code&gt;&lt;/p&gt;<a name="line.69"></a>
+<span class="sourceLineNo">070</span> * &lt;p&gt;<a name="line.70"></a>
+<span class="sourceLineNo">071</span> * Since percentile estimation usually involves interpolation between array<a name="line.71"></a>
+<span class="sourceLineNo">072</span> * elements, arrays containing  &lt;code&gt;NaN&lt;/code&gt; or infinite values will often<a name="line.72"></a>
+<span class="sourceLineNo">073</span> * result in &lt;code&gt;NaN&lt;/code&gt; or infinite values returned.&lt;/p&gt;<a name="line.73"></a>
+<span class="sourceLineNo">074</span> * &lt;p&gt;<a name="line.74"></a>
+<span class="sourceLineNo">075</span> * Further, to include different estimation types such as R1, R2 as mentioned in<a name="line.75"></a>
+<span class="sourceLineNo">076</span> * &lt;a href="http://en.wikipedia.org/wiki/Quantile"&gt;Quantile page(wikipedia)&lt;/a&gt;,<a name="line.76"></a>
+<span class="sourceLineNo">077</span> * a type specific NaN handling strategy is used to closely match with the<a name="line.77"></a>
+<span class="sourceLineNo">078</span> * typically observed results from popular tools like R(R1-R9), Excel(R7).&lt;/p&gt;<a name="line.78"></a>
+<span class="sourceLineNo">079</span> * &lt;p&gt;<a name="line.79"></a>
+<span class="sourceLineNo">080</span> * Since 2.2, Percentile uses only selection instead of complete sorting<a name="line.80"></a>
+<span class="sourceLineNo">081</span> * and caches selection algorithm state between calls to the various<a name="line.81"></a>
+<span class="sourceLineNo">082</span> * {@code evaluate} methods. This greatly improves efficiency, both for a single<a name="line.82"></a>
+<span class="sourceLineNo">083</span> * percentile and multiple percentile computations. To maximize performance when<a name="line.83"></a>
+<span class="sourceLineNo">084</span> * multiple percentiles are computed based on the same data, users should set the<a name="line.84"></a>
+<span class="sourceLineNo">085</span> * data array once using either one of the {@link #evaluate(double[], double)} or<a name="line.85"></a>
+<span class="sourceLineNo">086</span> * {@link #setData(double[])} methods and thereafter {@link #evaluate(double)}<a name="line.86"></a>
+<span class="sourceLineNo">087</span> * with just the percentile provided.<a name="line.87"></a>
+<span class="sourceLineNo">088</span> * &lt;/p&gt;<a name="line.88"></a>
+<span class="sourceLineNo">089</span> * &lt;p&gt;<a name="line.89"></a>
+<span class="sourceLineNo">090</span> * &lt;strong&gt;Note that this implementation is not synchronized.&lt;/strong&gt; If<a name="line.90"></a>
+<span class="sourceLineNo">091</span> * multiple threads access an instance of this class concurrently, and at least<a name="line.91"></a>
+<span class="sourceLineNo">092</span> * one of the threads invokes the &lt;code&gt;increment()&lt;/code&gt; or<a name="line.92"></a>
+<span class="sourceLineNo">093</span> * &lt;code&gt;clear()&lt;/code&gt; method, it must be synchronized externally.&lt;/p&gt;<a name="line.93"></a>
+<span class="sourceLineNo">094</span> *<a name="line.94"></a>
+<span class="sourceLineNo">095</span> */<a name="line.95"></a>
+<span class="sourceLineNo">096</span>public class Percentile extends AbstractUnivariateStatistic implements Serializable {<a name="line.96"></a>
+<span class="sourceLineNo">097</span><a name="line.97"></a>
+<span class="sourceLineNo">098</span>    /** Serializable version identifier */<a name="line.98"></a>
+<span class="sourceLineNo">099</span>    private static final long serialVersionUID = -8091216485095130416L;<a name="line.99"></a>
+<span class="sourceLineNo">100</span><a name="line.100"></a>
+<span class="sourceLineNo">101</span>    /** Maximum number of partitioning pivots cached (each level double the number of pivots). */<a name="line.101"></a>
+<span class="sourceLineNo">102</span>    private static final int MAX_CACHED_LEVELS = 10;<a name="line.102"></a>
+<span class="sourceLineNo">103</span><a name="line.103"></a>
+<span class="sourceLineNo">104</span>    /** Maximum number of cached pivots in the pivots cached array */<a name="line.104"></a>
+<span class="sourceLineNo">105</span>    private static final int PIVOTS_HEAP_LENGTH = 0x1 &lt;&lt; MAX_CACHED_LEVELS - 1;<a name="line.105"></a>
+<span class="sourceLineNo">106</span><a name="line.106"></a>
+<span class="sourceLineNo">107</span>    /** Default KthSelector used with default pivoting strategy */<a name="line.107"></a>
+<span class="sourceLineNo">108</span>    private final KthSelector kthSelector;<a name="line.108"></a>
+<span class="sourceLineNo">109</span><a name="line.109"></a>
+<span class="sourceLineNo">110</span>    /** Any of the {@link EstimationType}s such as {@link EstimationType#LEGACY CM} can be used. */<a name="line.110"></a>
+<span class="sourceLineNo">111</span>    private final EstimationType estimationType;<a name="line.111"></a>
+<span class="sourceLineNo">112</span><a name="line.112"></a>
+<span class="sourceLineNo">113</span>    /** NaN Handling of the input as defined by {@link NaNStrategy} */<a name="line.113"></a>
+<span class="sourceLineNo">114</span>    private final NaNStrategy nanStrategy;<a name="line.114"></a>
+<span class="sourceLineNo">115</span><a name="line.115"></a>
+<span class="sourceLineNo">116</span>    /** Determines what percentile is computed when evaluate() is activated<a name="line.116"></a>
+<span class="sourceLineNo">117</span>     * with no quantile argument */<a name="line.117"></a>
+<span class="sourceLineNo">118</span>    private double quantile;<a name="line.118"></a>
+<span class="sourceLineNo">119</span><a name="line.119"></a>
+<span class="sourceLineNo">120</span>    /** Cached pivots. */<a name="line.120"></a>
+<span class="sourceLineNo">121</span>    private int[] cachedPivots;<a name="line.121"></a>
+<span class="sourceLineNo">122</span><a name="line.122"></a>
+<span class="sourceLineNo">123</span>    /**<a name="line.123"></a>
+<span class="sourceLineNo">124</span>     * Constructs a Percentile with the following defaults.<a name="line.124"></a>
+<span class="sourceLineNo">125</span>     * &lt;ul&gt;<a name="line.125"></a>
+<span class="sourceLineNo">126</span>     *   &lt;li&gt;default quantile: 50.0, can be reset with {@link #setQuantile(double)}&lt;/li&gt;<a name="line.126"></a>
+<span class="sourceLineNo">127</span>     *   &lt;li&gt;default estimation type: {@link EstimationType#LEGACY},<a name="line.127"></a>
+<span class="sourceLineNo">128</span>     *   can be reset with {@link #withEstimationType(EstimationType)}&lt;/li&gt;<a name="line.128"></a>
+<span class="sourceLineNo">129</span>     *   &lt;li&gt;default NaN strategy: {@link NaNStrategy#REMOVED},<a name="line.129"></a>
+<span class="sourceLineNo">130</span>     *   can be reset with {@link #withNaNStrategy(NaNStrategy)}&lt;/li&gt;<a name="line.130"></a>
+<span class="sourceLineNo">131</span>     *   &lt;li&gt;a KthSelector that makes use of {@link MedianOf3PivotingStrategy},<a name="line.131"></a>
+<span class="sourceLineNo">132</span>     *   can be reset with {@link #withKthSelector(KthSelector)}&lt;/li&gt;<a name="line.132"></a>
+<span class="sourceLineNo">133</span>     * &lt;/ul&gt;<a name="line.133"></a>
+<span class="sourceLineNo">134</span>     */<a name="line.134"></a>
+<span class="sourceLineNo">135</span>    public Percentile() {<a name="line.135"></a>
+<span class="sourceLineNo">136</span>        // No try-catch or advertised exception here - arg is valid<a name="line.136"></a>
+<span class="sourceLineNo">137</span>        this(50.0);<a name="line.137"></a>
+<span class="sourceLineNo">138</span>    }<a name="line.138"></a>
+<span class="sourceLineNo">139</span><a name="line.139"></a>
+<span class="sourceLineNo">140</span>    /**<a name="line.140"></a>
+<span class="sourceLineNo">141</span>     * Constructs a Percentile with the specific quantile value and the following<a name="line.141"></a>
+<span class="sourceLineNo">142</span>     * &lt;ul&gt;<a name="line.142"></a>
+<span class="sourceLineNo">143</span>     *   &lt;li&gt;default method type: {@link EstimationType#LEGACY}&lt;/li&gt;<a name="line.143"></a>
+<span class="sourceLineNo">144</span>     *   &lt;li&gt;default NaN strategy: {@link NaNStrategy#REMOVED}&lt;/li&gt;<a name="line.144"></a>
+<span class="sourceLineNo">145</span>     *   &lt;li&gt;a Kth Selector : {@link KthSelector}&lt;/li&gt;<a name="line.145"></a>
+<span class="sourceLineNo">146</span>     * &lt;/ul&gt;<a name="line.146"></a>
+<span class="sourceLineNo">147</span>     * @param quantile the quantile<a name="line.147"></a>
+<span class="sourceLineNo">148</span>     * @throws MathIllegalArgumentException  if p is not greater than 0 and less<a name="line.148"></a>
+<span class="sourceLineNo">149</span>     * than or equal to 100<a name="line.149"></a>
+<span class="sourceLineNo">150</span>     */<a name="line.150"></a>
+<span class="sourceLineNo">151</span>    public Percentile(final double quantile) throws MathIllegalArgumentException {<a name="line.151"></a>
+<span class="sourceLineNo">152</span>        this(quantile, EstimationType.LEGACY, NaNStrategy.REMOVED,<a name="line.152"></a>
+<span class="sourceLineNo">153</span>             new KthSelector(new MedianOf3PivotingStrategy()));<a name="line.153"></a>
+<span class="sourceLineNo">154</span>    }<a name="line.154"></a>
+<span class="sourceLineNo">155</span><a name="line.155"></a>
+<span class="sourceLineNo">156</span>    /**<a name="line.156"></a>
+<span class="sourceLineNo">157</span>     * Copy constructor, creates a new {@code Percentile} identical<a name="line.157"></a>
+<span class="sourceLineNo">158</span>     * to the {@code original}<a name="line.158"></a>
+<span class="sourceLineNo">159</span>     *<a name="line.159"></a>
+<span class="sourceLineNo">160</span>     * @param original the {@code Percentile} instance to copy<a name="line.160"></a>
+<span class="sourceLineNo">161</span>     * @throws NullArgumentException if original is null<a name="line.161"></a>
+<span class="sourceLineNo">162</span>     */<a name="line.162"></a>
+<span class="sourceLineNo">163</span>    public Percentile(final Percentile original) throws NullArgumentException {<a name="line.163"></a>
+<span class="sourceLineNo">164</span><a name="line.164"></a>
+<span class="sourceLineNo">165</span>        MathUtils.checkNotNull(original);<a name="line.165"></a>
+<span class="sourceLineNo">166</span>        estimationType   = original.getEstimationType();<a name="line.166"></a>
+<span class="sourceLineNo">167</span>        nanStrategy      = original.getNaNStrategy();<a name="line.167"></a>
+<span class="sourceLineNo">168</span>        kthSelector      = original.getKthSelector();<a name="line.168"></a>
+<span class="sourceLineNo">169</span><a name="line.169"></a>
+<span class="sourceLineNo">170</span>        setData(original.getDataRef());<a name="line.170"></a>
+<span class="sourceLineNo">171</span>        if (original.cachedPivots != null) {<a name="line.171"></a>
+<span class="sourceLineNo">172</span>            System.arraycopy(original.cachedPivots, 0, cachedPivots, 0, original.cachedPivots.length);<a name="line.172"></a>
+<span class="sourceLineNo">173</span>        }<a name="line.173"></a>
+<span class="sourceLineNo">174</span>        setQuantile(original.quantile);<a name="line.174"></a>
+<span class="sourceLineNo">175</span><a name="line.175"></a>
+<span class="sourceLineNo">176</span>    }<a name="line.176"></a>
+<span class="sourceLineNo">177</span><a name="line.177"></a>
+<span class="sourceLineNo">178</span>    /**<a name="line.178"></a>
+<span class="sourceLineNo">179</span>     * Constructs a Percentile with the specific quantile value,<a name="line.179"></a>
+<span class="sourceLineNo">180</span>     * {@link EstimationType}, {@link NaNStrategy} and {@link KthSelector}.<a name="line.180"></a>
+<span class="sourceLineNo">181</span>     *<a name="line.181"></a>
+<span class="sourceLineNo">182</span>     * @param quantile the quantile to be computed<a name="line.182"></a>
+<span class="sourceLineNo">183</span>     * @param estimationType one of the percentile {@link EstimationType  estimation types}<a name="line.183"></a>
+<span class="sourceLineNo">184</span>     * @param nanStrategy one of {@link NaNStrategy} to handle with NaNs<a name="line.184"></a>
+<span class="sourceLineNo">185</span>     * @param kthSelector a {@link KthSelector} to use for pivoting during search<a name="line.185"></a>
+<span class="sourceLineNo">186</span>     * @throws MathIllegalArgumentException if p is not within (0,100]<a name="line.186"></a>
+<span class="sourceLineNo">187</span>     * @throws NullArgumentException if type or NaNStrategy passed is null<a name="line.187"></a>
+<span class="sourceLineNo">188</span>     */<a name="line.188"></a>
+<span class="sourceLineNo">189</span>    protected Percentile(final double quantile,<a name="line.189"></a>
+<span class="sourceLineNo">190</span>                         final EstimationType estimationType,<a name="line.190"></a>
+<span class="sourceLineNo">191</span>                         final NaNStrategy nanStrategy,<a name="line.191"></a>
+<span class="sourceLineNo">192</span>                         final KthSelector kthSelector)<a name="line.192"></a>
+<span class="sourceLineNo">193</span>        throws MathIllegalArgumentException {<a name="line.193"></a>
+<span class="sourceLineNo">194</span>        setQuantile(quantile);<a name="line.194"></a>
+<span class="sourceLineNo">195</span>        cachedPivots = null;<a name="line.195"></a>
+<span class="sourceLineNo">196</span>        MathUtils.checkNotNull(estimationType);<a name="line.196"></a>
+<span class="sourceLineNo">197</span>        MathUtils.checkNotNull(nanStrategy);<a name="line.197"></a>
+<span class="sourceLineNo">198</span>        MathUtils.checkNotNull(kthSelector);<a name="line.198"></a>
+<span class="sourceLineNo">199</span>        this.estimationType = estimationType;<a name="line.199"></a>
+<span class="sourceLineNo">200</span>        this.nanStrategy = nanStrategy;<a name="line.200"></a>
+<span class="sourceLineNo">201</span>        this.kthSelector = kthSelector;<a name="line.201"></a>
+<span class="sourceLineNo">202</span>    }<a name="line.202"></a>
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+<span class="sourceLineNo">654</span>     * This method is intended to be used as part of a fluent-type builder<a name="line.654"></a>
+<span class="sourceLineNo">655</span>     * pattern. Building finely tune instances should be done as follows:<a name="line.655"></a>
+<span class="sourceLineNo">656</span>     * &lt;/p&gt;<a name="line.656"></a>
+<span class="sourceLineNo">657</span>     * &lt;pre&gt;<a name="line.657"></a>
+<span class="sourceLineNo">658</span>     *   Percentile customized = new Percentile(quantile).<a name="line.658"></a>
+<span class="sourceLineNo">659</span>     *                           withEstimationType(estimationType).<a name="line.659"></a>
+<span class="sourceLineNo">660</span>     *                           withNaNStrategy(nanStrategy).<a name="line.660"></a>
+<span class="sourceLineNo">661</span>     *                           withKthSelector(newKthSelector);<a name="line.661"></a>
+<span class="sourceLineNo">662</span>     * &lt;/pre&gt;<a name="line.662"></a>
+<span class="sourceLineNo">663</span>     * &lt;p&gt;<a name="line.663"></a>
+<span class="sourceLineNo">664</span>     * If any of the {@code withXxx} method is omitted, the default value for<a name="line.664"></a>
+<span class="sourceLineNo">665</span>     * the corresponding customization parameter will be used.<a name="line.665"></a>
+<span class="sourceLineNo">666</span>     * &lt;/p&gt;<a name="line.666"></a>
+<span class="sourceLineNo">667</span>     * @param newKthSelector KthSelector for the new instance<a name="line.667"></a>
+<span class="sourceLineNo">668</span>     * @return a new instance, with changed KthSelector<a name="line.668"></a>
+<span class="sourceLineNo">669</span>     * @throws NullArgumentException when newKthSelector is null<a name="line.669"></a>
+<span class="sourceLineNo">670</span>     */<a name="line.670"></a>
+<span class="sourceLineNo">671</span>    public Percentile withKthSelector(final KthSelector newKthSelector) {<a name="line.671"></a>
+<span class="sourceLineNo">672</span>        return new Percentile(quantile, estimationType, nanStrategy,<a name="line.672"></a>
+<span class="sourceLineNo">673</span>                                newKthSelector);<a name="line.673"></a>
+<span class="sourceLineNo">674</span>    }<a name="line.674"></a>
+<span class="sourceLineNo">675</span><a name="line.675"></a>
+<span class="sourceLineNo">676</span>    /**<a name="line.676"></a>
+<span class="sourceLineNo">677</span>     * An enum for various estimation strategies of a percentile referred in<a name="line.677"></a>
+<span class="sourceLineNo">678</span>     * &lt;a href="http://en.wikipedia.org/wiki/Quantile"&gt;wikipedia on quantile&lt;/a&gt;<a name="line.678"></a>
+<span class="sourceLineNo">679</span>     * with the names of enum matching those of types mentioned in<a name="line.679"></a>
+<span class="sourceLineNo">680</span>     * wikipedia.<a name="line.680"></a>
+<span class="sourceLineNo">681</span>     * &lt;p&gt;<a name="line.681"></a>
+<span class="sourceLineNo">682</span>     * Each enum corresponding to the specific type of estimation in wikipedia<a name="line.682"></a>
+<span class="sourceLineNo">683</span>     * implements  the respective formulae that specializes in the below aspects<a name="line.683"></a>
+<span class="sourceLineNo">684</span>     * &lt;ul&gt;<a name="line.684"></a>
+<span class="sourceLineNo">685</span>     * &lt;li&gt;An &lt;b&gt;index method&lt;/b&gt; to calculate approximate index of the<a name="line.685"></a>
+<span class="sourceLineNo">686</span>     * estimate&lt;/li&gt;<a name="line.686"></a>
+<span class="sourceLineNo">687</span>     * &lt;li&gt;An &lt;b&gt;estimate method&lt;/b&gt; to estimate a value found at the earlier<a name="line.687"></a>
+<span class="sourceLineNo">688</span>     * computed index&lt;/li&gt;<a name="line.688"></a>
+<span class="sourceLineNo">689</span>     * &lt;li&gt;A &lt;b&gt; minLimit&lt;/b&gt; on the quantile for which first element of sorted<a name="line.689"></a>
+<span class="sourceLineNo">690</span>     * input is returned as an estimate &lt;/li&gt;<a name="line.690"></a>
+<span class="sourceLineNo">691</span>     * &lt;li&gt;A &lt;b&gt; maxLimit&lt;/b&gt; on the quantile for which last element of sorted<a name="line.691"></a>
+<span class="sourceLineNo">692</span>     * input is returned as an estimate &lt;/li&gt;<a name="line.692"></a>
+<span class="sourceLineNo">693</span>     * &lt;/ul&gt;<a name="line.693"></a>
+<span class="sourceLineNo">694</span>     * &lt;p&gt;<a name="line.694"></a>
+<span class="sourceLineNo">695</span>     * Users can now create {@link Percentile} by explicitly passing this enum;<a name="line.695"></a>
+<span class="sourceLineNo">696</span>     * such as by invoking {@link Percentile#withEstimationType(EstimationType)}<a name="line.696"></a>
+<span class="sourceLineNo">697</span>     * &lt;p&gt;<a name="line.697"></a>
+<span class="sourceLineNo">698</span>     * References:<a name="line.698"></a>
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+<span class="sourceLineNo">700</span>     * &lt;li&gt;<a name="line.700"></a>
+<span class="sourceLineNo">701</span>     * &lt;a href="http://en.wikipedia.org/wiki/Quantile"&gt;Wikipedia on quantile&lt;/a&gt;<a name="line.701"></a>
+<span class="sourceLineNo">702</span>     * &lt;/li&gt;<a name="line.702"></a>
+<span class="sourceLineNo">703</span>     * &lt;li&gt;<a name="line.703"></a>
+<span class="sourceLineNo">704</span>     * &lt;a href="https://www.amherst.edu/media/view/129116/.../Sample+Quantiles.pdf"&gt;<a name="line.704"></a>
+<span class="sourceLineNo">705</span>     * Hyndman, R. J. and Fan, Y. (1996) Sample quantiles in statistical<a name="line.705"></a>
+<span class="sourceLineNo">706</span>     * packages, American Statistician 50, 361–365&lt;/a&gt; &lt;/li&gt;<a name="line.706"></a>
+<span class="sourceLineNo">707</span>     * &lt;li&gt;<a name="line.707"></a>
+<span class="sourceLineNo">708</span>     * &lt;a href="http://stat.ethz.ch/R-manual/R-devel/library/stats/html/quantile.html"&gt;<a name="line.708"></a>
+<span class="sourceLineNo">709</span>     * R-Manual &lt;/a&gt;&lt;/li&gt;<a name="line.709"></a>
+<span class="sourceLineNo">710</span>     * &lt;/ol&gt;<a name="line.710"></a>
+<span class="sourceLineNo">711</span>     *<a name="line.711"></a>
+<span class="sourceLineNo">712</span>     */<a name="line.712"></a>
+<span class="sourceLineNo">713</span>    public static enum EstimationType {<a name="line.713"></a>
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+<span class="sourceLineNo">716</span>         * has the following formulae for index and estimates&lt;br&gt;<a name="line.716"></a>
+<span class="sourceLineNo">717</span>         * \( \begin{align}<a name="line.717"></a>
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+<span class="sourceLineNo">720</span>         * &amp;amp;minLimit = 0 \\<a name="line.720"></a>
+<span class="sourceLineNo">721</span>         * &amp;amp;maxLimit = 1 \\<a name="line.721"></a>
+<span class="sourceLineNo">722</span>         * \end{align}\)<a name="line.722"></a>
+<span class="sourceLineNo">723</span>         */<a name="line.723"></a>
+<span class="sourceLineNo">724</span>        LEGACY("Legacy Apache Commons Math") {<a name="line.724"></a>
+<span class="sourceLineNo">725</span>            /**<a name="line.725"></a>
+<span class="sourceLineNo">726</span>             * {@inheritDoc}.This method in particular makes use of existing<a name="line.726"></a>
+<span class="sourceLineNo">727</span>             * Apache Commons Math style of picking up the index.<a name="line.727"></a>
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+<span class="sourceLineNo">738</span>        /**<a name="line.738"></a>
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+<span class="sourceLineNo">740</span>         * \( \begin{align}<a name="line.740"></a>
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+<span class="sourceLineNo">746</span>        R_1("R-1") {<a name="line.746"></a>
+<span class="sourceLineNo">747</span><a name="line.747"></a>
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+<span class="sourceLineNo">753</span><a name="line.753"></a>
+<span class="sourceLineNo">754</span>            /**<a name="line.754"></a>
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+<span class="sourceLineNo">756</span>             */<a name="line.756"></a>
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+<span class="sourceLineNo">763</span><a name="line.763"></a>
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+<span class="sourceLineNo">767</span>         * \( \begin{align}<a name="line.767"></a>
+<span class="sourceLineNo">768</span>         * &amp;amp;index= Np + 1/2\, \\<a name="line.768"></a>
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+<span class="sourceLineNo">771</span>         * &amp;amp;minLimit = 0 \\<a name="line.771"></a>
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+<span class="sourceLineNo">776</span><a name="line.776"></a>
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+<span class="sourceLineNo">797</span>                return (low + high) / 2;<a name="line.797"></a>
+<span class="sourceLineNo">798</span>            }<a name="line.798"></a>
+<span class="sourceLineNo">799</span><a name="line.799"></a>
+<span class="sourceLineNo">800</span>        },<a name="line.800"></a>
+<span class="sourceLineNo">801</span>        /**<a name="line.801"></a>
+<span class="sourceLineNo">802</span>         * The method R_3 has the following formulae for index and estimates&lt;br&gt;<a name="line.802"></a>
+<span class="sourceLineNo">803</span>         * \( \begin{align}<a name="line.803"></a>
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+<span class="sourceLineNo">808</span>         */<a name="line.808"></a>
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+<span class="sourceLineNo">811</span>            protected double index(final double p, final int length) {<a name="line.811"></a>
+<span class="sourceLineNo">812</span>                final double minLimit = 1d/2 / length;<a name="line.812"></a>
+<span class="sourceLineNo">813</span>                return Double.compare(p, minLimit) &lt;= 0 ?<a name="line.813"></a>
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+<span class="sourceLineNo">815</span>            }<a name="line.815"></a>
+<span class="sourceLineNo">816</span><a name="line.816"></a>
+<span class="sourceLineNo">817</span>        },<a name="line.817"></a>
+<span class="sourceLineNo">818</span>        /**<a name="line.818"></a>
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+<span class="sourceLineNo">820</span>         * \( \begin{align}<a name="line.820"></a>
+<span class="sourceLineNo">821</span>         * &amp;amp;index= Np\, \\<a name="line.821"></a>
+<span class="sourceLineNo">822</span>         * &amp;amp;estimate= x_{\lfloor h \rfloor} + (h -<a name="line.822"></a>
+<span class="sourceLineNo">823</span>         * \lfloor h \rfloor) (x_{\lfloor h \rfloor + 1} - x_{\lfloor h<a name="line.823"></a>
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+<span class="sourceLineNo">825</span>         * &amp;amp;minLimit = 1/N \\<a name="line.825"></a>
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+<span class="sourceLineNo">830</span>            @Override<a name="line.830"></a>
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+<span class="sourceLineNo">833</span>                final double maxLimit = 1d;<a name="line.833"></a>
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+<span class="sourceLineNo">836</span>            }<a name="line.836"></a>
+<span class="sourceLineNo">837</span><a name="line.837"></a>
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+<span class="sourceLineNo">839</span>        /**<a name="line.839"></a>
+<span class="sourceLineNo">840</span>         * The method R_5 has the following formulae for index and estimates&lt;br&gt;<a name="line.840"></a>
+<span class="sourceLineNo">841</span>         * \( \begin{align}<a name="line.841"></a>
+<span class="sourceLineNo">842</span>         * &amp;amp;index= Np + 1/2\\<a name="line.842"></a>
+<span class="sourceLineNo">843</span>         * &amp;amp;estimate= x_{\lfloor h \rfloor} + (h -<a name="line.843"></a>

[... 294 lines stripped ...]


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