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 * 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
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 */
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 Also:
Chi-squared distribution (Wikipedia)
Chi-squared Distribution (MathWorld)/**
 * 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/**
     * Default inverse cumulative probability accuracy
     * @since 2.1
     */
    public static final double DEFAULT_INVERSE_ABSOLUTE_ACCURACY = 1e-9;
    
Serializable version identifier /** Serializable version identifier */
    private static final long serialVersionUID = -8352658048349159782L;
    
Internal Gamma distribution. /** Internal Gamma distribution. */
    private final GammaDistribution gamma;
    
Inverse cumulative probability accuracy /** Inverse cumulative probability accuracy */
    private final double solverAbsoluteAccuracy;

    
Create a Chi-Squared distribution with the given degrees of freedom.
Params:
degreesOfFreedom – Degrees of freedom./**
     * 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.

Note: this constructor will implicitly create an instance of Well19937c as random generator to be used for sampling only (see AbstractRealDistribution.sample() and AbstractRealDistribution.sample(int)). In case no sampling is needed for the created distribution, it is advised to pass null as random generator via the appropriate constructors to avoid the additional initialisation overhead. 
Params:
degreesOfFreedom – Degrees of freedom.
inverseCumAccuracy – the maximum absolute error in inverse cumulative probability estimates (defaults to DEFAULT_INVERSE_ABSOLUTE_ACCURACY).
Since:
2.1/**
     * 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.
Params:
rng – Random number generator.
degreesOfFreedom – Degrees of freedom.
Since:
3.3/**
     * 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.
Params:
rng – Random number generator.
degreesOfFreedom – Degrees of freedom.
inverseCumAccuracy – the maximum absolute error in inverse cumulative probability estimates (defaults to DEFAULT_INVERSE_ABSOLUTE_ACCURACY).
Since:
3.1/**
     * 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.
Returns:
the degrees of freedom./**
     * Access the number of degrees of freedom.
     *
     * @return the degrees of freedom.
     */
    public double getDegreesOfFreedom() {
        return gamma.getShape() * 2.0;
    }

    
{@inheritDoc} /** {@inheritDoc} */
    public double density(double x) {
        return gamma.density(x);
    }

    
{@inheritDoc} /** {@inheritDoc} **/
    @Override
    public double logDensity(double x) {
        return gamma.logDensity(x);
    }

    
{@inheritDoc} /** {@inheritDoc} */
    public double cumulativeProbability(double x)  {
        return gamma.cumulativeProbability(x);
    }

    
{@inheritDoc} /** {@inheritDoc} */
    @Override
    protected double getSolverAbsoluteAccuracy() {
        return solverAbsoluteAccuracy;
    }

    
{@inheritDoc} For k degrees of freedom, the mean is k. /**
     * {@inheritDoc}
     *
     * For {@code k} degrees of freedom, the mean is {@code k}.
     */
    public double getNumericalMean() {
        return getDegreesOfFreedom();
    }

    
{@inheritDoc}
Returns:
2 * k, where k is the number of degrees of freedom./**
     * {@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.
Returns:
zero./**
     * {@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.
Returns:
Double.POSITIVE_INFINITY./**
     * {@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} /** {@inheritDoc} */
    public boolean isSupportLowerBoundInclusive() {
        return true;
    }

    
{@inheritDoc} /** {@inheritDoc} */
    public boolean isSupportUpperBoundInclusive() {
        return false;
    }

    
{@inheritDoc}
The support of this distribution is connected.
Returns:
true/**
     * {@inheritDoc}
     *
     * The support of this distribution is connected.
     *
     * @return {@code true}
     */
    public boolean isSupportConnected() {
        return true;
    }
}