1 /* 2 * Licensed to the Apache Software Foundation (ASF) under one or more 3 * contributor license agreements. See the NOTICE file distributed with 4 * this work for additional information regarding copyright ownership. 5 * The ASF licenses this file to You under the Apache License, Version 2.0 6 * (the "License"); you may not use this file except in compliance with 7 * the License. You may obtain a copy of the License at 8 * 9 * http://www.apache.org/licenses/LICENSE-2.0 10 * 11 * Unless required by applicable law or agreed to in writing, software 12 * distributed under the License is distributed on an "AS IS" BASIS, 13 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. 14 * See the License for the specific language governing permissions and 15 * limitations under the License. 16 */ 17 package org.apache.commons.rng.sampling.distribution; 18 19 /** 20 * Interface for a discrete distribution that can be sampled using 21 * the <a href="https://en.wikipedia.org/wiki/Inverse_transform_sampling"> 22 * inversion method</a>. 23 */ 24 public interface DiscreteInverseCumulativeProbabilityFunction { 25 /** 26 * Computes the quantile function of the distribution. 27 * For a random variable {@code X} distributed according to this distribution, 28 * the returned value is 29 * <ul> 30 * <li>\( \inf_{x \in \mathcal{Z}} P(X \le x) \ge p \) for \( 0 \lt p \le 1 \)</li> 31 * <li>\( \inf_{x \in \mathcal{Z}} P(X \le x) \gt 0 \) for \( p = 0 \)</li> 32 * </ul> 33 * 34 * @param p Cumulative probability. 35 * @return the smallest {@code p}-quantile of the distribution 36 * (largest 0-quantile for {@code p = 0}). 37 * @throws IllegalArgumentException if {@code p < 0} or {@code p > 1}. 38 */ 39 int inverseCumulativeProbability(double p); 40 }