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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.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.util.FastMath;
/**
* Implementation of the geometric distribution.
*
* @see Geometric distribution (Wikipedia)
* @see Geometric Distribution (MathWorld)
* @since 3.3
*/
public class GeometricDistribution extends AbstractIntegerDistribution {
/** Serializable version identifier. */
private static final long serialVersionUID = 20130507L;
/** The probability of success. */
private final double probabilityOfSuccess;
/** {@code log(p)} where p is the probability of success. */
private final double logProbabilityOfSuccess;
/** {@code log(1 - p)} where p is the probability of success. */
private final double log1mProbabilityOfSuccess;
/**
* Create a geometric distribution with the given 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 p probability of success.
* @throws OutOfRangeException if {@code p <= 0} or {@code p > 1}.
*/
public GeometricDistribution(double p) {
this(new Well19937c(), p);
}
/**
* Creates a geometric distribution.
*
* @param rng Random number generator.
* @param p Probability of success.
* @throws OutOfRangeException if {@code p <= 0} or {@code p > 1}.
*/
public GeometricDistribution(RandomGenerator rng, double p) {
super(rng);
if (p <= 0 || p > 1) {
throw new OutOfRangeException(LocalizedFormats.OUT_OF_RANGE_LEFT, p, 0, 1);
}
probabilityOfSuccess = p;
logProbabilityOfSuccess = FastMath.log(p);
log1mProbabilityOfSuccess = FastMath.log1p(-p);
}
/**
* Access the probability of success for this distribution.
*
* @return the probability of success.
*/
public double getProbabilityOfSuccess() {
return probabilityOfSuccess;
}
/** {@inheritDoc} */
public double probability(int x) {
if (x < 0) {
return 0.0;
} else {
return FastMath.exp(log1mProbabilityOfSuccess * x) * probabilityOfSuccess;
}
}
/** {@inheritDoc} */
@Override
public double logProbability(int x) {
if (x < 0) {
return Double.NEGATIVE_INFINITY;
} else {
return x * log1mProbabilityOfSuccess + logProbabilityOfSuccess;
}
}
/** {@inheritDoc} */
public double cumulativeProbability(int x) {
if (x < 0) {
return 0.0;
} else {
return -FastMath.expm1(log1mProbabilityOfSuccess * (x + 1));
}
}
/**
* {@inheritDoc}
*
* For probability parameter {@code p}, the mean is {@code (1 - p) / p}.
*/
public double getNumericalMean() {
return (1 - probabilityOfSuccess) / probabilityOfSuccess;
}
/**
* {@inheritDoc}
*
* For probability parameter {@code p}, the variance is
* {@code (1 - p) / (p * p)}.
*/
public double getNumericalVariance() {
return (1 - probabilityOfSuccess) / (probabilityOfSuccess * probabilityOfSuccess);
}
/**
* {@inheritDoc}
*
* The lower bound of the support is always 0.
*
* @return lower bound of the support (always 0)
*/
public int getSupportLowerBound() {
return 0;
}
/**
* {@inheritDoc}
*
* The upper bound of the support is infinite (which we approximate as
* {@code Integer.MAX_VALUE}).
*
* @return upper bound of the support (always Integer.MAX_VALUE)
*/
public int getSupportUpperBound() {
return Integer.MAX_VALUE;
}
/**
* {@inheritDoc}
*
* The support of this distribution is connected.
*
* @return {@code true}
*/
public boolean isSupportConnected() {
return true;
}
/**
* {@inheritDoc}
*/
@Override
public int inverseCumulativeProbability(double p) throws OutOfRangeException {
if (p < 0 || p > 1) {
throw new OutOfRangeException(p, 0, 1);
}
if (p == 1) {
return Integer.MAX_VALUE;
}
if (p == 0) {
return 0;
}
return Math.max(0, (int) Math.ceil(FastMath.log1p(-p)/log1mProbabilityOfSuccess-1));
}
}