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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 <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. */
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.
*
* <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.
*
* <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.
*
* @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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