mirror of https://github.com/jlizier/jidt
278 lines
10 KiB
Java
278 lines
10 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.NotStrictlyPositiveException;
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import infodynamics.utils.commonsmath3.exception.OutOfRangeException;
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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.special.Beta;
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import infodynamics.utils.commonsmath3.util.CombinatoricsUtils;
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import infodynamics.utils.commonsmath3.util.FastMath;
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/**
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* <p>
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* Implementation of the Pascal distribution. The Pascal distribution is a
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* special case of the Negative Binomial distribution where the number of
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* successes parameter is an integer.
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* </p>
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* <p>
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* There are various ways to express the probability mass and distribution
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* functions for the Pascal distribution. The present implementation represents
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* the distribution of the number of failures before {@code r} successes occur.
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* This is the convention adopted in e.g.
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* <a href="http://mathworld.wolfram.com/NegativeBinomialDistribution.html">MathWorld</a>,
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* but <em>not</em> in
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* <a href="http://en.wikipedia.org/wiki/Negative_binomial_distribution">Wikipedia</a>.
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* </p>
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* <p>
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* For a random variable {@code X} whose values are distributed according to this
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* distribution, the probability mass function is given by<br/>
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* {@code P(X = k) = C(k + r - 1, r - 1) * p^r * (1 - p)^k,}<br/>
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* where {@code r} is the number of successes, {@code p} is the probability of
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* success, and {@code X} is the total number of failures. {@code C(n, k)} is
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* the binomial coefficient ({@code n} choose {@code k}). The mean and variance
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* of {@code X} are<br/>
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* {@code E(X) = (1 - p) * r / p, var(X) = (1 - p) * r / p^2.}<br/>
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* Finally, the cumulative distribution function is given by<br/>
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* {@code P(X <= k) = I(p, r, k + 1)},
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* where I is the regularized incomplete Beta function.
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* </p>
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*
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* @see <a href="http://en.wikipedia.org/wiki/Negative_binomial_distribution">
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* Negative binomial distribution (Wikipedia)</a>
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* @see <a href="http://mathworld.wolfram.com/NegativeBinomialDistribution.html">
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* Negative binomial distribution (MathWorld)</a>
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* @since 1.2 (changed to concrete class in 3.0)
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*/
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public class PascalDistribution extends AbstractIntegerDistribution {
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/** Serializable version identifier. */
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private static final long serialVersionUID = 6751309484392813623L;
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/** The number of successes. */
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private final int numberOfSuccesses;
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/** The probability of success. */
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private final double probabilityOfSuccess;
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/** The value of {@code log(p)}, where {@code p} is the probability of success,
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* stored for faster computation. */
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private final double logProbabilityOfSuccess;
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/** The value of {@code log(1-p)}, where {@code p} is the probability of success,
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* stored for faster computation. */
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private final double log1mProbabilityOfSuccess;
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/**
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* Create a Pascal distribution with the given number of successes and
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* probability of success.
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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 r Number of successes.
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* @param p Probability of success.
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* @throws NotStrictlyPositiveException if the number of successes is not positive
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* @throws OutOfRangeException if the probability of success is not in the
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* range {@code [0, 1]}.
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*/
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public PascalDistribution(int r, double p)
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throws NotStrictlyPositiveException, OutOfRangeException {
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this(new Well19937c(), r, p);
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}
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/**
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* Create a Pascal distribution with the given number of successes and
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* probability of success.
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*
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* @param rng Random number generator.
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* @param r Number of successes.
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* @param p Probability of success.
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* @throws NotStrictlyPositiveException if the number of successes is not positive
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* @throws OutOfRangeException if the probability of success is not in the
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* range {@code [0, 1]}.
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* @since 3.1
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*/
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public PascalDistribution(RandomGenerator rng,
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int r,
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double p)
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throws NotStrictlyPositiveException, OutOfRangeException {
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super(rng);
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if (r <= 0) {
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throw new NotStrictlyPositiveException(LocalizedFormats.NUMBER_OF_SUCCESSES,
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r);
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}
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if (p < 0 || p > 1) {
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throw new OutOfRangeException(p, 0, 1);
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}
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numberOfSuccesses = r;
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probabilityOfSuccess = p;
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logProbabilityOfSuccess = FastMath.log(p);
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log1mProbabilityOfSuccess = FastMath.log1p(-p);
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}
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/**
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* Access the number of successes for this distribution.
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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 probability of success for this distribution.
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*
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* @return the probability of success.
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*/
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public double getProbabilityOfSuccess() {
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return probabilityOfSuccess;
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}
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/** {@inheritDoc} */
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public double probability(int x) {
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double ret;
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if (x < 0) {
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ret = 0.0;
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} else {
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ret = CombinatoricsUtils.binomialCoefficientDouble(x +
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numberOfSuccesses - 1, numberOfSuccesses - 1) *
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FastMath.pow(probabilityOfSuccess, numberOfSuccesses) *
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FastMath.pow(1.0 - probabilityOfSuccess, x);
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}
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return ret;
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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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if (x < 0) {
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ret = Double.NEGATIVE_INFINITY;
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} else {
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ret = CombinatoricsUtils.binomialCoefficientLog(x +
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numberOfSuccesses - 1, numberOfSuccesses - 1) +
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logProbabilityOfSuccess * numberOfSuccesses +
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log1mProbabilityOfSuccess * x;
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}
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return ret;
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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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if (x < 0) {
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ret = 0.0;
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} else {
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ret = Beta.regularizedBeta(probabilityOfSuccess,
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numberOfSuccesses, x + 1.0);
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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 number of successes {@code r} and probability of success {@code p},
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* the mean is {@code r * (1 - p) / p}.
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*/
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public double getNumericalMean() {
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final double p = getProbabilityOfSuccess();
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final double r = getNumberOfSuccesses();
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return (r * (1 - p)) / p;
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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 r} and probability of success {@code p},
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* the variance is {@code r * (1 - p) / p^2}.
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*/
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public double getNumericalVariance() {
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final double p = getProbabilityOfSuccess();
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final double r = getNumberOfSuccesses();
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return r * (1 - p) / (p * p);
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}
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/**
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* {@inheritDoc}
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*
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* The lower bound of the support is always 0 no matter the parameters.
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*
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* @return lower bound of the support (always 0)
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*/
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public int getSupportLowerBound() {
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return 0;
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}
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/**
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* {@inheritDoc}
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*
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* The upper bound of the support is always positive infinity no matter the
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* parameters. Positive infinity is symbolized by {@code Integer.MAX_VALUE}.
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*
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* @return upper bound of the support (always {@code Integer.MAX_VALUE}
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* for positive infinity)
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*/
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public int getSupportUpperBound() {
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return Integer.MAX_VALUE;
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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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