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 * 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
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package org.apache.commons.math3.distribution;

import org.apache.commons.math3.exception.NotStrictlyPositiveException;
import org.apache.commons.math3.exception.NumberIsTooSmallException;
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.Gamma;
import org.apache.commons.math3.util.FastMath;

This class implements the Nakagami distribution.
See Also:
Nakagami Distribution (Wikipedia)
Since:
3.4/**
 * This class implements the Nakagami distribution.
 *
 * @see <a href="http://en.wikipedia.org/wiki/Nakagami_distribution">Nakagami Distribution (Wikipedia)</a>
 *
 * @since 3.4
 */
public class NakagamiDistribution extends AbstractRealDistribution {

    
Default inverse cumulative probability accuracy. /** Default inverse cumulative probability accuracy. */
    public static final double DEFAULT_INVERSE_ABSOLUTE_ACCURACY = 1e-9;

    
Serializable version identifier. /** Serializable version identifier. */
    private static final long serialVersionUID = 20141003;

    
The shape parameter. /** The shape parameter. */
    private final double mu;
    
The scale parameter. /** The scale parameter. */
    private final double omega;
    
Inverse cumulative probability accuracy. /** Inverse cumulative probability accuracy. */
    private final double inverseAbsoluteAccuracy;

    
Build a new instance.

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:
mu – shape parameter
omega – scale parameter (must be positive)
Throws:
NumberIsTooSmallException – if mu < 0.5
NotStrictlyPositiveException – if omega <= 0/**
     * Build a new instance.
     * <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 mu shape parameter
     * @param omega scale parameter (must be positive)
     * @throws NumberIsTooSmallException if {@code mu < 0.5}
     * @throws NotStrictlyPositiveException if {@code omega <= 0}
     */
    public NakagamiDistribution(double mu, double omega) {
        this(mu, omega, DEFAULT_INVERSE_ABSOLUTE_ACCURACY);
    }

    
Build a new instance.

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:
mu – shape parameter
omega – scale parameter (must be positive)
inverseAbsoluteAccuracy – the maximum absolute error in inverse cumulative probability estimates (defaults to DEFAULT_INVERSE_ABSOLUTE_ACCURACY).
Throws:
NumberIsTooSmallException – if mu < 0.5
NotStrictlyPositiveException – if omega <= 0/**
     * Build a new instance.
     * <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 mu shape parameter
     * @param omega scale parameter (must be positive)
     * @param inverseAbsoluteAccuracy the maximum absolute error in inverse
     * cumulative probability estimates (defaults to {@link #DEFAULT_INVERSE_ABSOLUTE_ACCURACY}).
     * @throws NumberIsTooSmallException if {@code mu < 0.5}
     * @throws NotStrictlyPositiveException if {@code omega <= 0}
     */
    public NakagamiDistribution(double mu, double omega, double inverseAbsoluteAccuracy) {
        this(new Well19937c(), mu, omega, inverseAbsoluteAccuracy);
    }

    
Build a new instance.
Params:
rng – Random number generator
mu – shape parameter
omega – scale parameter (must be positive)
inverseAbsoluteAccuracy – the maximum absolute error in inverse cumulative probability estimates (defaults to DEFAULT_INVERSE_ABSOLUTE_ACCURACY).
Throws:
NumberIsTooSmallException – if mu < 0.5
NotStrictlyPositiveException – if omega <= 0/**
     * Build a new instance.
     *
     * @param rng Random number generator
     * @param mu shape parameter
     * @param omega scale parameter (must be positive)
     * @param inverseAbsoluteAccuracy the maximum absolute error in inverse
     * cumulative probability estimates (defaults to {@link #DEFAULT_INVERSE_ABSOLUTE_ACCURACY}).
     * @throws NumberIsTooSmallException if {@code mu < 0.5}
     * @throws NotStrictlyPositiveException if {@code omega <= 0}
     */
    public NakagamiDistribution(RandomGenerator rng, double mu, double omega, double inverseAbsoluteAccuracy) {
        super(rng);

        if (mu < 0.5) {
            throw new NumberIsTooSmallException(mu, 0.5, true);
        }
        if (omega <= 0) {
            throw new NotStrictlyPositiveException(LocalizedFormats.NOT_POSITIVE_SCALE, omega);
        }

        this.mu = mu;
        this.omega = omega;
        this.inverseAbsoluteAccuracy = inverseAbsoluteAccuracy;
    }

    
Access the shape parameter, mu. 
Returns:
the shape parameter./**
     * Access the shape parameter, {@code mu}.
     *
     * @return the shape parameter.
     */
    public double getShape() {
        return mu;
    }

    
Access the scale parameter, omega. 
Returns:
the scale parameter./**
     * Access the scale parameter, {@code omega}.
     *
     * @return the scale parameter.
     */
    public double getScale() {
        return omega;
    }

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

    
{@inheritDoc} /** {@inheritDoc} */
    public double density(double x) {
        if (x <= 0) {
            return 0.0;
        }
        return 2.0 * FastMath.pow(mu, mu) / (Gamma.gamma(mu) * FastMath.pow(omega, mu)) *
                     FastMath.pow(x, 2 * mu - 1) * FastMath.exp(-mu * x * x / omega);
    }

    
{@inheritDoc} /** {@inheritDoc} */
    public double cumulativeProbability(double x) {
        return Gamma.regularizedGammaP(mu, mu * x * x / omega);
    }

    
{@inheritDoc} /** {@inheritDoc} */
    public double getNumericalMean() {
        return Gamma.gamma(mu + 0.5) / Gamma.gamma(mu) * FastMath.sqrt(omega / mu);
    }

    
{@inheritDoc} /** {@inheritDoc} */
    public double getNumericalVariance() {
        double v = Gamma.gamma(mu + 0.5) / Gamma.gamma(mu);
        return omega * (1 - 1 / mu * v * v);
    }

    
{@inheritDoc} /** {@inheritDoc} */
    public double getSupportLowerBound() {
        return 0;
    }

    
{@inheritDoc} /** {@inheritDoc} */
    public double getSupportUpperBound() {
        return Double.POSITIVE_INFINITY;
    }

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

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

    
{@inheritDoc} /** {@inheritDoc} */
    public boolean isSupportConnected() {
        return true;
    }

}