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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   * @since 1.0
25   */
26  public interface DiscreteInverseCumulativeProbabilityFunction {
27      /**
28       * Computes the quantile function of the distribution.
29       * For a random variable {@code X} distributed according to this distribution,
30       * the returned value is
31       * <ul>
32       *  <li>\( \inf_{x \in \mathcal{Z}} P(X \le x) \ge p \) for \( 0 \lt p \le 1 \)</li>
33       *  <li>\( \inf_{x \in \mathcal{Z}} P(X \le x) \gt 0 \) for \( p = 0 \)</li>
34       * </ul>
35       *
36       * @param p Cumulative probability.
37       * @return the smallest {@code p}-quantile of the distribution
38       * (largest 0-quantile for {@code p = 0}).
39       * @throws IllegalArgumentException if {@code p < 0} or {@code p > 1}.
40       */
41      int inverseCumulativeProbability(double p);
42  }