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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.OutOfRangeException;
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.util.FastMath;
import org.apache.commons.math3.util.MathUtils;
/**
* This class implements the Gumbel distribution.
*
* @see <a href="http://en.wikipedia.org/wiki/Gumbel_distribution">Gumbel Distribution
* (Wikipedia)</a>
* @see <a href="http://mathworld.wolfram.com/GumbelDistribution.html">Gumbel Distribution
* (Mathworld)</a>
* @since 3.4
*/
public class GumbelDistribution extends AbstractRealDistribution {
/** Serializable version identifier. */
private static final long serialVersionUID = 20141003;
/**
* Approximation of Euler's constant see
* http://mathworld.wolfram.com/Euler-MascheroniConstantApproximations.html
*/
private static final double EULER = FastMath.PI / (2 * FastMath.E);
/** The location parameter. */
private final double mu;
/** The scale parameter. */
private final double beta;
/**
* 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 location parameter
* @param beta scale parameter (must be positive)
* @throws NotStrictlyPositiveException if {@code beta <= 0}
*/
public GumbelDistribution(double mu, double beta) {
this(new Well19937c(), mu, beta);
}
/**
* Build a new instance.
*
* @param rng Random number generator
* @param mu location parameter
* @param beta scale parameter (must be positive)
* @throws NotStrictlyPositiveException if {@code beta <= 0}
*/
public GumbelDistribution(RandomGenerator rng, double mu, double beta) {
super(rng);
if (beta <= 0) {
throw new NotStrictlyPositiveException(LocalizedFormats.SCALE, beta);
}
this.beta = beta;
this.mu = mu;
}
/**
* Access the location parameter, {@code mu}.
*
* @return the location parameter.
*/
public double getLocation() {
return mu;
}
/**
* Access the scale parameter, {@code beta}.
*
* @return the scale parameter.
*/
public double getScale() {
return beta;
}
/** {@inheritDoc} */
public double density(double x) {
final double z = (x - mu) / beta;
final double t = FastMath.exp(-z);
return FastMath.exp(-z - t) / beta;
}
/** {@inheritDoc} */
public double cumulativeProbability(double x) {
final double z = (x - mu) / beta;
return FastMath.exp(-FastMath.exp(-z));
}
/** {@inheritDoc} */
@Override
public double inverseCumulativeProbability(double p) throws OutOfRangeException {
if (p < 0.0 || p > 1.0) {
throw new OutOfRangeException(p, 0.0, 1.0);
} else if (p == 0) {
return Double.NEGATIVE_INFINITY;
} else if (p == 1) {
return Double.POSITIVE_INFINITY;
}
return mu - FastMath.log(-FastMath.log(p)) * beta;
}
/** {@inheritDoc} */
public double getNumericalMean() {
return mu + EULER * beta;
}
/** {@inheritDoc} */
public double getNumericalVariance() {
return (MathUtils.PI_SQUARED) / 6.0 * (beta * beta);
}
/** {@inheritDoc} */
public double getSupportLowerBound() {
return Double.NEGATIVE_INFINITY;
}
/** {@inheritDoc} */
public double getSupportUpperBound() {
return Double.POSITIVE_INFINITY;
}
/** {@inheritDoc} */
public boolean isSupportLowerBoundInclusive() {
return false;
}
/** {@inheritDoc} */
public boolean isSupportUpperBoundInclusive() {
return false;
}
/** {@inheritDoc} */
public boolean isSupportConnected() {
return true;
}
}
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