/* * 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.NumberIsTooLargeException; import org.apache.commons.math3.exception.OutOfRangeException; /** * Base interface for distributions on the reals. * * @since 3.0 */ public interface RealDistribution { /** * For a random variable {@code X} whose values are distributed according to this distribution, * this method returns {@code P(X = x)}. In other words, this method represents the probability * mass function (PMF) for the distribution. * * @param x the point at which the PMF is evaluated * @return the value of the probability mass function at point {@code x} */ double probability(double x); /** * Returns the probability density function (PDF) of this distribution evaluated at the * specified point {@code x}. In general, the PDF is the derivative of the {@link * #cumulativeProbability(double) CDF}. If the derivative does not exist at {@code x}, then an * appropriate replacement should be returned, e.g. {@code Double.POSITIVE_INFINITY}, {@code * Double.NaN}, or the limit inferior or limit superior of the difference quotient. * * @param x the point at which the PDF is evaluated * @return the value of the probability density function at point {@code x} */ double density(double x); /** * For a random variable {@code X} whose values are distributed according to this distribution, * this method returns {@code P(X <= x)}. In other words, this method represents the * (cumulative) distribution function (CDF) for this distribution. * * @param x the point at which the CDF is evaluated * @return the probability that a random variable with this distribution takes a value less than * or equal to {@code x} */ double cumulativeProbability(double x); /** * For a random variable {@code X} whose values are distributed according to this distribution, * this method returns {@code P(x0 < X <= x1)}. * * @param x0 the exclusive lower bound * @param x1 the inclusive upper bound * @return the probability that a random variable with this distribution takes a value between * {@code x0} and {@code x1}, excluding the lower and including the upper endpoint * @throws NumberIsTooLargeException if {@code x0 > x1} * @deprecated As of 3.1. In 4.0, this method will be renamed {@code probability(double x0, * double x1)}. */ @Deprecated double cumulativeProbability(double x0, double x1) throws NumberIsTooLargeException; /** * Computes the quantile function of this distribution. For a random variable {@code X} * distributed according to this distribution, the returned value is * *
inf{x in R | P(X<=x) >= p}
for {@code 0 < p <= 1},
* inf{x in R | P(X<=x) > 0}
for {@code p = 0}.
* inf {x in R | P(X <= x) > 0}
.
*
* @return lower bound of the support (might be {@code Double.NEGATIVE_INFINITY})
*/
double getSupportLowerBound();
/**
* Access the upper bound of the support. This method must return the same value as {@code
* inverseCumulativeProbability(1)}. In other words, this method must return
*
*
inf {x in R | P(X <= x) = 1}
.
*
* @return upper bound of the support (might be {@code Double.POSITIVE_INFINITY})
*/
double getSupportUpperBound();
/**
* Whether or not the lower bound of support is in the domain of the density function. Returns
* true iff {@code getSupporLowerBound()} is finite and {@code density(getSupportLowerBound())}
* returns a non-NaN, non-infinite value.
*
* @return true if the lower bound of support is finite and the density function returns a
* non-NaN, non-infinite value there
* @deprecated to be removed in 4.0
*/
@Deprecated
boolean isSupportLowerBoundInclusive();
/**
* Whether or not the upper bound of support is in the domain of the density function. Returns
* true iff {@code getSupportUpperBound()} is finite and {@code density(getSupportUpperBound())}
* returns a non-NaN, non-infinite value.
*
* @return true if the upper bound of support is finite and the density function returns a
* non-NaN, non-infinite value there
* @deprecated to be removed in 4.0
*/
@Deprecated
boolean isSupportUpperBoundInclusive();
/**
* Use this method to get information about whether the support is connected, i.e. whether all
* values between the lower and upper bound of the support are included in the support.
*
* @return whether the support is connected or not
*/
boolean isSupportConnected();
/**
* Reseed the random generator used to generate samples.
*
* @param seed the new seed
*/
void reseedRandomGenerator(long seed);
/**
* Generate a random value sampled from this distribution.
*
* @return a random value.
*/
double sample();
/**
* Generate a random sample from the distribution.
*
* @param sampleSize the number of random values to generate
* @return an array representing the random sample
* @throws org.apache.commons.math3.exception.NotStrictlyPositiveException if {@code sampleSize}
* is not positive
*/
double[] sample(int sampleSize);
}