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 * 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
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 *      http://www.apache.org/licenses/LICENSE-2.0
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package org.apache.commons.math3.distribution;

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;

Implementation of the geometric distribution.
See Also:
Geometric distribution (Wikipedia)
Geometric Distribution (MathWorld)
Since:
3.3/**
 * Implementation of the geometric distribution.
 *
 * @see <a href="http://en.wikipedia.org/wiki/Geometric_distribution">Geometric distribution (Wikipedia)</a>
 * @see <a href="http://mathworld.wolfram.com/GeometricDistribution.html">Geometric Distribution (MathWorld)</a>
 * @since 3.3
 */
public class GeometricDistribution extends AbstractIntegerDistribution {

    
Serializable version identifier. /** Serializable version identifier. */
    private static final long serialVersionUID = 20130507L;
    
The probability of success. /** The probability of success. */
    private final double probabilityOfSuccess;
    
log(p) where p is the probability of success. /** {@code log(p)} where p is the probability of success. */
    private final double logProbabilityOfSuccess;
    
log(1 - p) where p is the probability of success. /** {@code log(1 - p)} where p is the probability of success. */
    private final double log1mProbabilityOfSuccess;

    
Create a geometric distribution with the given probability of success.

Note: this constructor will implicitly create an instance of Well19937c as random generator to be used for sampling only (see AbstractIntegerDistribution.sample() and AbstractIntegerDistribution.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:
p – probability of success.
Throws:
OutOfRangeException – if p <= 0 or p > 1./**
     * Create a geometric distribution with the given probability of success.
     * <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 p probability of success.
     * @throws OutOfRangeException if {@code p <= 0} or {@code p > 1}.
     */
    public GeometricDistribution(double p) {
        this(new Well19937c(), p);
    }

    
Creates a geometric distribution.
Params:
rng – Random number generator.
p – Probability of success.
Throws:
OutOfRangeException – if p <= 0 or p > 1./**
     * Creates a geometric distribution.
     *
     * @param rng Random number generator.
     * @param p Probability of success.
     * @throws OutOfRangeException if {@code p <= 0} or {@code p > 1}.
     */
    public GeometricDistribution(RandomGenerator rng, double p) {
        super(rng);

        if (p <= 0 || p > 1) {
            throw new OutOfRangeException(LocalizedFormats.OUT_OF_RANGE_LEFT, p, 0, 1);
        }

        probabilityOfSuccess = p;
        logProbabilityOfSuccess = FastMath.log(p);
        log1mProbabilityOfSuccess = FastMath.log1p(-p);
    }

    
Access the probability of success for this distribution.
Returns:
the probability of success./**
     * Access the probability of success for this distribution.
     *
     * @return the probability of success.
     */
    public double getProbabilityOfSuccess() {
        return probabilityOfSuccess;
    }

    
{@inheritDoc} /** {@inheritDoc} */
    public double probability(int x) {
        if (x < 0) {
            return 0.0;
        } else {
            return FastMath.exp(log1mProbabilityOfSuccess * x) * probabilityOfSuccess;
        }
    }

    
{@inheritDoc} /** {@inheritDoc} */
    @Override
    public double logProbability(int x) {
        if (x < 0) {
            return Double.NEGATIVE_INFINITY;
        } else {
            return x * log1mProbabilityOfSuccess + logProbabilityOfSuccess;
        }
    }

    
{@inheritDoc} /** {@inheritDoc} */
    public double cumulativeProbability(int x) {
        if (x < 0) {
            return 0.0;
        } else {
            return -FastMath.expm1(log1mProbabilityOfSuccess * (x + 1));
        }
    }

    
{@inheritDoc} For probability parameter p, the mean is (1 - p) / p. /**
     * {@inheritDoc}
     *
     * For probability parameter {@code p}, the mean is {@code (1 - p) / p}.
     */
    public double getNumericalMean() {
        return (1 - probabilityOfSuccess) / probabilityOfSuccess;
    }

    
{@inheritDoc} For probability parameter p, the variance is (1 - p) / (p * p). /**
     * {@inheritDoc}
     *
     * For probability parameter {@code p}, the variance is
     * {@code (1 - p) / (p * p)}.
     */
    public double getNumericalVariance() {
        return (1 - probabilityOfSuccess) / (probabilityOfSuccess * probabilityOfSuccess);
    }

    
{@inheritDoc}
The lower bound of the support is always 0.
Returns:
lower bound of the support (always 0)/**
     * {@inheritDoc}
     *
     * The lower bound of the support is always 0.
     *
     * @return lower bound of the support (always 0)
     */
    public int getSupportLowerBound() {
        return 0;
    }

    
{@inheritDoc} The upper bound of the support is infinite (which we approximate as Integer.MAX_VALUE). 
Returns:
upper bound of the support (always Integer.MAX_VALUE)/**
     * {@inheritDoc}
     *
     * The upper bound of the support is infinite (which we approximate as
     * {@code Integer.MAX_VALUE}).
     *
     * @return upper bound of the support (always Integer.MAX_VALUE)
     */
    public int getSupportUpperBound() {
        return Integer.MAX_VALUE;
    }

    
{@inheritDoc}
The support of this distribution is connected.
Returns:
true/**
     * {@inheritDoc}
     *
     * The support of this distribution is connected.
     *
     * @return {@code true}
     */
    public boolean isSupportConnected() {
        return true;
    }

    
{@inheritDoc}
/**
     * {@inheritDoc}
     */
    @Override
    public int inverseCumulativeProbability(double p) throws OutOfRangeException {
        if (p < 0 || p > 1) {
            throw new OutOfRangeException(p, 0, 1);
        }
        if (p == 1) {
            return Integer.MAX_VALUE;
        }
        if (p == 0) {
            return 0;
        }
        return Math.max(0, (int) Math.ceil(FastMath.log1p(-p)/log1mProbabilityOfSuccess-1));
    }
}