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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.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 Nakagami Distribution (Wikipedia)
 *
 * @since 3.4
 */
public class NakagamiDistribution extends AbstractRealDistribution {

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

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

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

    /**
     * Build a new instance.
     * 

* Note: 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 * {@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. * * @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, {@code mu}. * * @return the shape parameter. */ public double getShape() { return mu; } /** * Access the scale parameter, {@code omega}. * * @return the scale parameter. */ public double getScale() { return omega; } /** {@inheritDoc} */ @Override protected double getSolverAbsoluteAccuracy() { return inverseAbsoluteAccuracy; } /** {@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} */ public double cumulativeProbability(double x) { return Gamma.regularizedGammaP(mu, mu * x * x / omega); } /** {@inheritDoc} */ public double getNumericalMean() { return Gamma.gamma(mu + 0.5) / Gamma.gamma(mu) * FastMath.sqrt(omega / mu); } /** {@inheritDoc} */ public double getNumericalVariance() { double v = Gamma.gamma(mu + 0.5) / Gamma.gamma(mu); return omega * (1 - 1 / mu * v * v); } /** {@inheritDoc} */ public double getSupportLowerBound() { return 0; } /** {@inheritDoc} */ public double getSupportUpperBound() { return Double.POSITIVE_INFINITY; } /** {@inheritDoc} */ public boolean isSupportLowerBoundInclusive() { return true; } /** {@inheritDoc} */ public boolean isSupportUpperBoundInclusive() { return false; } /** {@inheritDoc} */ public boolean isSupportConnected() { return true; } }





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