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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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 * distributed under the License is distributed on an "AS IS" BASIS,
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package org.apache.commons.math3.distribution;

import org.apache.commons.math3.exception.NotPositiveException;
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.special.Beta;
import org.apache.commons.math3.util.FastMath;

Implementation of the binomial distribution.
See Also:
Binomial distribution (Wikipedia)
Binomial Distribution (MathWorld)/**
 * Implementation of the binomial distribution.
 *
 * @see <a href="http://en.wikipedia.org/wiki/Binomial_distribution">Binomial distribution (Wikipedia)</a>
 * @see <a href="http://mathworld.wolfram.com/BinomialDistribution.html">Binomial Distribution (MathWorld)</a>
 */
public class BinomialDistribution extends AbstractIntegerDistribution {
    
Serializable version identifier. /** Serializable version identifier. */
    private static final long serialVersionUID = 6751309484392813623L;
    
The number of trials. /** The number of trials. */
    private final int numberOfTrials;
    
The probability of success. /** The probability of success. */
    private final double probabilityOfSuccess;

    
Create a binomial distribution with the given number of trials and
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:
trials – Number of trials.
p – Probability of success.
Throws:
NotPositiveException – if trials < 0.
OutOfRangeException – if p < 0 or p > 1./**
     * Create a binomial distribution with the given number of trials and
     * 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 trials Number of trials.
     * @param p Probability of success.
     * @throws NotPositiveException if {@code trials < 0}.
     * @throws OutOfRangeException if {@code p < 0} or {@code p > 1}.
     */
    public BinomialDistribution(int trials, double p) {
        this(new Well19937c(), trials, p);
    }

    
Creates a binomial distribution.
Params:
rng – Random number generator.
trials – Number of trials.
p – Probability of success.
Throws:
NotPositiveException – if trials < 0.
OutOfRangeException – if p < 0 or p > 1.
Since:
3.1/**
     * Creates a binomial distribution.
     *
     * @param rng Random number generator.
     * @param trials Number of trials.
     * @param p Probability of success.
     * @throws NotPositiveException if {@code trials < 0}.
     * @throws OutOfRangeException if {@code p < 0} or {@code p > 1}.
     * @since 3.1
     */
    public BinomialDistribution(RandomGenerator rng,
                                int trials,
                                double p) {
        super(rng);

        if (trials < 0) {
            throw new NotPositiveException(LocalizedFormats.NUMBER_OF_TRIALS,
                                           trials);
        }
        if (p < 0 || p > 1) {
            throw new OutOfRangeException(p, 0, 1);
        }

        probabilityOfSuccess = p;
        numberOfTrials = trials;
    }

    
Access the number of trials for this distribution.
Returns:
the number of trials./**
     * Access the number of trials for this distribution.
     *
     * @return the number of trials.
     */
    public int getNumberOfTrials() {
        return numberOfTrials;
    }

    
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) {
        final double logProbability = logProbability(x);
        return logProbability == Double.NEGATIVE_INFINITY ? 0 : FastMath.exp(logProbability);
    }

    
{@inheritDoc} /** {@inheritDoc} **/
    @Override
    public double logProbability(int x) {
        if (numberOfTrials == 0) {
            return (x == 0) ? 0. : Double.NEGATIVE_INFINITY;
        }
        double ret;
        if (x < 0 || x > numberOfTrials) {
            ret = Double.NEGATIVE_INFINITY;
        } else {
            ret = SaddlePointExpansion.logBinomialProbability(x,
                    numberOfTrials, probabilityOfSuccess,
                    1.0 - probabilityOfSuccess);
        }
        return ret;
    }

    
{@inheritDoc} /** {@inheritDoc} */
    public double cumulativeProbability(int x) {
        double ret;
        if (x < 0) {
            ret = 0.0;
        } else if (x >= numberOfTrials) {
            ret = 1.0;
        } else {
            ret = 1.0 - Beta.regularizedBeta(probabilityOfSuccess,
                    x + 1.0, numberOfTrials - x);
        }
        return ret;
    }

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

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

    
{@inheritDoc} The lower bound of the support is always 0 except for the probability parameter p = 1. 
Returns:
lower bound of the support (0 or the number of trials)/**
     * {@inheritDoc}
     *
     * The lower bound of the support is always 0 except for the probability
     * parameter {@code p = 1}.
     *
     * @return lower bound of the support (0 or the number of trials)
     */
    public int getSupportLowerBound() {
        return probabilityOfSuccess < 1.0 ? 0 : numberOfTrials;
    }

    
{@inheritDoc} The upper bound of the support is the number of trials except for the probability parameter p = 0. 
Returns:
upper bound of the support (number of trials or 0)/**
     * {@inheritDoc}
     *
     * The upper bound of the support is the number of trials except for the
     * probability parameter {@code p = 0}.
     *
     * @return upper bound of the support (number of trials or 0)
     */
    public int getSupportUpperBound() {
        return probabilityOfSuccess > 0.0 ? numberOfTrials : 0;
    }

    
{@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;
    }
}