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* Licensed to the Apache Software Foundation (ASF) under one or more
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* contributor license agreements. See the NOTICE file distributed with
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* this work for additional information regarding copyright ownership.
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* The ASF licenses this file to You under the Apache License, Version 2.0
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* (the "License"); you may not use this file except in compliance with
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* the License. You may obtain a copy of the License at
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* http://www.apache.org/licenses/LICENSE-2.0
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* Unless required by applicable law or agreed to in writing, software
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* distributed under the License is distributed on an "AS IS" BASIS,
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* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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* See the License for the specific language governing permissions and
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* limitations under the License.
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package org.apache.commons.math.distribution;
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import java.io.Serializable;
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import org.apache.commons.math.MathException;
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* The default implementation of {@link ChiSquaredDistribution}
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* @version $Revision: 617953 $ $Date: 2008-02-02 22:54:00 -0700 (Sat, 02 Feb 2008) $
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public class ChiSquaredDistributionImpl
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extends AbstractContinuousDistribution
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implements ChiSquaredDistribution, Serializable {
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/** Serializable version identifier */
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private static final long serialVersionUID = -8352658048349159782L;
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/** Internal Gamma distribution. */
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private GammaDistribution gamma;
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* Create a Chi-Squared distribution with the given degrees of freedom.
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* @param df degrees of freedom.
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public ChiSquaredDistributionImpl(double df) {
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this(df, new GammaDistributionImpl(df / 2.0, 2.0));
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* Create a Chi-Squared distribution with the given degrees of freedom.
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* @param df degrees of freedom.
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* @param g the underlying gamma distribution used to compute probabilities.
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public ChiSquaredDistributionImpl(double df, GammaDistribution g) {
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setDegreesOfFreedom(df);
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* Modify the degrees of freedom.
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* @param degreesOfFreedom the new degrees of freedom.
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public void setDegreesOfFreedom(double degreesOfFreedom) {
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getGamma().setAlpha(degreesOfFreedom / 2.0);
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* Access the degrees of freedom.
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* @return the degrees of freedom.
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public double getDegreesOfFreedom() {
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return getGamma().getAlpha() * 2.0;
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* For this disbution, X, this method returns P(X < x).
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* @param x the value at which the CDF is evaluated.
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* @return CDF for this distribution.
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* @throws MathException if the cumulative probability can not be
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* computed due to convergence or other numerical errors.
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public double cumulativeProbability(double x) throws MathException {
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return getGamma().cumulativeProbability(x);
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* For this distribution, X, this method returns the critical point x, such
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* that P(X < x) = <code>p</code>.
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* Returns 0 for p=0 and <code>Double.POSITIVE_INFINITY</code> for p=1.</p>
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* @param p the desired probability
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* @return x, such that P(X < x) = <code>p</code>
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* @throws MathException if the inverse cumulative probability can not be
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* computed due to convergence or other numerical errors.
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* @throws IllegalArgumentException if <code>p</code> is not a valid
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public double inverseCumulativeProbability(final double p)
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throws MathException {
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return Double.POSITIVE_INFINITY;
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return super.inverseCumulativeProbability(p);
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* Access the domain value lower bound, based on <code>p</code>, used to
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* bracket a CDF root. This method is used by
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* {@link #inverseCumulativeProbability(double)} to find critical values.
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* @param p the desired probability for the critical value
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* @return domain value lower bound, i.e.
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* P(X < <i>lower bound</i>) < <code>p</code>
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protected double getDomainLowerBound(double p) {
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return Double.MIN_VALUE * getGamma().getBeta();
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* Access the domain value upper bound, based on <code>p</code>, used to
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* bracket a CDF root. This method is used by
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* {@link #inverseCumulativeProbability(double)} to find critical values.
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* @param p the desired probability for the critical value
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* @return domain value upper bound, i.e.
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* P(X < <i>upper bound</i>) > <code>p</code>
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protected double getDomainUpperBound(double p) {
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// NOTE: chi squared is skewed to the left
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// NOTE: therefore, P(X < μ) > .5
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ret = getDegreesOfFreedom();
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ret = Double.MAX_VALUE;
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* Access the initial domain value, based on <code>p</code>, used to
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* bracket a CDF root. This method is used by
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* {@link #inverseCumulativeProbability(double)} to find critical values.
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* @param p the desired probability for the critical value
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* @return initial domain value
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protected double getInitialDomain(double p) {
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// NOTE: chi squared is skewed to the left
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// NOTE: therefore, P(X < μ) > .5
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ret = getDegreesOfFreedom() * .5;
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ret = getDegreesOfFreedom();
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* Modify the underlying gamma distribution. The caller is responsible for
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* insuring the gamma distribution has the proper parameter settings.
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* @param g the new distribution.
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* @since 1.2 made public
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public void setGamma(GammaDistribution g) {
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* Access the Gamma distribution.
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* @return the internal Gamma distribution.
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private GammaDistribution getGamma() {
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src/java/org/apache/commons/math/distribution/ChiSquaredDistributionImpl.java
