/*
* 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.math3.distribution;
import org.apache.commons.math3.random.RandomGenerator;
import org.apache.commons.math3.random.Well19937c;
/**
* Implementation of the chi-squared distribution.
*
* @see <a href="http://en.wikipedia.org/wiki/Chi-squared_distribution">Chi-squared distribution (Wikipedia)</a>
* @see <a href="http://mathworld.wolfram.com/Chi-SquaredDistribution.html">Chi-squared Distribution (MathWorld)</a>
*/
public class ChiSquaredDistribution extends AbstractRealDistribution {
/**
* 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 final GammaDistribution gamma;
/** Inverse cumulative probability accuracy */
private final double solverAbsoluteAccuracy;
/**
* Create a Chi-Squared distribution with the given degrees of freedom.
*
* @param degreesOfFreedom Degrees of freedom.
*/
public ChiSquaredDistribution(double degreesOfFreedom) {
this(degreesOfFreedom, DEFAULT_INVERSE_ABSOLUTE_ACCURACY);
}
/**
* Create a Chi-Squared distribution with the given degrees of freedom and
* inverse cumulative probability accuracy.
* <p>
* <b>Note:</b> this constructor will implicitly create an instance of
* {@link Well19937c} as random generator to be used for sampling only (see
* {@link #sample()} and {@link #sample(int)}). In case no sampling is
* needed for the created distribution, it is advised to pass {@code null}
* as random generator via the appropriate constructors to avoid the
* additional initialisation overhead.
*
* @param degreesOfFreedom 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 ChiSquaredDistribution(double degreesOfFreedom,
double inverseCumAccuracy) {
this(new Well19937c(), degreesOfFreedom, inverseCumAccuracy);
}
/**
* Create a Chi-Squared distribution with the given degrees of freedom.
*
* @param rng Random number generator.
* @param degreesOfFreedom Degrees of freedom.
* @since 3.3
*/
public ChiSquaredDistribution(RandomGenerator rng, double degreesOfFreedom) {
this(rng, degreesOfFreedom, DEFAULT_INVERSE_ABSOLUTE_ACCURACY);
}
/**
* Create a Chi-Squared distribution with the given degrees of freedom and
* inverse cumulative probability accuracy.
*
* @param rng Random number generator.
* @param degreesOfFreedom Degrees of freedom.
* @param inverseCumAccuracy the maximum absolute error in inverse
* cumulative probability estimates (defaults to
* {@link #DEFAULT_INVERSE_ABSOLUTE_ACCURACY}).
* @since 3.1
*/
public ChiSquaredDistribution(RandomGenerator rng,
double degreesOfFreedom,
double inverseCumAccuracy) {
super(rng);
gamma = new GammaDistribution(degreesOfFreedom / 2, 2);
solverAbsoluteAccuracy = inverseCumAccuracy;
}
/**
* Access the number of degrees of freedom.
*
* @return the degrees of freedom.
*/
public double getDegreesOfFreedom() {
return gamma.getShape() * 2.0;
}
/** {@inheritDoc} */
public double density(double x) {
return gamma.density(x);
}
/** {@inheritDoc} **/
@Override
public double logDensity(double x) {
return gamma.logDensity(x);
}
/** {@inheritDoc} */
public double cumulativeProbability(double x) {
return gamma.cumulativeProbability(x);
}
/** {@inheritDoc} */
@Override
protected double getSolverAbsoluteAccuracy() {
return solverAbsoluteAccuracy;
}
/**
* {@inheritDoc}
*
* For {@code k} degrees of freedom, the mean is {@code k}.
*/
public double getNumericalMean() {
return getDegreesOfFreedom();
}
/**
* {@inheritDoc}
*
* @return {@code 2 * k}, where {@code k} is the number of degrees of freedom.
*/
public double getNumericalVariance() {
return 2 * getDegreesOfFreedom();
}
/**
* {@inheritDoc}
*
* The lower bound of the support is always 0 no matter the
* degrees of freedom.
*
* @return zero.
*/
public double getSupportLowerBound() {
return 0;
}
/**
* {@inheritDoc}
*
* The upper bound of the support is always positive infinity no matter the
* degrees of freedom.
*
* @return {@code Double.POSITIVE_INFINITY}.
*/
public double getSupportUpperBound() {
return Double.POSITIVE_INFINITY;
}
/** {@inheritDoc} */
public boolean isSupportLowerBoundInclusive() {
return true;
}
/** {@inheritDoc} */
public boolean isSupportUpperBoundInclusive() {
return false;
}
/**
* {@inheritDoc}
*
* The support of this distribution is connected.
*
* @return {@code true}
*/
public boolean isSupportConnected() {
return true;
}
}