1 /* 2 * Licensed to the Apache Software Foundation (ASF) under one or more 3 * contributor license agreements. See the NOTICE file distributed with 4 * this work for additional information regarding copyright ownership. 5 * The ASF licenses this file to You under the Apache License, Version 2.0 6 * (the "License"); you may not use this file except in compliance with 7 * the License. You may obtain a copy of the License at 8 * 9 * http://www.apache.org/licenses/LICENSE-2.0 10 * 11 * Unless required by applicable law or agreed to in writing, software 12 * distributed under the License is distributed on an "AS IS" BASIS, 13 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. 14 * See the License for the specific language governing permissions and 15 * limitations under the License. 16 */ 17 package org.apache.commons.math.distribution; 18 19 import java.io.Serializable; 20 21 import org.apache.commons.math.MathException; 22 23 /** 24 * The default implementation of {@link ChiSquaredDistribution} 25 * 26 * @version $Revision: 762087 $ $Date: 2009-04-05 10:20:18 -0400 (Sun, 05 Apr 2009) $ 27 */ 28 public class ChiSquaredDistributionImpl 29 extends AbstractContinuousDistribution 30 implements ChiSquaredDistribution, Serializable { 31 32 /** Serializable version identifier */ 33 private static final long serialVersionUID = -8352658048349159782L; 34 35 /** Internal Gamma distribution. */ 36 private GammaDistribution gamma; 37 38 /** 39 * Create a Chi-Squared distribution with the given degrees of freedom. 40 * @param df degrees of freedom. 41 */ 42 public ChiSquaredDistributionImpl(double df) { 43 this(df, new GammaDistributionImpl(df / 2.0, 2.0)); 44 } 45 46 /** 47 * Create a Chi-Squared distribution with the given degrees of freedom. 48 * @param df degrees of freedom. 49 * @param g the underlying gamma distribution used to compute probabilities. 50 * @since 1.2 51 */ 52 public ChiSquaredDistributionImpl(double df, GammaDistribution g) { 53 super(); 54 setGamma(g); 55 setDegreesOfFreedom(df); 56 } 57 58 /** 59 * Modify the degrees of freedom. 60 * @param degreesOfFreedom the new degrees of freedom. 61 */ 62 public void setDegreesOfFreedom(double degreesOfFreedom) { 63 getGamma().setAlpha(degreesOfFreedom / 2.0); 64 } 65 66 /** 67 * Access the degrees of freedom. 68 * @return the degrees of freedom. 69 */ 70 public double getDegreesOfFreedom() { 71 return getGamma().getAlpha() * 2.0; 72 } 73 74 /** 75 * Return the probability density for a particular point. 76 * 77 * @param x The point at which the density should be computed. 78 * @return The pdf at point x. 79 */ 80 public double density(Double x) { 81 return gamma.density(x); 82 } 83 84 /** 85 * For this distribution, X, this method returns P(X < x). 86 * @param x the value at which the CDF is evaluated. 87 * @return CDF for this distribution. 88 * @throws MathException if the cumulative probability can not be 89 * computed due to convergence or other numerical errors. 90 */ 91 public double cumulativeProbability(double x) throws MathException { 92 return getGamma().cumulativeProbability(x); 93 } 94 95 /** 96 * For this distribution, X, this method returns the critical point x, such 97 * that P(X < x) = <code>p</code>. 98 * <p> 99 * Returns 0 for p=0 and <code>Double.POSITIVE_INFINITY</code> for p=1.</p> 100 * 101 * @param p the desired probability 102 * @return x, such that P(X < x) = <code>p</code> 103 * @throws MathException if the inverse cumulative probability can not be 104 * computed due to convergence or other numerical errors. 105 * @throws IllegalArgumentException if <code>p</code> is not a valid 106 * probability. 107 */ 108 @Override 109 public double inverseCumulativeProbability(final double p) 110 throws MathException { 111 if (p == 0) { 112 return 0d; 113 } 114 if (p == 1) { 115 return Double.POSITIVE_INFINITY; 116 } 117 return super.inverseCumulativeProbability(p); 118 } 119 120 /** 121 * Access the domain value lower bound, based on <code>p</code>, used to 122 * bracket a CDF root. This method is used by 123 * {@link #inverseCumulativeProbability(double)} to find critical values. 124 * 125 * @param p the desired probability for the critical value 126 * @return domain value lower bound, i.e. 127 * P(X < <i>lower bound</i>) < <code>p</code> 128 */ 129 @Override 130 protected double getDomainLowerBound(double p) { 131 return Double.MIN_VALUE * getGamma().getBeta(); 132 } 133 134 /** 135 * Access the domain value upper bound, based on <code>p</code>, used to 136 * bracket a CDF root. This method is used by 137 * {@link #inverseCumulativeProbability(double)} to find critical values. 138 * 139 * @param p the desired probability for the critical value 140 * @return domain value upper bound, i.e. 141 * P(X < <i>upper bound</i>) > <code>p</code> 142 */ 143 @Override 144 protected double getDomainUpperBound(double p) { 145 // NOTE: chi squared is skewed to the left 146 // NOTE: therefore, P(X < μ) > .5 147 148 double ret; 149 150 if (p < .5) { 151 // use mean 152 ret = getDegreesOfFreedom(); 153 } else { 154 // use max 155 ret = Double.MAX_VALUE; 156 } 157 158 return ret; 159 } 160 161 /** 162 * Access the initial domain value, based on <code>p</code>, used to 163 * bracket a CDF root. This method is used by 164 * {@link #inverseCumulativeProbability(double)} to find critical values. 165 * 166 * @param p the desired probability for the critical value 167 * @return initial domain value 168 */ 169 @Override 170 protected double getInitialDomain(double p) { 171 // NOTE: chi squared is skewed to the left 172 // NOTE: therefore, P(X < μ) > .5 173 174 double ret; 175 176 if (p < .5) { 177 // use 1/2 mean 178 ret = getDegreesOfFreedom() * .5; 179 } else { 180 // use mean 181 ret = getDegreesOfFreedom(); 182 } 183 184 return ret; 185 } 186 187 /** 188 * Modify the underlying gamma distribution. The caller is responsible for 189 * insuring the gamma distribution has the proper parameter settings. 190 * @param g the new distribution. 191 * @since 1.2 made public 192 */ 193 public void setGamma(GammaDistribution g) { 194 this.gamma = g; 195 196 } 197 198 /** 199 * Access the Gamma distribution. 200 * @return the internal Gamma distribution. 201 */ 202 private GammaDistribution getGamma() { 203 return gamma; 204 } 205 }