| /* |
| * 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.statistics.distribution; |
| |
| import org.apache.commons.numbers.gamma.RegularizedGamma; |
| import org.apache.commons.rng.UniformRandomProvider; |
| import org.apache.commons.rng.sampling.distribution.PoissonSampler; |
| |
| /** |
| * Implementation of the <a href="http://en.wikipedia.org/wiki/Poisson_distribution">Poisson distribution</a>. |
| */ |
| public class PoissonDistribution extends AbstractDiscreteDistribution { |
| /** ln(2 π). */ |
| private static final double LOG_TWO_PI = Math.log(2 * Math.PI); |
| /** Default maximum number of iterations. */ |
| private static final int DEFAULT_MAX_ITERATIONS = 10000000; |
| /** Default convergence criterion. */ |
| private static final double DEFAULT_EPSILON = 1e-12; |
| /** Distribution used to compute normal approximation. */ |
| private final NormalDistribution normal; |
| /** Mean of the distribution. */ |
| private final double mean; |
| /** Maximum number of iterations for cumulative probability. */ |
| private final int maxIterations; |
| /** Convergence criterion for cumulative probability. */ |
| private final double epsilon; |
| |
| /** |
| * Creates a new Poisson distribution with specified mean. |
| * |
| * @param p the Poisson mean |
| * @throws IllegalArgumentException if {@code p <= 0}. |
| */ |
| public PoissonDistribution(double p) { |
| this(p, DEFAULT_EPSILON, DEFAULT_MAX_ITERATIONS); |
| } |
| |
| /** |
| * Creates a new Poisson distribution with specified mean, convergence |
| * criterion and maximum number of iterations. |
| * |
| * @param p Poisson mean. |
| * @param epsilon Convergence criterion for cumulative probabilities. |
| * @param maxIterations Maximum number of iterations for cumulative |
| * probabilities. |
| * @throws IllegalArgumentException if {@code p <= 0}. |
| */ |
| private PoissonDistribution(double p, |
| double epsilon, |
| int maxIterations) { |
| if (p <= 0) { |
| throw new DistributionException(DistributionException.NOT_STRICTLY_POSITIVE, p); |
| } |
| mean = p; |
| this.epsilon = epsilon; |
| this.maxIterations = maxIterations; |
| |
| normal = new NormalDistribution(p, Math.sqrt(p)); |
| } |
| |
| /** {@inheritDoc} */ |
| @Override |
| public double probability(int x) { |
| final double logProbability = logProbability(x); |
| return logProbability == Double.NEGATIVE_INFINITY ? 0 : Math.exp(logProbability); |
| } |
| |
| /** {@inheritDoc} */ |
| @Override |
| public double logProbability(int x) { |
| double ret; |
| if (x < 0 || x == Integer.MAX_VALUE) { |
| ret = Double.NEGATIVE_INFINITY; |
| } else if (x == 0) { |
| ret = -mean; |
| } else { |
| ret = -SaddlePointExpansionUtils.getStirlingError(x) - |
| SaddlePointExpansionUtils.getDeviancePart(x, mean) - |
| 0.5 * LOG_TWO_PI - 0.5 * Math.log(x); |
| } |
| return ret; |
| } |
| |
| /** {@inheritDoc} */ |
| @Override |
| public double cumulativeProbability(int x) { |
| if (x < 0) { |
| return 0; |
| } |
| if (x == Integer.MAX_VALUE) { |
| return 1; |
| } |
| return RegularizedGamma.Q.value((double) x + 1, mean, epsilon, |
| maxIterations); |
| } |
| |
| /** |
| * Calculates the Poisson distribution function using a normal |
| * approximation. The {@code N(mean, sqrt(mean))} distribution is used |
| * to approximate the Poisson distribution. The computation uses |
| * "half-correction" (evaluating the normal distribution function at |
| * {@code x + 0.5}). |
| * |
| * @param x Upper bound, inclusive. |
| * @return the distribution function value calculated using a normal |
| * approximation. |
| */ |
| public double normalApproximateProbability(int x) { |
| // Calculate the probability using half-correction. |
| return normal.cumulativeProbability(x + 0.5); |
| } |
| |
| /** {@inheritDoc} */ |
| @Override |
| public double getMean() { |
| return mean; |
| } |
| |
| /** |
| * {@inheritDoc} |
| * |
| * The variance is equal to the {@link #getMean() mean}. |
| */ |
| @Override |
| public double getVariance() { |
| return getMean(); |
| } |
| |
| /** |
| * {@inheritDoc} |
| * |
| * The lower bound of the support is always 0 no matter the mean parameter. |
| * |
| * @return lower bound of the support (always 0) |
| */ |
| @Override |
| public int getSupportLowerBound() { |
| return 0; |
| } |
| |
| /** |
| * {@inheritDoc} |
| * |
| * The upper bound of the support is positive infinity, |
| * regardless of the parameter values. There is no integer infinity, |
| * so this method returns {@code Integer.MAX_VALUE}. |
| * |
| * @return upper bound of the support (always {@code Integer.MAX_VALUE} for |
| * positive infinity) |
| */ |
| @Override |
| public int getSupportUpperBound() { |
| return Integer.MAX_VALUE; |
| } |
| |
| /** |
| * {@inheritDoc} |
| * |
| * The support of this distribution is connected. |
| * |
| * @return {@code true} |
| */ |
| @Override |
| public boolean isSupportConnected() { |
| return true; |
| } |
| |
| /**{@inheritDoc} */ |
| @Override |
| public DiscreteDistribution.Sampler createSampler(final UniformRandomProvider rng) { |
| // Poisson distribution sampler. |
| return new PoissonSampler(rng, mean)::sample; |
| } |
| } |