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 * 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
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 * See the License for the specific language governing permissions and
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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 Also:
Gumbel Distribution (Wikipedia)
Gumbel Distribution (Mathworld)
Since:
3.4/**
 * 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. /** Serializable version identifier. */
    private static final long serialVersionUID = 20141003;

    
Approximation of Euler's constant
see http://mathworld.wolfram.com/Euler-MascheroniConstantApproximations.html
/**
     * 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. /** The location parameter. */
    private final double mu;
    
The scale parameter. /** The scale parameter. */
    private final double beta;

    
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 – location parameter
beta – scale parameter (must be positive)
Throws:
NotStrictlyPositiveException – if beta <= 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 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.
Params:
rng – Random number generator
mu – location parameter
beta – scale parameter (must be positive)
Throws:
NotStrictlyPositiveException – if beta <= 0/**
     * 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, mu. 
Returns:
the location parameter./**
     * Access the location parameter, {@code mu}.
     *
     * @return the location parameter.
     */
    public double getLocation() {
        return mu;
    }

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

    
{@inheritDoc} /** {@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} /** {@inheritDoc} */
    public double cumulativeProbability(double x) {
        final double z = (x - mu) / beta;
        return FastMath.exp(-FastMath.exp(-z));
    }

    
{@inheritDoc} /** {@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} /** {@inheritDoc} */
    public double getNumericalMean() {
        return mu + EULER * beta;
    }

    
{@inheritDoc} /** {@inheritDoc} */
    public double getNumericalVariance() {
        return (MathUtils.PI_SQUARED) / 6.0 * (beta * beta);
    }

    
{@inheritDoc} /** {@inheritDoc} */
    public double getSupportLowerBound() {
        return Double.NEGATIVE_INFINITY;
    }

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

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

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

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

}