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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; /** * Interface for distributions on the integers. * * @version $Id: IntegerDistribution.java 1416643 2012-12-03 19:37:14Z tn $ */ public interface IntegerDistribution { /** * 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 {@code x} */ double probability(int 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(int 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 * will take a value between {@code x0} and {@code x1}, * excluding the lower and including the upper endpoint * @throws NumberIsTooLargeException if {@code x0 > x1} */ double cumulativeProbability(int x0, int 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 Z | P(X<=x) >= p}</code> for {@code 0 < p <= 1},</li> * <li><code>inf{x in Z | P(X<=x) > 0}</code> for {@code p = 0}.</li> * </ul> * If the result exceeds the range of the data type {@code int}, * then {@code Integer.MIN_VALUE} or {@code Integer.MAX_VALUE} is returned. * * @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} */ int 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} 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 Z | P(X <= x) > 0}</code>.</p> * * @return lower bound of the support ({@code Integer.MIN_VALUE} * for negative infinity) */ int 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 ({@code Integer.MAX_VALUE} * for positive infinity) */ int getSupportUpperBound(); /** * Use this method to get information about whether the support is * connected, i.e. whether all integers 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 * @since 3.0 */ void reseedRandomGenerator(long seed); /** * Generate a random value sampled from this distribution. * * @return a random value * @since 3.0 */ int 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 * @since 3.0 */ int[] sample(int sampleSize); }