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/*
* Licensed to the Apache Software Foundation (ASF) under one or more
* contributor license agreements. See the NOTICE file distributed with
* this work for additional information regarding copyright ownership.
* The ASF licenses this file to You under the Apache License, Version 2.0
* (the "License"); you may not use this file except in compliance with
* the License. You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*/
package org.apache.commons.math.distribution;
import java.io.Serializable;
import org.apache.commons.math.MathException;
/**
* The default implementation of {@link ChiSquaredDistribution}
*
* @version $Revision: 1054524 $ $Date: 2011-01-03 05:59:18 +0100 (lun. 03 janv. 2011) $
*/
public class ChiSquaredDistributionImpl
extends AbstractContinuousDistribution
implements ChiSquaredDistribution, Serializable {
/**
* Default inverse cumulative probability accuracy
* @since 2.1
*/
public static final double DEFAULT_INVERSE_ABSOLUTE_ACCURACY = 1e-9;
/** Serializable version identifier */
private static final long serialVersionUID = -8352658048349159782L;
/** Internal Gamma distribution. */
private GammaDistribution gamma;
/** Inverse cumulative probability accuracy */
private final double solverAbsoluteAccuracy;
/**
* Create a Chi-Squared distribution with the given degrees of freedom.
* @param df degrees of freedom.
*/
public ChiSquaredDistributionImpl(double df) {
this(df, new GammaDistributionImpl(df / 2.0, 2.0));
}
/**
* Create a Chi-Squared distribution with the given degrees of freedom.
* @param df degrees of freedom.
* @param g the underlying gamma distribution used to compute probabilities.
* @since 1.2
* @deprecated as of 2.1 (to avoid possibly inconsistent state, the
* "GammaDistribution" will be instantiated internally)
*/
@Deprecated
public ChiSquaredDistributionImpl(double df, GammaDistribution g) {
super();
setGammaInternal(g);
setDegreesOfFreedomInternal(df);
solverAbsoluteAccuracy = DEFAULT_INVERSE_ABSOLUTE_ACCURACY;
}
/**
* Create a Chi-Squared distribution with the given degrees of freedom and
* inverse cumulative probability accuracy.
* @param df degrees of freedom.
* @param inverseCumAccuracy the maximum absolute error in inverse cumulative probability estimates
* (defaults to {@link #DEFAULT_INVERSE_ABSOLUTE_ACCURACY})
* @since 2.1
*/
public ChiSquaredDistributionImpl(double df, double inverseCumAccuracy) {
super();
gamma = new GammaDistributionImpl(df / 2.0, 2.0);
setDegreesOfFreedomInternal(df);
solverAbsoluteAccuracy = inverseCumAccuracy;
}
/**
* Modify the degrees of freedom.
* @param degreesOfFreedom the new degrees of freedom.
* @deprecated as of 2.1 (class will become immutable in 3.0)
*/
@Deprecated
public void setDegreesOfFreedom(double degreesOfFreedom) {
setDegreesOfFreedomInternal(degreesOfFreedom);
}
/**
* Modify the degrees of freedom.
* @param degreesOfFreedom the new degrees of freedom.
*/
private void setDegreesOfFreedomInternal(double degreesOfFreedom) {
gamma.setAlpha(degreesOfFreedom / 2.0);
}
/**
* Access the degrees of freedom.
* @return the degrees of freedom.
*/
public double getDegreesOfFreedom() {
return gamma.getAlpha() * 2.0;
}
/**
* Return the probability density for a particular point.
*
* @param x The point at which the density should be computed.
* @return The pdf at point x.
* @deprecated
*/
@Deprecated
public double density(Double x) {
return density(x.doubleValue());
}
/**
* Return the probability density for a particular point.
*
* @param x The point at which the density should be computed.
* @return The pdf at point x.
* @since 2.1
*/
@Override
public double density(double x) {
return gamma.density(x);
}
/**
* For this distribution, X, this method returns P(X < x).
* @param x the value at which the CDF is evaluated.
* @return CDF for this distribution.
* @throws MathException if the cumulative probability can not be
* computed due to convergence or other numerical errors.
*/
public double cumulativeProbability(double x) throws MathException {
return gamma.cumulativeProbability(x);
}
/**
* For this distribution, X, this method returns the critical point x, such
* that P(X < x) = p.
*
* Returns 0 for p=0 and Double.POSITIVE_INFINITY for p=1.
*
* @param p the desired probability
* @return x, such that P(X < x) = p
* @throws MathException if the inverse cumulative probability can not be
* computed due to convergence or other numerical errors.
* @throws IllegalArgumentException if p is not a valid
* probability.
*/
@Override
public double inverseCumulativeProbability(final double p)
throws MathException {
if (p == 0) {
return 0d;
}
if (p == 1) {
return Double.POSITIVE_INFINITY;
}
return super.inverseCumulativeProbability(p);
}
/**
* Access the domain value lower bound, based on p, used to
* bracket a CDF root. This method is used by
* {@link #inverseCumulativeProbability(double)} to find critical values.
*
* @param p the desired probability for the critical value
* @return domain value lower bound, i.e.
* P(X < lower bound) < p
*/
@Override
protected double getDomainLowerBound(double p) {
return Double.MIN_VALUE * gamma.getBeta();
}
/**
* Access the domain value upper bound, based on p, used to
* bracket a CDF root. This method is used by
* {@link #inverseCumulativeProbability(double)} to find critical values.
*
* @param p the desired probability for the critical value
* @return domain value upper bound, i.e.
* P(X < upper bound) > p
*/
@Override
protected double getDomainUpperBound(double p) {
// NOTE: chi squared is skewed to the left
// NOTE: therefore, P(X < μ) > .5
double ret;
if (p < .5) {
// use mean
ret = getDegreesOfFreedom();
} else {
// use max
ret = Double.MAX_VALUE;
}
return ret;
}
/**
* Access the initial domain value, based on p, used to
* bracket a CDF root. This method is used by
* {@link #inverseCumulativeProbability(double)} to find critical values.
*
* @param p the desired probability for the critical value
* @return initial domain value
*/
@Override
protected double getInitialDomain(double p) {
// NOTE: chi squared is skewed to the left
// NOTE: therefore, P(X < μ) > .5
double ret;
if (p < .5) {
// use 1/2 mean
ret = getDegreesOfFreedom() * .5;
} else {
// use mean
ret = getDegreesOfFreedom();
}
return ret;
}
/**
* Modify the underlying gamma distribution. The caller is responsible for
* insuring the gamma distribution has the proper parameter settings.
* @param g the new distribution.
* @since 1.2 made public
* @deprecated as of 2.1 (class will become immutable in 3.0)
*/
@Deprecated
public void setGamma(GammaDistribution g) {
setGammaInternal(g);
}
/**
* Modify the underlying gamma distribution. The caller is responsible for
* insuring the gamma distribution has the proper parameter settings.
* @param g the new distribution.
* @since 1.2 made public
*/
private void setGammaInternal(GammaDistribution g) {
this.gamma = g;
}
/**
* Return the absolute accuracy setting of the solver used to estimate
* inverse cumulative probabilities.
*
* @return the solver absolute accuracy
* @since 2.1
*/
@Override
protected double getSolverAbsoluteAccuracy() {
return solverAbsoluteAccuracy;
}
/**
* Returns the lower bound of the support for the distribution.
*
* The lower bound of the support is always 0 no matter the
* degrees of freedom.
*
* @return lower bound of the support (always 0)
* @since 2.2
*/
public double getSupportLowerBound() {
return 0;
}
/**
* Returns the upper bound for the support for the distribution.
*
* The upper bound of the support is always positive infinity no matter the
* degrees of freedom.
*
* @return upper bound of the support (always Double.POSITIVE_INFINITY)
* @since 2.2
*/
public double getSupportUpperBound() {
return Double.POSITIVE_INFINITY;
}
/**
* Returns the mean of the distribution.
*
* For k degrees of freedom, the mean is
* k
*
* @return the mean
* @since 2.2
*/
public double getNumericalMean() {
return getDegreesOfFreedom();
}
/**
* Returns the variance of the distribution.
*
* For k degrees of freedom, the variance is
* 2 * k
*
* @return the variance
* @since 2.2
*/
public double getNumericalVariance() {
return 2*getDegreesOfFreedom();
}
}
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