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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.distribution;<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.ConvergenceException;<a name="line.21"></a> <FONT color="green">022</FONT> import org.apache.commons.math.FunctionEvaluationException;<a name="line.22"></a> <FONT color="green">023</FONT> import org.apache.commons.math.MathException;<a name="line.23"></a> <FONT color="green">024</FONT> import org.apache.commons.math.MathRuntimeException;<a name="line.24"></a> <FONT color="green">025</FONT> import org.apache.commons.math.analysis.UnivariateRealFunction;<a name="line.25"></a> <FONT color="green">026</FONT> import org.apache.commons.math.analysis.solvers.BrentSolver;<a name="line.26"></a> <FONT color="green">027</FONT> import org.apache.commons.math.analysis.solvers.UnivariateRealSolverUtils;<a name="line.27"></a> <FONT color="green">028</FONT> <a name="line.28"></a> <FONT color="green">029</FONT> /**<a name="line.29"></a> <FONT color="green">030</FONT> * Base class for continuous distributions. Default implementations are<a name="line.30"></a> <FONT color="green">031</FONT> * provided for some of the methods that do not vary from distribution to<a name="line.31"></a> <FONT color="green">032</FONT> * distribution.<a name="line.32"></a> <FONT color="green">033</FONT> *<a name="line.33"></a> <FONT color="green">034</FONT> * @version $Revision: 925812 $ $Date: 2010-03-21 11:49:31 -0400 (Sun, 21 Mar 2010) $<a name="line.34"></a> <FONT color="green">035</FONT> */<a name="line.35"></a> <FONT color="green">036</FONT> public abstract class AbstractContinuousDistribution<a name="line.36"></a> <FONT color="green">037</FONT> extends AbstractDistribution<a name="line.37"></a> <FONT color="green">038</FONT> implements ContinuousDistribution, Serializable {<a name="line.38"></a> <FONT color="green">039</FONT> <a name="line.39"></a> <FONT color="green">040</FONT> /** Serializable version identifier */<a name="line.40"></a> <FONT color="green">041</FONT> private static final long serialVersionUID = -38038050983108802L;<a name="line.41"></a> <FONT color="green">042</FONT> <a name="line.42"></a> <FONT color="green">043</FONT> /**<a name="line.43"></a> <FONT color="green">044</FONT> * Solver absolute accuracy for inverse cum computation<a name="line.44"></a> <FONT color="green">045</FONT> * @since 2.1<a name="line.45"></a> <FONT color="green">046</FONT> */<a name="line.46"></a> <FONT color="green">047</FONT> private double solverAbsoluteAccuracy = BrentSolver.DEFAULT_ABSOLUTE_ACCURACY;<a name="line.47"></a> <FONT color="green">048</FONT> <a name="line.48"></a> <FONT color="green">049</FONT> /**<a name="line.49"></a> <FONT color="green">050</FONT> * Default constructor.<a name="line.50"></a> <FONT color="green">051</FONT> */<a name="line.51"></a> <FONT color="green">052</FONT> protected AbstractContinuousDistribution() {<a name="line.52"></a> <FONT color="green">053</FONT> super();<a name="line.53"></a> <FONT color="green">054</FONT> }<a name="line.54"></a> <FONT color="green">055</FONT> <a name="line.55"></a> <FONT color="green">056</FONT> /**<a name="line.56"></a> <FONT color="green">057</FONT> * Return the probability density for a particular point.<a name="line.57"></a> <FONT color="green">058</FONT> * @param x The point at which the density should be computed.<a name="line.58"></a> <FONT color="green">059</FONT> * @return The pdf at point x.<a name="line.59"></a> <FONT color="green">060</FONT> * @throws MathRuntimeException if the specialized class hasn't implemented this function<a name="line.60"></a> <FONT color="green">061</FONT> * @since 2.1<a name="line.61"></a> <FONT color="green">062</FONT> */<a name="line.62"></a> <FONT color="green">063</FONT> public double density(double x) throws MathRuntimeException {<a name="line.63"></a> <FONT color="green">064</FONT> throw new MathRuntimeException(new UnsupportedOperationException(),<a name="line.64"></a> <FONT color="green">065</FONT> "This distribution does not have a density function implemented");<a name="line.65"></a> <FONT color="green">066</FONT> }<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> * For this distribution, X, this method returns the critical point x, such<a name="line.69"></a> <FONT color="green">070</FONT> * that P(X &lt; x) = <code>p</code>.<a name="line.70"></a> <FONT color="green">071</FONT> *<a name="line.71"></a> <FONT color="green">072</FONT> * @param p the desired probability<a name="line.72"></a> <FONT color="green">073</FONT> * @return x, such that P(X &lt; x) = <code>p</code><a name="line.73"></a> <FONT color="green">074</FONT> * @throws MathException if the inverse cumulative probability can not be<a name="line.74"></a> <FONT color="green">075</FONT> * computed due to convergence or other numerical errors.<a name="line.75"></a> <FONT color="green">076</FONT> * @throws IllegalArgumentException if <code>p</code> is not a valid<a name="line.76"></a> <FONT color="green">077</FONT> * probability.<a name="line.77"></a> <FONT color="green">078</FONT> */<a name="line.78"></a> <FONT color="green">079</FONT> public double inverseCumulativeProbability(final double p)<a name="line.79"></a> <FONT color="green">080</FONT> throws MathException {<a name="line.80"></a> <FONT color="green">081</FONT> if (p < 0.0 || p > 1.0) {<a name="line.81"></a> <FONT color="green">082</FONT> throw MathRuntimeException.createIllegalArgumentException(<a name="line.82"></a> <FONT color="green">083</FONT> "{0} out of [{1}, {2}] range", p, 0.0, 1.0);<a name="line.83"></a> <FONT color="green">084</FONT> }<a name="line.84"></a> <FONT color="green">085</FONT> <a name="line.85"></a> <FONT color="green">086</FONT> // by default, do simple root finding using bracketing and default solver.<a name="line.86"></a> <FONT color="green">087</FONT> // subclasses can override if there is a better method.<a name="line.87"></a> <FONT color="green">088</FONT> UnivariateRealFunction rootFindingFunction =<a name="line.88"></a> <FONT color="green">089</FONT> new UnivariateRealFunction() {<a name="line.89"></a> <FONT color="green">090</FONT> public double value(double x) throws FunctionEvaluationException {<a name="line.90"></a> <FONT color="green">091</FONT> double ret = Double.NaN;<a name="line.91"></a> <FONT color="green">092</FONT> try {<a name="line.92"></a> <FONT color="green">093</FONT> ret = cumulativeProbability(x) - p;<a name="line.93"></a> <FONT color="green">094</FONT> } catch (MathException ex) {<a name="line.94"></a> <FONT color="green">095</FONT> throw new FunctionEvaluationException(ex, x, ex.getPattern(), ex.getArguments());<a name="line.95"></a> <FONT color="green">096</FONT> }<a name="line.96"></a> <FONT color="green">097</FONT> if (Double.isNaN(ret)) {<a name="line.97"></a> <FONT color="green">098</FONT> throw new FunctionEvaluationException(x,<a name="line.98"></a> <FONT color="green">099</FONT> "Cumulative probability function returned NaN for argument {0} p = {1}", x, p);<a name="line.99"></a> <FONT color="green">100</FONT> }<a name="line.100"></a> <FONT color="green">101</FONT> return ret;<a name="line.101"></a> <FONT color="green">102</FONT> }<a name="line.102"></a> <FONT color="green">103</FONT> };<a name="line.103"></a> <FONT color="green">104</FONT> <a name="line.104"></a> <FONT color="green">105</FONT> // Try to bracket root, test domain endoints if this fails<a name="line.105"></a> <FONT color="green">106</FONT> double lowerBound = getDomainLowerBound(p);<a name="line.106"></a> <FONT color="green">107</FONT> double upperBound = getDomainUpperBound(p);<a name="line.107"></a> <FONT color="green">108</FONT> double[] bracket = null;<a name="line.108"></a> <FONT color="green">109</FONT> try {<a name="line.109"></a> <FONT color="green">110</FONT> bracket = UnivariateRealSolverUtils.bracket(<a name="line.110"></a> <FONT color="green">111</FONT> rootFindingFunction, getInitialDomain(p),<a name="line.111"></a> <FONT color="green">112</FONT> lowerBound, upperBound);<a name="line.112"></a> <FONT color="green">113</FONT> } catch (ConvergenceException ex) {<a name="line.113"></a> <FONT color="green">114</FONT> /*<a name="line.114"></a> <FONT color="green">115</FONT> * Check domain endpoints to see if one gives value that is within<a name="line.115"></a> <FONT color="green">116</FONT> * the default solver's defaultAbsoluteAccuracy of 0 (will be the<a name="line.116"></a> <FONT color="green">117</FONT> * case if density has bounded support and p is 0 or 1).<a name="line.117"></a> <FONT color="green">118</FONT> */<a name="line.118"></a> <FONT color="green">119</FONT> if (Math.abs(rootFindingFunction.value(lowerBound)) < getSolverAbsoluteAccuracy()) {<a name="line.119"></a> <FONT color="green">120</FONT> return lowerBound;<a name="line.120"></a> <FONT color="green">121</FONT> }<a name="line.121"></a> <FONT color="green">122</FONT> if (Math.abs(rootFindingFunction.value(upperBound)) < getSolverAbsoluteAccuracy()) {<a name="line.122"></a> <FONT color="green">123</FONT> return upperBound;<a name="line.123"></a> <FONT color="green">124</FONT> }<a name="line.124"></a> <FONT color="green">125</FONT> // Failed bracket convergence was not because of corner solution<a name="line.125"></a> <FONT color="green">126</FONT> throw new MathException(ex);<a name="line.126"></a> <FONT color="green">127</FONT> }<a name="line.127"></a> <FONT color="green">128</FONT> <a name="line.128"></a> <FONT color="green">129</FONT> // find root<a name="line.129"></a> <FONT color="green">130</FONT> double root = UnivariateRealSolverUtils.solve(rootFindingFunction,<a name="line.130"></a> <FONT color="green">131</FONT> // override getSolverAbsoluteAccuracy() to use a Brent solver with<a name="line.131"></a> <FONT color="green">132</FONT> // absolute accuracy different from BrentSolver default<a name="line.132"></a> <FONT color="green">133</FONT> bracket[0],bracket[1], getSolverAbsoluteAccuracy());<a name="line.133"></a> <FONT color="green">134</FONT> return root;<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> /**<a name="line.137"></a> <FONT color="green">138</FONT> * Access the initial domain value, based on <code>p</code>, used to<a name="line.138"></a> <FONT color="green">139</FONT> * bracket a CDF root. This method is used by<a name="line.139"></a> <FONT color="green">140</FONT> * {@link #inverseCumulativeProbability(double)} to find critical values.<a name="line.140"></a> <FONT color="green">141</FONT> *<a name="line.141"></a> <FONT color="green">142</FONT> * @param p the desired probability for the critical value<a name="line.142"></a> <FONT color="green">143</FONT> * @return initial domain value<a name="line.143"></a> <FONT color="green">144</FONT> */<a name="line.144"></a> <FONT color="green">145</FONT> protected abstract double getInitialDomain(double p);<a name="line.145"></a> <FONT color="green">146</FONT> <a name="line.146"></a> <FONT color="green">147</FONT> /**<a name="line.147"></a> <FONT color="green">148</FONT> * Access the domain value lower bound, based on <code>p</code>, used to<a name="line.148"></a> <FONT color="green">149</FONT> * bracket a CDF root. This method is used by<a name="line.149"></a> <FONT color="green">150</FONT> * {@link #inverseCumulativeProbability(double)} to find critical values.<a name="line.150"></a> <FONT color="green">151</FONT> *<a name="line.151"></a> <FONT color="green">152</FONT> * @param p the desired probability for the critical value<a name="line.152"></a> <FONT color="green">153</FONT> * @return domain value lower bound, i.e.<a name="line.153"></a> <FONT color="green">154</FONT> * P(X &lt; <i>lower bound</i>) &lt; <code>p</code><a name="line.154"></a> <FONT color="green">155</FONT> */<a name="line.155"></a> <FONT color="green">156</FONT> protected abstract double getDomainLowerBound(double p);<a name="line.156"></a> <FONT color="green">157</FONT> <a name="line.157"></a> <FONT color="green">158</FONT> /**<a name="line.158"></a> <FONT color="green">159</FONT> * Access the domain value upper bound, based on <code>p</code>, used to<a name="line.159"></a> <FONT color="green">160</FONT> * bracket a CDF root. This method is used by<a name="line.160"></a> <FONT color="green">161</FONT> * {@link #inverseCumulativeProbability(double)} to find critical values.<a name="line.161"></a> <FONT color="green">162</FONT> *<a name="line.162"></a> <FONT color="green">163</FONT> * @param p the desired probability for the critical value<a name="line.163"></a> <FONT color="green">164</FONT> * @return domain value upper bound, i.e.<a name="line.164"></a> <FONT color="green">165</FONT> * P(X &lt; <i>upper bound</i>) &gt; <code>p</code><a name="line.165"></a> <FONT color="green">166</FONT> */<a name="line.166"></a> <FONT color="green">167</FONT> protected abstract double getDomainUpperBound(double p);<a name="line.167"></a> <FONT color="green">168</FONT> <a name="line.168"></a> <FONT color="green">169</FONT> /**<a name="line.169"></a> <FONT color="green">170</FONT> * Returns the solver absolute accuracy for inverse cum computation.<a name="line.170"></a> <FONT color="green">171</FONT> *<a name="line.171"></a> <FONT color="green">172</FONT> * @return the maximum absolute error in inverse cumulative probability estimates<a name="line.172"></a> <FONT color="green">173</FONT> * @since 2.1<a name="line.173"></a> <FONT color="green">174</FONT> */<a name="line.174"></a> <FONT color="green">175</FONT> protected double getSolverAbsoluteAccuracy() {<a name="line.175"></a> <FONT color="green">176</FONT> return solverAbsoluteAccuracy;<a name="line.176"></a> <FONT color="green">177</FONT> }<a name="line.177"></a> <FONT color="green">178</FONT> }<a name="line.178"></a> </PRE> </BODY> </HTML>