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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.NumberIsTooLargeException; import org.apache.commons.math3.exception.OutOfRangeException; /** * Base interface for distributions on the reals. * * @version $Id: RealDistribution.java 1416643 2012-12-03 19:37:14Z tn $ * @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 * <ul> * <li><code>inf{x in R | P(X<=x) >= p}</code> for {@code 0 < p <= 1},</li> * <li><code>inf{x in R | P(X<=x) > 0}</code> for {@code p = 0}.</li> * </ul> * * @param p the cumulative probability * @return the smallest {@code p}-quantile of this distribution * (largest 0-quantile for {@code p = 0}) * @throws OutOfRangeException if {@code p < 0} or {@code p > 1} */ double inverseCumulativeProbability(double p) throws OutOfRangeException; /** * Use this method to get the numerical value of the mean of this * distribution. * * @return the mean or {@code Double.NaN} if it is not defined */ double getNumericalMean(); /** * Use this method to get the numerical value of the variance of this * distribution. * * @return the variance (possibly {@code Double.POSITIVE_INFINITY} as * for certain cases in {@link TDistribution}) or {@code Double.NaN} if it * is not defined */ double getNumericalVariance(); /** * Access the lower bound of the support. This method must return the same * value as {@code inverseCumulativeProbability(0)}. In other words, this * method must return * <p><code>inf {x in R | P(X <= x) > 0}</code>.</p> * * @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 * <p><code>inf {x in R | P(X <= x) = 1}</code>.</p> * * @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 */ 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 */ 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); }