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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 <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. */
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.
*
* <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.
*
* @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}
*
* <p>For {@code n} trials and probability parameter {@code p}, the mean is {@code n * p}.
*/
public double getNumericalMean() {
return numberOfTrials * probabilityOfSuccess;
}
/**
* {@inheritDoc}
*
* <p>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}
*
* <p>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}
*
* <p>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}
*
* <p>The support of this distribution is connected.
*
* @return {@code true}
*/
public boolean isSupportConnected() {
return true;
}
}
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