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| author | dwinter |
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| date | Tue, 04 Jan 2011 10:02:07 +0100 |
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<HTML> <BODY BGCOLOR="white"> <PRE> <FONT color="green">001</FONT> /*<a name="line.1"></a> <FONT color="green">002</FONT> * Licensed to the Apache Software Foundation (ASF) under one or more<a name="line.2"></a> <FONT color="green">003</FONT> * contributor license agreements. See the NOTICE file distributed with<a name="line.3"></a> <FONT color="green">004</FONT> * this work for additional information regarding copyright ownership.<a name="line.4"></a> <FONT color="green">005</FONT> * The ASF licenses this file to You under the Apache License, Version 2.0<a name="line.5"></a> <FONT color="green">006</FONT> * (the "License"); you may not use this file except in compliance with<a name="line.6"></a> <FONT color="green">007</FONT> * the License. You may obtain a copy of the License at<a name="line.7"></a> <FONT color="green">008</FONT> *<a name="line.8"></a> <FONT color="green">009</FONT> * http://www.apache.org/licenses/LICENSE-2.0<a name="line.9"></a> <FONT color="green">010</FONT> *<a name="line.10"></a> <FONT color="green">011</FONT> * Unless required by applicable law or agreed to in writing, software<a name="line.11"></a> <FONT color="green">012</FONT> * distributed under the License is distributed on an "AS IS" BASIS,<a name="line.12"></a> <FONT color="green">013</FONT> * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.<a name="line.13"></a> <FONT color="green">014</FONT> * See the License for the specific language governing permissions and<a name="line.14"></a> <FONT color="green">015</FONT> * limitations under the License.<a name="line.15"></a> <FONT color="green">016</FONT> */<a name="line.16"></a> <FONT color="green">017</FONT> package org.apache.commons.math.stat.descriptive.moment;<a name="line.17"></a> <FONT color="green">018</FONT> <a name="line.18"></a> <FONT color="green">019</FONT> import java.io.Serializable;<a name="line.19"></a> <FONT color="green">020</FONT> <a name="line.20"></a> <FONT color="green">021</FONT> import org.apache.commons.math.MathRuntimeException;<a name="line.21"></a> <FONT color="green">022</FONT> import org.apache.commons.math.stat.descriptive.AbstractStorelessUnivariateStatistic;<a name="line.22"></a> <FONT color="green">023</FONT> <a name="line.23"></a> <FONT color="green">024</FONT> <a name="line.24"></a> <FONT color="green">025</FONT> /**<a name="line.25"></a> <FONT color="green">026</FONT> * Computes the Kurtosis of the available values.<a name="line.26"></a> <FONT color="green">027</FONT> * <p><a name="line.27"></a> <FONT color="green">028</FONT> * We use the following (unbiased) formula to define kurtosis:</p><a name="line.28"></a> <FONT color="green">029</FONT> * <p><a name="line.29"></a> <FONT color="green">030</FONT> * kurtosis = { [n(n+1) / (n -1)(n - 2)(n-3)] sum[(x_i - mean)^4] / std^4 } - [3(n-1)^2 / (n-2)(n-3)]<a name="line.30"></a> <FONT color="green">031</FONT> * </p><p><a name="line.31"></a> <FONT color="green">032</FONT> * where n is the number of values, mean is the {@link Mean} and std is the<a name="line.32"></a> <FONT color="green">033</FONT> * {@link StandardDeviation}</p><a name="line.33"></a> <FONT color="green">034</FONT> * <p><a name="line.34"></a> <FONT color="green">035</FONT> * Note that this statistic is undefined for n < 4. <code>Double.Nan</code><a name="line.35"></a> <FONT color="green">036</FONT> * is returned when there is not sufficient data to compute the statistic.</p><a name="line.36"></a> <FONT color="green">037</FONT> * <p><a name="line.37"></a> <FONT color="green">038</FONT> * <strong>Note that this implementation is not synchronized.</strong> If<a name="line.38"></a> <FONT color="green">039</FONT> * multiple threads access an instance of this class concurrently, and at least<a name="line.39"></a> <FONT color="green">040</FONT> * one of the threads invokes the <code>increment()</code> or<a name="line.40"></a> <FONT color="green">041</FONT> * <code>clear()</code> method, it must be synchronized externally.</p><a name="line.41"></a> <FONT color="green">042</FONT> *<a name="line.42"></a> <FONT color="green">043</FONT> * @version $Revision: 811833 $ $Date: 2009-09-06 12:27:50 -0400 (Sun, 06 Sep 2009) $<a name="line.43"></a> <FONT color="green">044</FONT> */<a name="line.44"></a> <FONT color="green">045</FONT> public class Kurtosis extends AbstractStorelessUnivariateStatistic implements Serializable {<a name="line.45"></a> <FONT color="green">046</FONT> <a name="line.46"></a> <FONT color="green">047</FONT> /** Serializable version identifier */<a name="line.47"></a> <FONT color="green">048</FONT> private static final long serialVersionUID = 2784465764798260919L;<a name="line.48"></a> <FONT color="green">049</FONT> <a name="line.49"></a> <FONT color="green">050</FONT> /**Fourth Moment on which this statistic is based */<a name="line.50"></a> <FONT color="green">051</FONT> protected FourthMoment moment;<a name="line.51"></a> <FONT color="green">052</FONT> <a name="line.52"></a> <FONT color="green">053</FONT> /**<a name="line.53"></a> <FONT color="green">054</FONT> * Determines whether or not this statistic can be incremented or cleared.<a name="line.54"></a> <FONT color="green">055</FONT> * <p><a name="line.55"></a> <FONT color="green">056</FONT> * Statistics based on (constructed from) external moments cannot<a name="line.56"></a> <FONT color="green">057</FONT> * be incremented or cleared.</p><a name="line.57"></a> <FONT color="green">058</FONT> */<a name="line.58"></a> <FONT color="green">059</FONT> protected boolean incMoment;<a name="line.59"></a> <FONT color="green">060</FONT> <a name="line.60"></a> <FONT color="green">061</FONT> /**<a name="line.61"></a> <FONT color="green">062</FONT> * Construct a Kurtosis<a name="line.62"></a> <FONT color="green">063</FONT> */<a name="line.63"></a> <FONT color="green">064</FONT> public Kurtosis() {<a name="line.64"></a> <FONT color="green">065</FONT> incMoment = true;<a name="line.65"></a> <FONT color="green">066</FONT> moment = new FourthMoment();<a name="line.66"></a> <FONT color="green">067</FONT> }<a name="line.67"></a> <FONT color="green">068</FONT> <a name="line.68"></a> <FONT color="green">069</FONT> /**<a name="line.69"></a> <FONT color="green">070</FONT> * Construct a Kurtosis from an external moment<a name="line.70"></a> <FONT color="green">071</FONT> *<a name="line.71"></a> <FONT color="green">072</FONT> * @param m4 external Moment<a name="line.72"></a> <FONT color="green">073</FONT> */<a name="line.73"></a> <FONT color="green">074</FONT> public Kurtosis(final FourthMoment m4) {<a name="line.74"></a> <FONT color="green">075</FONT> incMoment = false;<a name="line.75"></a> <FONT color="green">076</FONT> this.moment = m4;<a name="line.76"></a> <FONT color="green">077</FONT> }<a name="line.77"></a> <FONT color="green">078</FONT> <a name="line.78"></a> <FONT color="green">079</FONT> /**<a name="line.79"></a> <FONT color="green">080</FONT> * Copy constructor, creates a new {@code Kurtosis} identical<a name="line.80"></a> <FONT color="green">081</FONT> * to the {@code original}<a name="line.81"></a> <FONT color="green">082</FONT> *<a name="line.82"></a> <FONT color="green">083</FONT> * @param original the {@code Kurtosis} instance to copy<a name="line.83"></a> <FONT color="green">084</FONT> */<a name="line.84"></a> <FONT color="green">085</FONT> public Kurtosis(Kurtosis original) {<a name="line.85"></a> <FONT color="green">086</FONT> copy(original, this);<a name="line.86"></a> <FONT color="green">087</FONT> }<a name="line.87"></a> <FONT color="green">088</FONT> <a name="line.88"></a> <FONT color="green">089</FONT> /**<a name="line.89"></a> <FONT color="green">090</FONT> * {@inheritDoc}<a name="line.90"></a> <FONT color="green">091</FONT> */<a name="line.91"></a> <FONT color="green">092</FONT> @Override<a name="line.92"></a> <FONT color="green">093</FONT> public void increment(final double d) {<a name="line.93"></a> <FONT color="green">094</FONT> if (incMoment) {<a name="line.94"></a> <FONT color="green">095</FONT> moment.increment(d);<a name="line.95"></a> <FONT color="green">096</FONT> } else {<a name="line.96"></a> <FONT color="green">097</FONT> throw MathRuntimeException.createIllegalStateException(<a name="line.97"></a> <FONT color="green">098</FONT> "statistics constructed from external moments cannot be incremented");<a name="line.98"></a> <FONT color="green">099</FONT> }<a name="line.99"></a> <FONT color="green">100</FONT> }<a name="line.100"></a> <FONT color="green">101</FONT> <a name="line.101"></a> <FONT color="green">102</FONT> /**<a name="line.102"></a> <FONT color="green">103</FONT> * {@inheritDoc}<a name="line.103"></a> <FONT color="green">104</FONT> */<a name="line.104"></a> <FONT color="green">105</FONT> @Override<a name="line.105"></a> <FONT color="green">106</FONT> public double getResult() {<a name="line.106"></a> <FONT color="green">107</FONT> double kurtosis = Double.NaN;<a name="line.107"></a> <FONT color="green">108</FONT> if (moment.getN() > 3) {<a name="line.108"></a> <FONT color="green">109</FONT> double variance = moment.m2 / (moment.n - 1);<a name="line.109"></a> <FONT color="green">110</FONT> if (moment.n <= 3 || variance < 10E-20) {<a name="line.110"></a> <FONT color="green">111</FONT> kurtosis = 0.0;<a name="line.111"></a> <FONT color="green">112</FONT> } else {<a name="line.112"></a> <FONT color="green">113</FONT> double n = moment.n;<a name="line.113"></a> <FONT color="green">114</FONT> kurtosis =<a name="line.114"></a> <FONT color="green">115</FONT> (n * (n + 1) * moment.m4 -<a name="line.115"></a> <FONT color="green">116</FONT> 3 * moment.m2 * moment.m2 * (n - 1)) /<a name="line.116"></a> <FONT color="green">117</FONT> ((n - 1) * (n -2) * (n -3) * variance * variance);<a name="line.117"></a> <FONT color="green">118</FONT> }<a name="line.118"></a> <FONT color="green">119</FONT> }<a name="line.119"></a> <FONT color="green">120</FONT> return kurtosis;<a name="line.120"></a> <FONT color="green">121</FONT> }<a name="line.121"></a> <FONT color="green">122</FONT> <a name="line.122"></a> <FONT color="green">123</FONT> /**<a name="line.123"></a> <FONT color="green">124</FONT> * {@inheritDoc}<a name="line.124"></a> <FONT color="green">125</FONT> */<a name="line.125"></a> <FONT color="green">126</FONT> @Override<a name="line.126"></a> <FONT color="green">127</FONT> public void clear() {<a name="line.127"></a> <FONT color="green">128</FONT> if (incMoment) {<a name="line.128"></a> <FONT color="green">129</FONT> moment.clear();<a name="line.129"></a> <FONT color="green">130</FONT> } else {<a name="line.130"></a> <FONT color="green">131</FONT> throw MathRuntimeException.createIllegalStateException(<a name="line.131"></a> <FONT color="green">132</FONT> "statistics constructed from external moments cannot be cleared");<a name="line.132"></a> <FONT color="green">133</FONT> }<a name="line.133"></a> <FONT color="green">134</FONT> }<a name="line.134"></a> <FONT color="green">135</FONT> <a name="line.135"></a> <FONT color="green">136</FONT> /**<a name="line.136"></a> <FONT color="green">137</FONT> * {@inheritDoc}<a name="line.137"></a> <FONT color="green">138</FONT> */<a name="line.138"></a> <FONT color="green">139</FONT> public long getN() {<a name="line.139"></a> <FONT color="green">140</FONT> return moment.getN();<a name="line.140"></a> <FONT color="green">141</FONT> }<a name="line.141"></a> <FONT color="green">142</FONT> <a name="line.142"></a> <FONT color="green">143</FONT> /* UnvariateStatistic Approach */<a name="line.143"></a> <FONT color="green">144</FONT> <a name="line.144"></a> <FONT color="green">145</FONT> /**<a name="line.145"></a> <FONT color="green">146</FONT> * Returns the kurtosis of the entries in the specified portion of the<a name="line.146"></a> <FONT color="green">147</FONT> * input array.<a name="line.147"></a> <FONT color="green">148</FONT> * <p><a name="line.148"></a> <FONT color="green">149</FONT> * See {@link Kurtosis} for details on the computing algorithm.</p><a name="line.149"></a> <FONT color="green">150</FONT> * <p><a name="line.150"></a> <FONT color="green">151</FONT> * Throws <code>IllegalArgumentException</code> if the array is null.</p><a name="line.151"></a> <FONT color="green">152</FONT> *<a name="line.152"></a> <FONT color="green">153</FONT> * @param values the input array<a name="line.153"></a> <FONT color="green">154</FONT> * @param begin index of the first array element to include<a name="line.154"></a> <FONT color="green">155</FONT> * @param length the number of elements to include<a name="line.155"></a> <FONT color="green">156</FONT> * @return the kurtosis of the values or Double.NaN if length is less than<a name="line.156"></a> <FONT color="green">157</FONT> * 4<a name="line.157"></a> <FONT color="green">158</FONT> * @throws IllegalArgumentException if the input array is null or the array<a name="line.158"></a> <FONT color="green">159</FONT> * index parameters are not valid<a name="line.159"></a> <FONT color="green">160</FONT> */<a name="line.160"></a> <FONT color="green">161</FONT> @Override<a name="line.161"></a> <FONT color="green">162</FONT> public double evaluate(final double[] values,final int begin, final int length) {<a name="line.162"></a> <FONT color="green">163</FONT> // Initialize the kurtosis<a name="line.163"></a> <FONT color="green">164</FONT> double kurt = Double.NaN;<a name="line.164"></a> <FONT color="green">165</FONT> <a name="line.165"></a> <FONT color="green">166</FONT> if (test(values, begin, length) && length > 3) {<a name="line.166"></a> <FONT color="green">167</FONT> <a name="line.167"></a> <FONT color="green">168</FONT> // Compute the mean and standard deviation<a name="line.168"></a> <FONT color="green">169</FONT> Variance variance = new Variance();<a name="line.169"></a> <FONT color="green">170</FONT> variance.incrementAll(values, begin, length);<a name="line.170"></a> <FONT color="green">171</FONT> double mean = variance.moment.m1;<a name="line.171"></a> <FONT color="green">172</FONT> double stdDev = Math.sqrt(variance.getResult());<a name="line.172"></a> <FONT color="green">173</FONT> <a name="line.173"></a> <FONT color="green">174</FONT> // Sum the ^4 of the distance from the mean divided by the<a name="line.174"></a> <FONT color="green">175</FONT> // standard deviation<a name="line.175"></a> <FONT color="green">176</FONT> double accum3 = 0.0;<a name="line.176"></a> <FONT color="green">177</FONT> for (int i = begin; i < begin + length; i++) {<a name="line.177"></a> <FONT color="green">178</FONT> accum3 += Math.pow(values[i] - mean, 4.0);<a name="line.178"></a> <FONT color="green">179</FONT> }<a name="line.179"></a> <FONT color="green">180</FONT> accum3 /= Math.pow(stdDev, 4.0d);<a name="line.180"></a> <FONT color="green">181</FONT> <a name="line.181"></a> <FONT color="green">182</FONT> // Get N<a name="line.182"></a> <FONT color="green">183</FONT> double n0 = length;<a name="line.183"></a> <FONT color="green">184</FONT> <a name="line.184"></a> <FONT color="green">185</FONT> double coefficientOne =<a name="line.185"></a> <FONT color="green">186</FONT> (n0 * (n0 + 1)) / ((n0 - 1) * (n0 - 2) * (n0 - 3));<a name="line.186"></a> <FONT color="green">187</FONT> double termTwo =<a name="line.187"></a> <FONT color="green">188</FONT> (3 * Math.pow(n0 - 1, 2.0)) / ((n0 - 2) * (n0 - 3));<a name="line.188"></a> <FONT color="green">189</FONT> <a name="line.189"></a> <FONT color="green">190</FONT> // Calculate kurtosis<a name="line.190"></a> <FONT color="green">191</FONT> kurt = (coefficientOne * accum3) - termTwo;<a name="line.191"></a> <FONT color="green">192</FONT> }<a name="line.192"></a> <FONT color="green">193</FONT> return kurt;<a name="line.193"></a> <FONT color="green">194</FONT> }<a name="line.194"></a> <FONT color="green">195</FONT> <a name="line.195"></a> <FONT color="green">196</FONT> /**<a name="line.196"></a> <FONT color="green">197</FONT> * {@inheritDoc}<a name="line.197"></a> <FONT color="green">198</FONT> */<a name="line.198"></a> <FONT color="green">199</FONT> @Override<a name="line.199"></a> <FONT color="green">200</FONT> public Kurtosis copy() {<a name="line.200"></a> <FONT color="green">201</FONT> Kurtosis result = new Kurtosis();<a name="line.201"></a> <FONT color="green">202</FONT> copy(this, result);<a name="line.202"></a> <FONT color="green">203</FONT> return result;<a name="line.203"></a> <FONT color="green">204</FONT> }<a name="line.204"></a> <FONT color="green">205</FONT> <a name="line.205"></a> <FONT color="green">206</FONT> /**<a name="line.206"></a> <FONT color="green">207</FONT> * Copies source to dest.<a name="line.207"></a> <FONT color="green">208</FONT> * <p>Neither source nor dest can be null.</p><a name="line.208"></a> <FONT color="green">209</FONT> *<a name="line.209"></a> <FONT color="green">210</FONT> * @param source Kurtosis to copy<a name="line.210"></a> <FONT color="green">211</FONT> * @param dest Kurtosis to copy to<a name="line.211"></a> <FONT color="green">212</FONT> * @throws NullPointerException if either source or dest is null<a name="line.212"></a> <FONT color="green">213</FONT> */<a name="line.213"></a> <FONT color="green">214</FONT> public static void copy(Kurtosis source, Kurtosis dest) {<a name="line.214"></a> <FONT color="green">215</FONT> dest.moment = source.moment.copy();<a name="line.215"></a> <FONT color="green">216</FONT> dest.incMoment = source.incMoment;<a name="line.216"></a> <FONT color="green">217</FONT> }<a name="line.217"></a> <FONT color="green">218</FONT> <a name="line.218"></a> <FONT color="green">219</FONT> }<a name="line.219"></a> </PRE> </BODY> </HTML>