mirror of https://github.com/jlizier/jidt
377 lines
14 KiB
Java
377 lines
14 KiB
Java
/*
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* Java Information Dynamics Toolkit (JIDT)
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* Copyright (C) 2017, Joseph T. Lizier
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*
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* This program is free software: you can redistribute it and/or modify
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* it under the terms of the GNU General Public License as published by
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* the Free Software Foundation, either version 3 of the License, or
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* (at your option) any later version.
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*
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* This program is distributed in the hope that it will be useful,
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* but WITHOUT ANY WARRANTY; without even the implied warranty of
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* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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* GNU General Public License for more details.
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*
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* You should have received a copy of the GNU General Public License
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* along with this program. If not, see <http://www.gnu.org/licenses/>.
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*/
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/*
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* This class was originally distributed as part of the Apache Commons
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* Math3 library (3.6.1), under the Apache License Version 2.0, which is
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* copied below. This Apache 2 software is now included as a derivative
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* work in the GPLv3 licensed JIDT project, as per:
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* http://www.apache.org/licenses/GPL-compatibility.html
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*
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* The original Apache source code has been modified as follows:
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* -- We have modified package names to sit inside the JIDT structure.
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*/
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/*
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* Licensed to the Apache Software Foundation (ASF) under one or more
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* contributor license agreements. See the NOTICE file distributed with
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* this work for additional information regarding copyright ownership.
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* The ASF licenses this file to You under the Apache License, Version 2.0
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* (the "License"); you may not use this file except in compliance with
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* the License. You may obtain a copy of the License at
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*
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* http://www.apache.org/licenses/LICENSE-2.0
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*
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* Unless required by applicable law or agreed to in writing, software
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* distributed under the License is distributed on an "AS IS" BASIS,
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* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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* See the License for the specific language governing permissions and
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* limitations under the License.
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*/
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package infodynamics.utils.commonsmath3.distribution;
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import infodynamics.utils.commonsmath3.exception.NotPositiveException;
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import infodynamics.utils.commonsmath3.exception.NotStrictlyPositiveException;
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import infodynamics.utils.commonsmath3.exception.NumberIsTooLargeException;
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import infodynamics.utils.commonsmath3.exception.util.LocalizedFormats;
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import infodynamics.utils.commonsmath3.random.RandomGenerator;
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import infodynamics.utils.commonsmath3.random.Well19937c;
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import infodynamics.utils.commonsmath3.util.FastMath;
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/**
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* Implementation of the hypergeometric distribution.
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*
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* @see <a href="http://en.wikipedia.org/wiki/Hypergeometric_distribution">Hypergeometric distribution (Wikipedia)</a>
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* @see <a href="http://mathworld.wolfram.com/HypergeometricDistribution.html">Hypergeometric distribution (MathWorld)</a>
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*/
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public class HypergeometricDistribution extends AbstractIntegerDistribution {
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/** Serializable version identifier. */
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private static final long serialVersionUID = -436928820673516179L;
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/** The number of successes in the population. */
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private final int numberOfSuccesses;
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/** The population size. */
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private final int populationSize;
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/** The sample size. */
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private final int sampleSize;
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/** Cached numerical variance */
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private double numericalVariance = Double.NaN;
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/** Whether or not the numerical variance has been calculated */
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private boolean numericalVarianceIsCalculated = false;
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/**
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* Construct a new hypergeometric distribution with the specified population
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* size, number of successes in the population, and sample size.
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* <p>
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* <b>Note:</b> this constructor will implicitly create an instance of
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* {@link Well19937c} as random generator to be used for sampling only (see
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* {@link #sample()} and {@link #sample(int)}). In case no sampling is
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* needed for the created distribution, it is advised to pass {@code null}
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* as random generator via the appropriate constructors to avoid the
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* additional initialisation overhead.
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*
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* @param populationSize Population size.
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* @param numberOfSuccesses Number of successes in the population.
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* @param sampleSize Sample size.
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* @throws NotPositiveException if {@code numberOfSuccesses < 0}.
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* @throws NotStrictlyPositiveException if {@code populationSize <= 0}.
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* @throws NumberIsTooLargeException if {@code numberOfSuccesses > populationSize},
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* or {@code sampleSize > populationSize}.
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*/
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public HypergeometricDistribution(int populationSize, int numberOfSuccesses, int sampleSize)
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throws NotPositiveException, NotStrictlyPositiveException, NumberIsTooLargeException {
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this(new Well19937c(), populationSize, numberOfSuccesses, sampleSize);
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}
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/**
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* Creates a new hypergeometric distribution.
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*
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* @param rng Random number generator.
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* @param populationSize Population size.
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* @param numberOfSuccesses Number of successes in the population.
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* @param sampleSize Sample size.
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* @throws NotPositiveException if {@code numberOfSuccesses < 0}.
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* @throws NotStrictlyPositiveException if {@code populationSize <= 0}.
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* @throws NumberIsTooLargeException if {@code numberOfSuccesses > populationSize},
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* or {@code sampleSize > populationSize}.
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* @since 3.1
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*/
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public HypergeometricDistribution(RandomGenerator rng,
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int populationSize,
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int numberOfSuccesses,
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int sampleSize)
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throws NotPositiveException, NotStrictlyPositiveException, NumberIsTooLargeException {
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super(rng);
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if (populationSize <= 0) {
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throw new NotStrictlyPositiveException(LocalizedFormats.POPULATION_SIZE,
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populationSize);
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}
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if (numberOfSuccesses < 0) {
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throw new NotPositiveException(LocalizedFormats.NUMBER_OF_SUCCESSES,
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numberOfSuccesses);
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}
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if (sampleSize < 0) {
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throw new NotPositiveException(LocalizedFormats.NUMBER_OF_SAMPLES,
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sampleSize);
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}
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if (numberOfSuccesses > populationSize) {
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throw new NumberIsTooLargeException(LocalizedFormats.NUMBER_OF_SUCCESS_LARGER_THAN_POPULATION_SIZE,
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numberOfSuccesses, populationSize, true);
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}
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if (sampleSize > populationSize) {
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throw new NumberIsTooLargeException(LocalizedFormats.SAMPLE_SIZE_LARGER_THAN_POPULATION_SIZE,
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sampleSize, populationSize, true);
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}
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this.numberOfSuccesses = numberOfSuccesses;
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this.populationSize = populationSize;
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this.sampleSize = sampleSize;
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}
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/** {@inheritDoc} */
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public double cumulativeProbability(int x) {
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double ret;
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int[] domain = getDomain(populationSize, numberOfSuccesses, sampleSize);
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if (x < domain[0]) {
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ret = 0.0;
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} else if (x >= domain[1]) {
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ret = 1.0;
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} else {
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ret = innerCumulativeProbability(domain[0], x, 1);
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}
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return ret;
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}
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/**
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* Return the domain for the given hypergeometric distribution parameters.
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*
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* @param n Population size.
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* @param m Number of successes in the population.
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* @param k Sample size.
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* @return a two element array containing the lower and upper bounds of the
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* hypergeometric distribution.
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*/
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private int[] getDomain(int n, int m, int k) {
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return new int[] { getLowerDomain(n, m, k), getUpperDomain(m, k) };
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}
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/**
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* Return the lowest domain value for the given hypergeometric distribution
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* parameters.
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*
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* @param n Population size.
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* @param m Number of successes in the population.
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* @param k Sample size.
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* @return the lowest domain value of the hypergeometric distribution.
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*/
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private int getLowerDomain(int n, int m, int k) {
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return FastMath.max(0, m - (n - k));
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}
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/**
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* Access the number of successes.
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*
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* @return the number of successes.
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*/
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public int getNumberOfSuccesses() {
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return numberOfSuccesses;
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}
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/**
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* Access the population size.
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*
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* @return the population size.
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*/
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public int getPopulationSize() {
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return populationSize;
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}
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/**
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* Access the sample size.
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*
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* @return the sample size.
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*/
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public int getSampleSize() {
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return sampleSize;
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}
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/**
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* Return the highest domain value for the given hypergeometric distribution
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* parameters.
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*
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* @param m Number of successes in the population.
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* @param k Sample size.
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* @return the highest domain value of the hypergeometric distribution.
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*/
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private int getUpperDomain(int m, int k) {
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return FastMath.min(k, m);
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}
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/** {@inheritDoc} */
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public double probability(int x) {
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final double logProbability = logProbability(x);
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return logProbability == Double.NEGATIVE_INFINITY ? 0 : FastMath.exp(logProbability);
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}
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/** {@inheritDoc} */
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@Override
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public double logProbability(int x) {
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double ret;
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int[] domain = getDomain(populationSize, numberOfSuccesses, sampleSize);
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if (x < domain[0] || x > domain[1]) {
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ret = Double.NEGATIVE_INFINITY;
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} else {
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double p = (double) sampleSize / (double) populationSize;
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double q = (double) (populationSize - sampleSize) / (double) populationSize;
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double p1 = SaddlePointExpansion.logBinomialProbability(x,
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numberOfSuccesses, p, q);
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double p2 =
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SaddlePointExpansion.logBinomialProbability(sampleSize - x,
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populationSize - numberOfSuccesses, p, q);
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double p3 =
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SaddlePointExpansion.logBinomialProbability(sampleSize, populationSize, p, q);
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ret = p1 + p2 - p3;
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}
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return ret;
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}
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/**
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* For this distribution, {@code X}, this method returns {@code P(X >= x)}.
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*
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* @param x Value at which the CDF is evaluated.
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* @return the upper tail CDF for this distribution.
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* @since 1.1
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*/
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public double upperCumulativeProbability(int x) {
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double ret;
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final int[] domain = getDomain(populationSize, numberOfSuccesses, sampleSize);
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if (x <= domain[0]) {
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ret = 1.0;
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} else if (x > domain[1]) {
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ret = 0.0;
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} else {
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ret = innerCumulativeProbability(domain[1], x, -1);
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}
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return ret;
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}
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/**
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* For this distribution, {@code X}, this method returns
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* {@code P(x0 <= X <= x1)}.
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* This probability is computed by summing the point probabilities for the
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* values {@code x0, x0 + 1, x0 + 2, ..., x1}, in the order directed by
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* {@code dx}.
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*
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* @param x0 Inclusive lower bound.
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* @param x1 Inclusive upper bound.
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* @param dx Direction of summation (1 indicates summing from x0 to x1, and
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* 0 indicates summing from x1 to x0).
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* @return {@code P(x0 <= X <= x1)}.
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*/
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private double innerCumulativeProbability(int x0, int x1, int dx) {
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double ret = probability(x0);
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while (x0 != x1) {
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x0 += dx;
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ret += probability(x0);
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}
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return ret;
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}
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/**
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* {@inheritDoc}
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*
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* For population size {@code N}, number of successes {@code m}, and sample
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* size {@code n}, the mean is {@code n * m / N}.
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*/
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public double getNumericalMean() {
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return getSampleSize() * (getNumberOfSuccesses() / (double) getPopulationSize());
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}
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/**
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* {@inheritDoc}
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*
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* For population size {@code N}, number of successes {@code m}, and sample
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* size {@code n}, the variance is
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* {@code [n * m * (N - n) * (N - m)] / [N^2 * (N - 1)]}.
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*/
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public double getNumericalVariance() {
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if (!numericalVarianceIsCalculated) {
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numericalVariance = calculateNumericalVariance();
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numericalVarianceIsCalculated = true;
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}
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return numericalVariance;
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}
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/**
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* Used by {@link #getNumericalVariance()}.
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*
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* @return the variance of this distribution
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*/
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protected double calculateNumericalVariance() {
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final double N = getPopulationSize();
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final double m = getNumberOfSuccesses();
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final double n = getSampleSize();
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return (n * m * (N - n) * (N - m)) / (N * N * (N - 1));
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}
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/**
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* {@inheritDoc}
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*
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* For population size {@code N}, number of successes {@code m}, and sample
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* size {@code n}, the lower bound of the support is
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* {@code max(0, n + m - N)}.
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*
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* @return lower bound of the support
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*/
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public int getSupportLowerBound() {
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return FastMath.max(0,
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getSampleSize() + getNumberOfSuccesses() - getPopulationSize());
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}
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/**
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* {@inheritDoc}
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*
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* For number of successes {@code m} and sample size {@code n}, the upper
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* bound of the support is {@code min(m, n)}.
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*
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* @return upper bound of the support
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*/
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public int getSupportUpperBound() {
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return FastMath.min(getNumberOfSuccesses(), getSampleSize());
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}
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/**
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* {@inheritDoc}
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*
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* The support of this distribution is connected.
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*
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* @return {@code true}
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*/
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public boolean isSupportConnected() {
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return true;
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}
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}
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