path: root/src/main/java/org/apache/commons/math3/distribution/PascalDistribution.java

/*
 * 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.special.Beta;
import org.apache.commons.math3.util.CombinatoricsUtils;
import org.apache.commons.math3.util.FastMath;

/**
 * Implementation of the Pascal distribution. The Pascal distribution is a special case of the
 * Negative Binomial distribution where the number of successes parameter is an integer.
 *
 * <p>There are various ways to express the probability mass and distribution functions for the
 * Pascal distribution. The present implementation represents the distribution of the number of
 * failures before {@code r} successes occur. This is the convention adopted in e.g. <a
 * href="http://mathworld.wolfram.com/NegativeBinomialDistribution.html">MathWorld</a>, but
 * <em>not</em> in <a
 * href="http://en.wikipedia.org/wiki/Negative_binomial_distribution">Wikipedia</a>.
 *
 * <p>For a random variable {@code X} whose values are distributed according to this distribution,
 * the probability mass function is given by<br>
 * {@code P(X = k) = C(k + r - 1, r - 1) * p^r * (1 - p)^k,}<br>
 * where {@code r} is the number of successes, {@code p} is the probability of success, and {@code
 * X} is the total number of failures. {@code C(n, k)} is the binomial coefficient ({@code n} choose
 * {@code k}). The mean and variance of {@code X} are<br>
 * {@code E(X) = (1 - p) * r / p, var(X) = (1 - p) * r / p^2.}<br>
 * Finally, the cumulative distribution function is given by<br>
 * {@code P(X <= k) = I(p, r, k + 1)}, where I is the regularized incomplete Beta function.
 *
 * @see <a href="http://en.wikipedia.org/wiki/Negative_binomial_distribution">Negative binomial
 *     distribution (Wikipedia)</a>
 * @see <a href="http://mathworld.wolfram.com/NegativeBinomialDistribution.html">Negative binomial
 *     distribution (MathWorld)</a>
 * @since 1.2 (changed to concrete class in 3.0)
 */
public class PascalDistribution extends AbstractIntegerDistribution {
    /** Serializable version identifier. */
    private static final long serialVersionUID = 6751309484392813623L;

    /** The number of successes. */
    private final int numberOfSuccesses;

    /** The probability of success. */
    private final double probabilityOfSuccess;

    /**
     * The value of {@code log(p)}, where {@code p} is the probability of success, stored for faster
     * computation.
     */
    private final double logProbabilityOfSuccess;

    /**
     * The value of {@code log(1-p)}, where {@code p} is the probability of success, stored for
     * faster computation.
     */
    private final double log1mProbabilityOfSuccess;

    /**
     * Create a Pascal distribution with the given number of successes 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 r Number of successes.
     * @param p Probability of success.
     * @throws NotStrictlyPositiveException if the number of successes is not positive
     * @throws OutOfRangeException if the probability of success is not in the range {@code [0, 1]}.
     */
    public PascalDistribution(int r, double p)
            throws NotStrictlyPositiveException, OutOfRangeException {
        this(new Well19937c(), r, p);
    }

    /**
     * Create a Pascal distribution with the given number of successes and probability of success.
     *
     * @param rng Random number generator.
     * @param r Number of successes.
     * @param p Probability of success.
     * @throws NotStrictlyPositiveException if the number of successes is not positive
     * @throws OutOfRangeException if the probability of success is not in the range {@code [0, 1]}.
     * @since 3.1
     */
    public PascalDistribution(RandomGenerator rng, int r, double p)
            throws NotStrictlyPositiveException, OutOfRangeException {
        super(rng);

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

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

    /**
     * Access the number of successes for this distribution.
     *
     * @return the number of successes.
     */
    public int getNumberOfSuccesses() {
        return numberOfSuccesses;
    }

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

    /** {@inheritDoc} */
    public double probability(int x) {
        double ret;
        if (x < 0) {
            ret = 0.0;
        } else {
            ret =
                    CombinatoricsUtils.binomialCoefficientDouble(
                                    x + numberOfSuccesses - 1, numberOfSuccesses - 1)
                            * FastMath.pow(probabilityOfSuccess, numberOfSuccesses)
                            * FastMath.pow(1.0 - probabilityOfSuccess, x);
        }
        return ret;
    }

    /** {@inheritDoc} */
    @Override
    public double logProbability(int x) {
        double ret;
        if (x < 0) {
            ret = Double.NEGATIVE_INFINITY;
        } else {
            ret =
                    CombinatoricsUtils.binomialCoefficientLog(
                                    x + numberOfSuccesses - 1, numberOfSuccesses - 1)
                            + logProbabilityOfSuccess * numberOfSuccesses
                            + log1mProbabilityOfSuccess * x;
        }
        return ret;
    }

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

    /**
     * {@inheritDoc}
     *
     * <p>For number of successes {@code r} and probability of success {@code p}, the mean is {@code
     * r * (1 - p) / p}.
     */
    public double getNumericalMean() {
        final double p = getProbabilityOfSuccess();
        final double r = getNumberOfSuccesses();
        return (r * (1 - p)) / p;
    }

    /**
     * {@inheritDoc}
     *
     * <p>For number of successes {@code r} and probability of success {@code p}, the variance is
     * {@code r * (1 - p) / p^2}.
     */
    public double getNumericalVariance() {
        final double p = getProbabilityOfSuccess();
        final double r = getNumberOfSuccesses();
        return r * (1 - p) / (p * p);
    }

    /**
     * {@inheritDoc}
     *
     * <p>The lower bound of the support is always 0 no matter the parameters.
     *
     * @return lower bound of the support (always 0)
     */
    public int getSupportLowerBound() {
        return 0;
    }

    /**
     * {@inheritDoc}
     *
     * <p>The upper bound of the support is always positive infinity no matter the parameters.
     * Positive infinity is symbolized by {@code Integer.MAX_VALUE}.
     *
     * @return upper bound of the support (always {@code Integer.MAX_VALUE} for positive infinity)
     */
    public int getSupportUpperBound() {
        return Integer.MAX_VALUE;
    }

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