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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.MathException;<a name="line.21"></a> <FONT color="green">022</FONT> import org.apache.commons.math.MathRuntimeException;<a name="line.22"></a> <FONT color="green">023</FONT> import org.apache.commons.math.special.Gamma;<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> * The default implementation of {@link GammaDistribution}.<a name="line.26"></a> <FONT color="green">027</FONT> *<a name="line.27"></a> <FONT color="green">028</FONT> * @version $Revision: 925812 $ $Date: 2010-03-21 11:49:31 -0400 (Sun, 21 Mar 2010) $<a name="line.28"></a> <FONT color="green">029</FONT> */<a name="line.29"></a> <FONT color="green">030</FONT> public class GammaDistributionImpl extends AbstractContinuousDistribution<a name="line.30"></a> <FONT color="green">031</FONT> implements GammaDistribution, Serializable {<a name="line.31"></a> <FONT color="green">032</FONT> <a name="line.32"></a> <FONT color="green">033</FONT> /**<a name="line.33"></a> <FONT color="green">034</FONT> * Default inverse cumulative probability accuracy<a name="line.34"></a> <FONT color="green">035</FONT> * @since 2.1<a name="line.35"></a> <FONT color="green">036</FONT> */<a name="line.36"></a> <FONT color="green">037</FONT> public static final double DEFAULT_INVERSE_ABSOLUTE_ACCURACY = 1e-9;<a name="line.37"></a> <FONT color="green">038</FONT> <a name="line.38"></a> <FONT color="green">039</FONT> /** Serializable version identifier */<a name="line.39"></a> <FONT color="green">040</FONT> private static final long serialVersionUID = -3239549463135430361L;<a name="line.40"></a> <FONT color="green">041</FONT> <a name="line.41"></a> <FONT color="green">042</FONT> /** The shape parameter. */<a name="line.42"></a> <FONT color="green">043</FONT> private double alpha;<a name="line.43"></a> <FONT color="green">044</FONT> <a name="line.44"></a> <FONT color="green">045</FONT> /** The scale parameter. */<a name="line.45"></a> <FONT color="green">046</FONT> private double beta;<a name="line.46"></a> <FONT color="green">047</FONT> <a name="line.47"></a> <FONT color="green">048</FONT> /** Inverse cumulative probability accuracy */<a name="line.48"></a> <FONT color="green">049</FONT> private final double solverAbsoluteAccuracy;<a name="line.49"></a> <FONT color="green">050</FONT> <a name="line.50"></a> <FONT color="green">051</FONT> /**<a name="line.51"></a> <FONT color="green">052</FONT> * Create a new gamma distribution with the given alpha and beta values.<a name="line.52"></a> <FONT color="green">053</FONT> * @param alpha the shape parameter.<a name="line.53"></a> <FONT color="green">054</FONT> * @param beta the scale parameter.<a name="line.54"></a> <FONT color="green">055</FONT> */<a name="line.55"></a> <FONT color="green">056</FONT> public GammaDistributionImpl(double alpha, double beta) {<a name="line.56"></a> <FONT color="green">057</FONT> this(alpha, beta, DEFAULT_INVERSE_ABSOLUTE_ACCURACY);<a name="line.57"></a> <FONT color="green">058</FONT> }<a name="line.58"></a> <FONT color="green">059</FONT> <a name="line.59"></a> <FONT color="green">060</FONT> /**<a name="line.60"></a> <FONT color="green">061</FONT> * Create a new gamma distribution with the given alpha and beta values.<a name="line.61"></a> <FONT color="green">062</FONT> * @param alpha the shape parameter.<a name="line.62"></a> <FONT color="green">063</FONT> * @param beta the scale parameter.<a name="line.63"></a> <FONT color="green">064</FONT> * @param inverseCumAccuracy the maximum absolute error in inverse cumulative probability estimates<a name="line.64"></a> <FONT color="green">065</FONT> * (defaults to {@link #DEFAULT_INVERSE_ABSOLUTE_ACCURACY})<a name="line.65"></a> <FONT color="green">066</FONT> * @since 2.1<a name="line.66"></a> <FONT color="green">067</FONT> */<a name="line.67"></a> <FONT color="green">068</FONT> public GammaDistributionImpl(double alpha, double beta, double inverseCumAccuracy) {<a name="line.68"></a> <FONT color="green">069</FONT> super();<a name="line.69"></a> <FONT color="green">070</FONT> setAlphaInternal(alpha);<a name="line.70"></a> <FONT color="green">071</FONT> setBetaInternal(beta);<a name="line.71"></a> <FONT color="green">072</FONT> solverAbsoluteAccuracy = inverseCumAccuracy;<a name="line.72"></a> <FONT color="green">073</FONT> }<a name="line.73"></a> <FONT color="green">074</FONT> <a name="line.74"></a> <FONT color="green">075</FONT> /**<a name="line.75"></a> <FONT color="green">076</FONT> * For this distribution, X, this method returns P(X &lt; x).<a name="line.76"></a> <FONT color="green">077</FONT> *<a name="line.77"></a> <FONT color="green">078</FONT> * The implementation of this method is based on:<a name="line.78"></a> <FONT color="green">079</FONT> * <ul><a name="line.79"></a> <FONT color="green">080</FONT> * <li><a name="line.80"></a> <FONT color="green">081</FONT> * <a href="http://mathworld.wolfram.com/Chi-SquaredDistribution.html"><a name="line.81"></a> <FONT color="green">082</FONT> * Chi-Squared Distribution</a>, equation (9).</li><a name="line.82"></a> <FONT color="green">083</FONT> * <li>Casella, G., & Berger, R. (1990). <i>Statistical Inference</i>.<a name="line.83"></a> <FONT color="green">084</FONT> * Belmont, CA: Duxbury Press.</li><a name="line.84"></a> <FONT color="green">085</FONT> * </ul><a name="line.85"></a> <FONT color="green">086</FONT> *<a name="line.86"></a> <FONT color="green">087</FONT> * @param x the value at which the CDF is evaluated.<a name="line.87"></a> <FONT color="green">088</FONT> * @return CDF for this distribution.<a name="line.88"></a> <FONT color="green">089</FONT> * @throws MathException if the cumulative probability can not be<a name="line.89"></a> <FONT color="green">090</FONT> * computed due to convergence or other numerical errors.<a name="line.90"></a> <FONT color="green">091</FONT> */<a name="line.91"></a> <FONT color="green">092</FONT> public double cumulativeProbability(double x) throws MathException{<a name="line.92"></a> <FONT color="green">093</FONT> double ret;<a name="line.93"></a> <FONT color="green">094</FONT> <a name="line.94"></a> <FONT color="green">095</FONT> if (x <= 0.0) {<a name="line.95"></a> <FONT color="green">096</FONT> ret = 0.0;<a name="line.96"></a> <FONT color="green">097</FONT> } else {<a name="line.97"></a> <FONT color="green">098</FONT> ret = Gamma.regularizedGammaP(alpha, x / beta);<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> 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> * For this distribution, X, this method returns the critical point x, such<a name="line.105"></a> <FONT color="green">106</FONT> * that P(X &lt; x) = <code>p</code>.<a name="line.106"></a> <FONT color="green">107</FONT> * <p><a name="line.107"></a> <FONT color="green">108</FONT> * Returns 0 for p=0 and <code>Double.POSITIVE_INFINITY</code> for p=1.</p><a name="line.108"></a> <FONT color="green">109</FONT> *<a name="line.109"></a> <FONT color="green">110</FONT> * @param p the desired probability<a name="line.110"></a> <FONT color="green">111</FONT> * @return x, such that P(X &lt; x) = <code>p</code><a name="line.111"></a> <FONT color="green">112</FONT> * @throws MathException if the inverse cumulative probability can not be<a name="line.112"></a> <FONT color="green">113</FONT> * computed due to convergence or other numerical errors.<a name="line.113"></a> <FONT color="green">114</FONT> * @throws IllegalArgumentException if <code>p</code> is not a valid<a name="line.114"></a> <FONT color="green">115</FONT> * probability.<a name="line.115"></a> <FONT color="green">116</FONT> */<a name="line.116"></a> <FONT color="green">117</FONT> @Override<a name="line.117"></a> <FONT color="green">118</FONT> public double inverseCumulativeProbability(final double p)<a name="line.118"></a> <FONT color="green">119</FONT> throws MathException {<a name="line.119"></a> <FONT color="green">120</FONT> if (p == 0) {<a name="line.120"></a> <FONT color="green">121</FONT> return 0d;<a name="line.121"></a> <FONT color="green">122</FONT> }<a name="line.122"></a> <FONT color="green">123</FONT> if (p == 1) {<a name="line.123"></a> <FONT color="green">124</FONT> return Double.POSITIVE_INFINITY;<a name="line.124"></a> <FONT color="green">125</FONT> }<a name="line.125"></a> <FONT color="green">126</FONT> return super.inverseCumulativeProbability(p);<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> /**<a name="line.129"></a> <FONT color="green">130</FONT> * Modify the shape parameter, alpha.<a name="line.130"></a> <FONT color="green">131</FONT> * @param alpha the new shape parameter.<a name="line.131"></a> <FONT color="green">132</FONT> * @throws IllegalArgumentException if <code>alpha</code> is not positive.<a name="line.132"></a> <FONT color="green">133</FONT> * @deprecated as of 2.1 (class will become immutable in 3.0)<a name="line.133"></a> <FONT color="green">134</FONT> */<a name="line.134"></a> <FONT color="green">135</FONT> @Deprecated<a name="line.135"></a> <FONT color="green">136</FONT> public void setAlpha(double alpha) {<a name="line.136"></a> <FONT color="green">137</FONT> setAlphaInternal(alpha);<a name="line.137"></a> <FONT color="green">138</FONT> }<a name="line.138"></a> <FONT color="green">139</FONT> <a name="line.139"></a> <FONT color="green">140</FONT> /**<a name="line.140"></a> <FONT color="green">141</FONT> * Modify the shape parameter, alpha.<a name="line.141"></a> <FONT color="green">142</FONT> * @param newAlpha the new shape parameter.<a name="line.142"></a> <FONT color="green">143</FONT> * @throws IllegalArgumentException if <code>newAlpha</code> is not positive.<a name="line.143"></a> <FONT color="green">144</FONT> */<a name="line.144"></a> <FONT color="green">145</FONT> private void setAlphaInternal(double newAlpha) {<a name="line.145"></a> <FONT color="green">146</FONT> if (newAlpha <= 0.0) {<a name="line.146"></a> <FONT color="green">147</FONT> throw MathRuntimeException.createIllegalArgumentException(<a name="line.147"></a> <FONT color="green">148</FONT> "alpha must be positive ({0})",<a name="line.148"></a> <FONT color="green">149</FONT> newAlpha);<a name="line.149"></a> <FONT color="green">150</FONT> }<a name="line.150"></a> <FONT color="green">151</FONT> this.alpha = newAlpha;<a name="line.151"></a> <FONT color="green">152</FONT> }<a name="line.152"></a> <FONT color="green">153</FONT> <a name="line.153"></a> <FONT color="green">154</FONT> /**<a name="line.154"></a> <FONT color="green">155</FONT> * Access the shape parameter, alpha<a name="line.155"></a> <FONT color="green">156</FONT> * @return alpha.<a name="line.156"></a> <FONT color="green">157</FONT> */<a name="line.157"></a> <FONT color="green">158</FONT> public double getAlpha() {<a name="line.158"></a> <FONT color="green">159</FONT> return alpha;<a name="line.159"></a> <FONT color="green">160</FONT> }<a name="line.160"></a> <FONT color="green">161</FONT> <a name="line.161"></a> <FONT color="green">162</FONT> /**<a name="line.162"></a> <FONT color="green">163</FONT> * Modify the scale parameter, beta.<a name="line.163"></a> <FONT color="green">164</FONT> * @param newBeta the new scale parameter.<a name="line.164"></a> <FONT color="green">165</FONT> * @throws IllegalArgumentException if <code>newBeta</code> is not positive.<a name="line.165"></a> <FONT color="green">166</FONT> * @deprecated as of 2.1 (class will become immutable in 3.0)<a name="line.166"></a> <FONT color="green">167</FONT> */<a name="line.167"></a> <FONT color="green">168</FONT> @Deprecated<a name="line.168"></a> <FONT color="green">169</FONT> public void setBeta(double newBeta) {<a name="line.169"></a> <FONT color="green">170</FONT> setBetaInternal(newBeta);<a name="line.170"></a> <FONT color="green">171</FONT> }<a name="line.171"></a> <FONT color="green">172</FONT> <a name="line.172"></a> <FONT color="green">173</FONT> /**<a name="line.173"></a> <FONT color="green">174</FONT> * Modify the scale parameter, beta.<a name="line.174"></a> <FONT color="green">175</FONT> * @param newBeta the new scale parameter.<a name="line.175"></a> <FONT color="green">176</FONT> * @throws IllegalArgumentException if <code>newBeta</code> is not positive.<a name="line.176"></a> <FONT color="green">177</FONT> */<a name="line.177"></a> <FONT color="green">178</FONT> private void setBetaInternal(double newBeta) {<a name="line.178"></a> <FONT color="green">179</FONT> if (newBeta <= 0.0) {<a name="line.179"></a> <FONT color="green">180</FONT> throw MathRuntimeException.createIllegalArgumentException(<a name="line.180"></a> <FONT color="green">181</FONT> "beta must be positive ({0})",<a name="line.181"></a> <FONT color="green">182</FONT> newBeta);<a name="line.182"></a> <FONT color="green">183</FONT> }<a name="line.183"></a> <FONT color="green">184</FONT> this.beta = newBeta;<a name="line.184"></a> <FONT color="green">185</FONT> }<a name="line.185"></a> <FONT color="green">186</FONT> <a name="line.186"></a> <FONT color="green">187</FONT> /**<a name="line.187"></a> <FONT color="green">188</FONT> * Access the scale parameter, beta<a name="line.188"></a> <FONT color="green">189</FONT> * @return beta.<a name="line.189"></a> <FONT color="green">190</FONT> */<a name="line.190"></a> <FONT color="green">191</FONT> public double getBeta() {<a name="line.191"></a> <FONT color="green">192</FONT> return beta;<a name="line.192"></a> <FONT color="green">193</FONT> }<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> * Returns the probability density for a particular point.<a name="line.196"></a> <FONT color="green">197</FONT> *<a name="line.197"></a> <FONT color="green">198</FONT> * @param x The point at which the density should be computed.<a name="line.198"></a> <FONT color="green">199</FONT> * @return The pdf at point x.<a name="line.199"></a> <FONT color="green">200</FONT> */<a name="line.200"></a> <FONT color="green">201</FONT> @Override<a name="line.201"></a> <FONT color="green">202</FONT> public double density(double x) {<a name="line.202"></a> <FONT color="green">203</FONT> if (x < 0) return 0;<a name="line.203"></a> <FONT color="green">204</FONT> return Math.pow(x / beta, alpha - 1) / beta * Math.exp(-x / beta) / Math.exp(Gamma.logGamma(alpha));<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> /**<a name="line.207"></a> <FONT color="green">208</FONT> * Return the probability density for a particular point.<a name="line.208"></a> <FONT color="green">209</FONT> *<a name="line.209"></a> <FONT color="green">210</FONT> * @param x The point at which the density should be computed.<a name="line.210"></a> <FONT color="green">211</FONT> * @return The pdf at point x.<a name="line.211"></a> <FONT color="green">212</FONT> * @deprecated<a name="line.212"></a> <FONT color="green">213</FONT> */<a name="line.213"></a> <FONT color="green">214</FONT> public double density(Double x) {<a name="line.214"></a> <FONT color="green">215</FONT> return density(x.doubleValue());<a name="line.215"></a> <FONT color="green">216</FONT> }<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> * Access the domain value lower bound, based on <code>p</code>, used to<a name="line.219"></a> <FONT color="green">220</FONT> * bracket a CDF root. This method is used by<a name="line.220"></a> <FONT color="green">221</FONT> * {@link #inverseCumulativeProbability(double)} to find critical values.<a name="line.221"></a> <FONT color="green">222</FONT> *<a name="line.222"></a> <FONT color="green">223</FONT> * @param p the desired probability for the critical value<a name="line.223"></a> <FONT color="green">224</FONT> * @return domain value lower bound, i.e.<a name="line.224"></a> <FONT color="green">225</FONT> * P(X &lt; <i>lower bound</i>) &lt; <code>p</code><a name="line.225"></a> <FONT color="green">226</FONT> */<a name="line.226"></a> <FONT color="green">227</FONT> @Override<a name="line.227"></a> <FONT color="green">228</FONT> protected double getDomainLowerBound(double p) {<a name="line.228"></a> <FONT color="green">229</FONT> // TODO: try to improve on this estimate<a name="line.229"></a> <FONT color="green">230</FONT> return Double.MIN_VALUE;<a name="line.230"></a> <FONT color="green">231</FONT> }<a name="line.231"></a> <FONT color="green">232</FONT> <a name="line.232"></a> <FONT color="green">233</FONT> /**<a name="line.233"></a> <FONT color="green">234</FONT> * Access the domain value upper bound, based on <code>p</code>, used to<a name="line.234"></a> <FONT color="green">235</FONT> * bracket a CDF root. This method is used by<a name="line.235"></a> <FONT color="green">236</FONT> * {@link #inverseCumulativeProbability(double)} to find critical values.<a name="line.236"></a> <FONT color="green">237</FONT> *<a name="line.237"></a> <FONT color="green">238</FONT> * @param p the desired probability for the critical value<a name="line.238"></a> <FONT color="green">239</FONT> * @return domain value upper bound, i.e.<a name="line.239"></a> <FONT color="green">240</FONT> * P(X &lt; <i>upper bound</i>) &gt; <code>p</code><a name="line.240"></a> <FONT color="green">241</FONT> */<a name="line.241"></a> <FONT color="green">242</FONT> @Override<a name="line.242"></a> <FONT color="green">243</FONT> protected double getDomainUpperBound(double p) {<a name="line.243"></a> <FONT color="green">244</FONT> // TODO: try to improve on this estimate<a name="line.244"></a> <FONT color="green">245</FONT> // NOTE: gamma is skewed to the left<a name="line.245"></a> <FONT color="green">246</FONT> // NOTE: therefore, P(X < &mu;) > .5<a name="line.246"></a> <FONT color="green">247</FONT> <a name="line.247"></a> <FONT color="green">248</FONT> double ret;<a name="line.248"></a> <FONT color="green">249</FONT> <a name="line.249"></a> <FONT color="green">250</FONT> if (p < .5) {<a name="line.250"></a> <FONT color="green">251</FONT> // use mean<a name="line.251"></a> <FONT color="green">252</FONT> ret = alpha * beta;<a name="line.252"></a> <FONT color="green">253</FONT> } else {<a name="line.253"></a> <FONT color="green">254</FONT> // use max value<a name="line.254"></a> <FONT color="green">255</FONT> ret = Double.MAX_VALUE;<a name="line.255"></a> <FONT color="green">256</FONT> }<a name="line.256"></a> <FONT color="green">257</FONT> <a name="line.257"></a> <FONT color="green">258</FONT> return ret;<a name="line.258"></a> <FONT color="green">259</FONT> }<a name="line.259"></a> <FONT color="green">260</FONT> <a name="line.260"></a> <FONT color="green">261</FONT> /**<a name="line.261"></a> <FONT color="green">262</FONT> * Access the initial domain value, based on <code>p</code>, used to<a name="line.262"></a> <FONT color="green">263</FONT> * bracket a CDF root. This method is used by<a name="line.263"></a> <FONT color="green">264</FONT> * {@link #inverseCumulativeProbability(double)} to find critical values.<a name="line.264"></a> <FONT color="green">265</FONT> *<a name="line.265"></a> <FONT color="green">266</FONT> * @param p the desired probability for the critical value<a name="line.266"></a> <FONT color="green">267</FONT> * @return initial domain value<a name="line.267"></a> <FONT color="green">268</FONT> */<a name="line.268"></a> <FONT color="green">269</FONT> @Override<a name="line.269"></a> <FONT color="green">270</FONT> protected double getInitialDomain(double p) {<a name="line.270"></a> <FONT color="green">271</FONT> // TODO: try to improve on this estimate<a name="line.271"></a> <FONT color="green">272</FONT> // Gamma is skewed to the left, therefore, P(X < &mu;) > .5<a name="line.272"></a> <FONT color="green">273</FONT> <a name="line.273"></a> <FONT color="green">274</FONT> double ret;<a name="line.274"></a> <FONT color="green">275</FONT> <a name="line.275"></a> <FONT color="green">276</FONT> if (p < .5) {<a name="line.276"></a> <FONT color="green">277</FONT> // use 1/2 mean<a name="line.277"></a> <FONT color="green">278</FONT> ret = alpha * beta * .5;<a name="line.278"></a> <FONT color="green">279</FONT> } else {<a name="line.279"></a> <FONT color="green">280</FONT> // use mean<a name="line.280"></a> <FONT color="green">281</FONT> ret = alpha * beta;<a name="line.281"></a> <FONT color="green">282</FONT> }<a name="line.282"></a> <FONT color="green">283</FONT> <a name="line.283"></a> <FONT color="green">284</FONT> return ret;<a name="line.284"></a> <FONT color="green">285</FONT> }<a name="line.285"></a> <FONT color="green">286</FONT> <a name="line.286"></a> <FONT color="green">287</FONT> /**<a name="line.287"></a> <FONT color="green">288</FONT> * Return the absolute accuracy setting of the solver used to estimate<a name="line.288"></a> <FONT color="green">289</FONT> * inverse cumulative probabilities.<a name="line.289"></a> <FONT color="green">290</FONT> *<a name="line.290"></a> <FONT color="green">291</FONT> * @return the solver absolute accuracy<a name="line.291"></a> <FONT color="green">292</FONT> * @since 2.1<a name="line.292"></a> <FONT color="green">293</FONT> */<a name="line.293"></a> <FONT color="green">294</FONT> @Override<a name="line.294"></a> <FONT color="green">295</FONT> protected double getSolverAbsoluteAccuracy() {<a name="line.295"></a> <FONT color="green">296</FONT> return solverAbsoluteAccuracy;<a name="line.296"></a> <FONT color="green">297</FONT> }<a name="line.297"></a> <FONT color="green">298</FONT> }<a name="line.298"></a> </PRE> </BODY> </HTML>