| /* |
| * 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.statistics.distribution; |
| |
| import org.apache.commons.rng.UniformRandomProvider; |
| |
| /** |
| * Interface for distributions on the integers. |
| */ |
| public interface DiscreteDistribution { |
| |
| /** |
| * 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 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(x0 < X <= x1)}. |
| * The default implementation uses the identity |
| * {@code P(x0 < X <= x1) = P(X <= x1) - P(X <= x0)} |
| * |
| * @param x0 Lower bound (exclusive). |
| * @param x1 Upper bound (inclusive). |
| * @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 IllegalArgumentException if {@code x0 > x1}. |
| */ |
| default double probability(int x0, |
| int x1) { |
| if (x0 > x1) { |
| throw new DistributionException(DistributionException.INVALID_RANGE_LOW_GT_HIGH, x0, x1); |
| } |
| return cumulativeProbability(x1) - cumulativeProbability(x0); |
| } |
| |
| /** |
| * For a random variable {@code X} whose values are distributed according |
| * to this distribution, this method returns {@code log(P(X = x))}, where |
| * {@code log} is the natural logarithm. |
| * |
| * @param x Point at which the PMF is evaluated. |
| * @return the logarithm of the value of the probability mass function at |
| * {@code x}. |
| */ |
| default double logProbability(int x) { |
| return Math.log(probability(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 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(X > x)}. |
| * In other words, this method represents the complementary cumulative |
| * distribution function. |
| * <p> |
| * By default, this is defined as {@code 1 - cumulativeProbability(x)}, but |
| * the specific implementation may be more accurate. |
| * |
| * @param x Point at which the survival function is evaluated. |
| * @return the probability that a random variable with this |
| * distribution takes a value greater than {@code x}. |
| */ |
| default double survivalProbability(int x) { |
| return 1.0 - cumulativeProbability(x); |
| } |
| |
| /** |
| * 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}} for {@code 0 < p <= 1},</li> |
| * <li>{@code inf{x in Z | P(X<=x) > 0}} 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 Cumulative probability. |
| * @return the smallest {@code p}-quantile of this distribution |
| * (largest 0-quantile for {@code p = 0}). |
| * @throws IllegalArgumentException if {@code p < 0} or {@code p > 1}. |
| */ |
| int inverseCumulativeProbability(double p); |
| |
| /** |
| * Gets the mean of this distribution. |
| * |
| * @return the mean, or {@code Double.NaN} if it is not defined. |
| */ |
| double getMean(); |
| |
| /** |
| * Gets the variance of this distribution. |
| * |
| * @return the variance, or {@code Double.NaN} if it is not defined. |
| */ |
| double getVariance(); |
| |
| /** |
| * Gets the lower bound of the support. |
| * This method must return the same value as |
| * {@code inverseCumulativeProbability(0)}, i.e. |
| * {@code inf {x in Z | P(X <= x) > 0}}. |
| * By convention, {@code Integer.MIN_VALUE} should be substituted |
| * for negative infinity. |
| * |
| * @return the lower bound of the support. |
| */ |
| int getSupportLowerBound(); |
| |
| /** |
| * Gets the upper bound of the support. |
| * This method must return the same value as |
| * {@code inverseCumulativeProbability(1)}, i.e. |
| * {@code inf {x in R | P(X <= x) = 1}}. |
| * By convention, {@code Integer.MAX_VALUE} should be substituted |
| * for positive infinity. |
| * |
| * @return the upper bound of the support. |
| */ |
| int getSupportUpperBound(); |
| |
| /** |
| * Indicates 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. |
| */ |
| boolean isSupportConnected(); |
| |
| /** |
| * Creates a sampler. |
| * |
| * @param rng Generator of uniformly distributed numbers. |
| * @return a sampler that produces random numbers according this |
| * distribution. |
| */ |
| Sampler createSampler(UniformRandomProvider rng); |
| |
| /** |
| * Sampling functionality. |
| */ |
| interface Sampler { |
| /** |
| * Generates a random value sampled from this distribution. |
| * |
| * @return a random value. |
| */ |
| int sample(); |
| } |
| } |