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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.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 Binomial distribution (Wikipedia)
 * @see Binomial Distribution (MathWorld)
 */
public class BinomialDistribution extends AbstractIntegerDistribution {
    /** Serializable version identifier. */
    private static final long serialVersionUID = 6751309484392813623L;
    /** The number of trials. */
    private final int numberOfTrials;
    /** 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 * {@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. * * @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. * * @return the number of trials. */ public int getNumberOfTrials() { return numberOfTrials; } /** * Access the probability of success for this distribution. * * @return the probability of success. */ public double getProbabilityOfSuccess() { return probabilityOfSuccess; } /** {@inheritDoc} */ public double probability(int x) { final double logProbability = logProbability(x); return logProbability == Double.NEGATIVE_INFINITY ? 0 : FastMath.exp(logProbability); } /** {@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} */ 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 {@code n} trials and probability parameter {@code p}, the mean is * {@code n * p}. */ public double getNumericalMean() { return numberOfTrials * probabilityOfSuccess; } /** * {@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 {@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 {@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. * * @return {@code true} */ public boolean isSupportConnected() { return true; } }





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