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package org.apache.commons.math3.distribution;

import org.apache.commons.math3.exception.NotStrictlyPositiveException;
import org.apache.commons.math3.exception.util.LocalizedFormats;
import org.apache.commons.math3.random.RandomGenerator;
import org.apache.commons.math3.random.Well19937c;
import org.apache.commons.math3.special.Beta;
import org.apache.commons.math3.util.FastMath;

Implementation of the F-distribution.
See Also:
F-distribution (Wikipedia)
F-distribution (MathWorld)/**
 * Implementation of the F-distribution.
 *
 * @see <a href="http://en.wikipedia.org/wiki/F-distribution">F-distribution (Wikipedia)</a>
 * @see <a href="http://mathworld.wolfram.com/F-Distribution.html">F-distribution (MathWorld)</a>
 */
public class FDistribution 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 = -8516354193418641566L;
    
The numerator degrees of freedom. /** The numerator degrees of freedom. */
    private final double numeratorDegreesOfFreedom;
    
The numerator degrees of freedom. /** The numerator degrees of freedom. */
    private final double denominatorDegreesOfFreedom;
    
Inverse cumulative probability accuracy. /** Inverse cumulative probability accuracy. */
    private final double solverAbsoluteAccuracy;
    
Cached numerical variance /** Cached numerical variance */
    private double numericalVariance = Double.NaN;
    
Whether or not the numerical variance has been calculated /** Whether or not the numerical variance has been calculated */
    private boolean numericalVarianceIsCalculated = false;

    
Creates an F distribution using the given degrees of freedom.

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:
numeratorDegreesOfFreedom – Numerator degrees of freedom.
denominatorDegreesOfFreedom – Denominator degrees of freedom.
Throws:
NotStrictlyPositiveException – if numeratorDegreesOfFreedom <= 0 or denominatorDegreesOfFreedom <= 0./**
     * Creates an F distribution using the given degrees of freedom.
     * <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 numeratorDegreesOfFreedom Numerator degrees of freedom.
     * @param denominatorDegreesOfFreedom Denominator degrees of freedom.
     * @throws NotStrictlyPositiveException if
     * {@code numeratorDegreesOfFreedom <= 0} or
     * {@code denominatorDegreesOfFreedom <= 0}.
     */
    public FDistribution(double numeratorDegreesOfFreedom,
                         double denominatorDegreesOfFreedom)
        throws NotStrictlyPositiveException {
        this(numeratorDegreesOfFreedom, denominatorDegreesOfFreedom,
             DEFAULT_INVERSE_ABSOLUTE_ACCURACY);
    }

    
Creates an F distribution using 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:
numeratorDegreesOfFreedom – Numerator degrees of freedom.
denominatorDegreesOfFreedom – Denominator degrees of freedom.
inverseCumAccuracy – the maximum absolute error in inverse
cumulative probability estimates.
Throws:
NotStrictlyPositiveException – if numeratorDegreesOfFreedom <= 0 or denominatorDegreesOfFreedom <= 0.
Since:
2.1/**
     * Creates an F distribution using 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 numeratorDegreesOfFreedom Numerator degrees of freedom.
     * @param denominatorDegreesOfFreedom Denominator degrees of freedom.
     * @param inverseCumAccuracy the maximum absolute error in inverse
     * cumulative probability estimates.
     * @throws NotStrictlyPositiveException if
     * {@code numeratorDegreesOfFreedom <= 0} or
     * {@code denominatorDegreesOfFreedom <= 0}.
     * @since 2.1
     */
    public FDistribution(double numeratorDegreesOfFreedom,
                         double denominatorDegreesOfFreedom,
                         double inverseCumAccuracy)
        throws NotStrictlyPositiveException {
        this(new Well19937c(), numeratorDegreesOfFreedom,
             denominatorDegreesOfFreedom, inverseCumAccuracy);
    }

    
Creates an F distribution.
Params:
rng – Random number generator.
numeratorDegreesOfFreedom – Numerator degrees of freedom.
denominatorDegreesOfFreedom – Denominator degrees of freedom.
Throws:
NotStrictlyPositiveException – if numeratorDegreesOfFreedom <= 0 or denominatorDegreesOfFreedom <= 0.
Since:
3.3/**
     * Creates an F distribution.
     *
     * @param rng Random number generator.
     * @param numeratorDegreesOfFreedom Numerator degrees of freedom.
     * @param denominatorDegreesOfFreedom Denominator degrees of freedom.
     * @throws NotStrictlyPositiveException if {@code numeratorDegreesOfFreedom <= 0} or
     * {@code denominatorDegreesOfFreedom <= 0}.
     * @since 3.3
     */
    public FDistribution(RandomGenerator rng,
                         double numeratorDegreesOfFreedom,
                         double denominatorDegreesOfFreedom)
        throws NotStrictlyPositiveException {
        this(rng, numeratorDegreesOfFreedom, denominatorDegreesOfFreedom, DEFAULT_INVERSE_ABSOLUTE_ACCURACY);
    }

    
Creates an F distribution.
Params:
rng – Random number generator.
numeratorDegreesOfFreedom – Numerator degrees of freedom.
denominatorDegreesOfFreedom – Denominator degrees of freedom.
inverseCumAccuracy – the maximum absolute error in inverse
cumulative probability estimates.
Throws:
NotStrictlyPositiveException – if numeratorDegreesOfFreedom <= 0 or denominatorDegreesOfFreedom <= 0.
Since:
3.1/**
     * Creates an F distribution.
     *
     * @param rng Random number generator.
     * @param numeratorDegreesOfFreedom Numerator degrees of freedom.
     * @param denominatorDegreesOfFreedom Denominator degrees of freedom.
     * @param inverseCumAccuracy the maximum absolute error in inverse
     * cumulative probability estimates.
     * @throws NotStrictlyPositiveException if {@code numeratorDegreesOfFreedom <= 0} or
     * {@code denominatorDegreesOfFreedom <= 0}.
     * @since 3.1
     */
    public FDistribution(RandomGenerator rng,
                         double numeratorDegreesOfFreedom,
                         double denominatorDegreesOfFreedom,
                         double inverseCumAccuracy)
        throws NotStrictlyPositiveException {
        super(rng);

        if (numeratorDegreesOfFreedom <= 0) {
            throw new NotStrictlyPositiveException(LocalizedFormats.DEGREES_OF_FREEDOM,
                                                   numeratorDegreesOfFreedom);
        }
        if (denominatorDegreesOfFreedom <= 0) {
            throw new NotStrictlyPositiveException(LocalizedFormats.DEGREES_OF_FREEDOM,
                                                   denominatorDegreesOfFreedom);
        }
        this.numeratorDegreesOfFreedom = numeratorDegreesOfFreedom;
        this.denominatorDegreesOfFreedom = denominatorDegreesOfFreedom;
        solverAbsoluteAccuracy = inverseCumAccuracy;
    }

    
{@inheritDoc}
Since:
2.1/**
     * {@inheritDoc}
     *
     * @since 2.1
     */
    public double density(double x) {
        return FastMath.exp(logDensity(x));
    }

    
{@inheritDoc} /** {@inheritDoc} **/
    @Override
    public double logDensity(double x) {
        final double nhalf = numeratorDegreesOfFreedom / 2;
        final double mhalf = denominatorDegreesOfFreedom / 2;
        final double logx = FastMath.log(x);
        final double logn = FastMath.log(numeratorDegreesOfFreedom);
        final double logm = FastMath.log(denominatorDegreesOfFreedom);
        final double lognxm = FastMath.log(numeratorDegreesOfFreedom * x +
                denominatorDegreesOfFreedom);
        return nhalf * logn + nhalf * logx - logx +
               mhalf * logm - nhalf * lognxm - mhalf * lognxm -
               Beta.logBeta(nhalf, mhalf);
    }

    
{@inheritDoc}
The implementation of this method is based on

 

  
  F-Distribution, equation (4).
 

/**
     * {@inheritDoc}
     *
     * The implementation of this method is based on
     * <ul>
     *  <li>
     *   <a href="http://mathworld.wolfram.com/F-Distribution.html">
     *   F-Distribution</a>, equation (4).
     *  </li>
     * </ul>
     */
    public double cumulativeProbability(double x)  {
        double ret;
        if (x <= 0) {
            ret = 0;
        } else {
            double n = numeratorDegreesOfFreedom;
            double m = denominatorDegreesOfFreedom;

            ret = Beta.regularizedBeta((n * x) / (m + n * x),
                0.5 * n,
                0.5 * m);
        }
        return ret;
    }

    
Access the numerator degrees of freedom.
Returns:
the numerator degrees of freedom./**
     * Access the numerator degrees of freedom.
     *
     * @return the numerator degrees of freedom.
     */
    public double getNumeratorDegreesOfFreedom() {
        return numeratorDegreesOfFreedom;
    }

    
Access the denominator degrees of freedom.
Returns:
the denominator degrees of freedom./**
     * Access the denominator degrees of freedom.
     *
     * @return the denominator degrees of freedom.
     */
    public double getDenominatorDegreesOfFreedom() {
        return denominatorDegreesOfFreedom;
    }

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

    
{@inheritDoc} For denominator degrees of freedom parameter b, the mean is 

 
if b > 2 then b / (b - 2),
 
else undefined (Double.NaN). 
/**
     * {@inheritDoc}
     *
     * For denominator degrees of freedom parameter {@code b}, the mean is
     * <ul>
     *  <li>if {@code b > 2} then {@code b / (b - 2)},</li>
     *  <li>else undefined ({@code Double.NaN}).
     * </ul>
     */
    public double getNumericalMean() {
        final double denominatorDF = getDenominatorDegreesOfFreedom();

        if (denominatorDF > 2) {
            return denominatorDF / (denominatorDF - 2);
        }

        return Double.NaN;
    }

    
{@inheritDoc} For numerator degrees of freedom parameter a and denominator degrees of freedom parameter b, the variance is 

 
 if b > 4 then [2 * b^2 * (a + b - 2)] / [a * (b - 2)^2 * (b - 4)], 
 
else undefined (Double.NaN). 
/**
     * {@inheritDoc}
     *
     * For numerator degrees of freedom parameter {@code a} and denominator
     * degrees of freedom parameter {@code b}, the variance is
     * <ul>
     *  <li>
     *    if {@code b > 4} then
     *    {@code [2 * b^2 * (a + b - 2)] / [a * (b - 2)^2 * (b - 4)]},
     *  </li>
     *  <li>else undefined ({@code Double.NaN}).
     * </ul>
     */
    public double getNumericalVariance() {
        if (!numericalVarianceIsCalculated) {
            numericalVariance = calculateNumericalVariance();
            numericalVarianceIsCalculated = true;
        }
        return numericalVariance;
    }

    
used by getNumericalVariance() 
Returns:
the variance of this distribution/**
     * used by {@link #getNumericalVariance()}
     *
     * @return the variance of this distribution
     */
    protected double calculateNumericalVariance() {
        final double denominatorDF = getDenominatorDegreesOfFreedom();

        if (denominatorDF > 4) {
            final double numeratorDF = getNumeratorDegreesOfFreedom();
            final double denomDFMinusTwo = denominatorDF - 2;

            return ( 2 * (denominatorDF * denominatorDF) * (numeratorDF + denominatorDF - 2) ) /
                   ( (numeratorDF * (denomDFMinusTwo * denomDFMinusTwo) * (denominatorDF - 4)) );
        }

        return Double.NaN;
    }

    
{@inheritDoc}
The lower bound of the support is always 0 no matter the parameters.
Returns:
lower bound of the support (always 0)/**
     * {@inheritDoc}
     *
     * The lower bound of the support is always 0 no matter the parameters.
     *
     * @return lower bound of the support (always 0)
     */
    public double getSupportLowerBound() {
        return 0;
    }

    
{@inheritDoc}
The upper bound of the support is always positive infinity
no matter the parameters.
Returns:
upper bound of the support (always Double.POSITIVE_INFINITY)/**
     * {@inheritDoc}
     *
     * The upper bound of the support is always positive infinity
     * no matter the parameters.
     *
     * @return upper bound of the support (always Double.POSITIVE_INFINITY)
     */
    public double getSupportUpperBound() {
        return Double.POSITIVE_INFINITY;
    }

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

    
{@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;
    }
}