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    1   /*
    2    * Copyright 2004 The Apache Software Foundation.
    3    *
    4    * Licensed under the Apache License, Version 2.0 (the "License");
    5    * you may not use this file except in compliance with the License.
    6    * You may obtain a copy of the License at
    7    *
    8    *      http://www.apache.org/licenses/LICENSE-2.0
    9    *
    10   * Unless required by applicable law or agreed to in writing, software
    11   * distributed under the License is distributed on an "AS IS" BASIS,
    12   * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
    13   * See the License for the specific language governing permissions and
    14   * limitations under the License.
    15   */
    16  package org.apache.commons.math.distribution;
    17
    18  import org.apache.commons.math.MathException;
    19
    20  /***
    21   * Interface for discrete distributions of integer-valued random variables.
    22   *
    23   * @version $Revision: 1.2 $ $Date: 2004/11/07 20:39:15 $
    24   */
    25  public interface IntegerDistribution extends DiscreteDistribution {
    26      /***
    27       * For a random variable X whose values are distributed according
    28       * to this distribution, this method returns P(X = x). In other words, this
    29       * method represents the probability mass function for the distribution.
    30       *
    31       * @param x the value at which the probability density function is evaluated.
    32       * @return the value of the probability density function at x
    33       */
    34      double probability(int x);
    35
    36      /***
    37       * For a random variable X whose values are distributed according
    38       * to this distribution, this method returns P(X &le; x).  In other words,
    39       * this method represents the probability distribution function, or PDF
    40       * for the distribution.
    41       *
    42       * @param x the value at which the PDF is evaluated.
    43       * @return PDF for this distribution.
    44       * @throws MathException if the cumulative probability can not be
    45       *            computed due to convergence or other numerical errors.
    46       */
    47      double cumulativeProbability(int x) throws MathException;
    48
    49      /***
    50       * For this distribution, X, this method returns P(x0 &le; X &le; x1).
    51       * @param x0 the inclusive, lower bound
    52       * @param x1 the inclusive, upper bound
    53       * @return the cumulative probability.
    54       * @throws MathException if the cumulative probability can not be
    55       *            computed due to convergence or other numerical errors.
    56       * @throws IllegalArgumentException if x0 > x1
    57       */
    58      double cumulativeProbability(int x0, int x1) throws MathException;
    59
    60      /***
    61       * For this distribution, X, this method returns the largest x such that
    62       * P(X &le; x) <= p.
    63       * <p>
    64       * Note that this definition implies: <ul>
    65       * <li> If there is a minimum value, <code>m</code>, with postive
    66       * probablility under (the density of) X, then <code>m - 1</code> is
    67       * returned by <code>inverseCumulativeProbability(0).</code>  If there is
    68       * no such value <code>m,  Integer.MIN_VALUE</code> is
    69       * returned.</li>
    70       * <li> If there is a maximum value, <code>M</code>, such that
    71       * P(X &le; M) =1, then <code>M</code> is returned by
    72       * <code>inverseCumulativeProbability(1).</code>
    73       * If there is no such value, <code>M, Integer.MAX_VALUE</code> is
    74       * returned.</li></ul>
    75       *
    76       * @param p the cumulative probability.
    77       * @return the largest x such that P(X &le; x) <= p
    78       * @throws MathException if the inverse cumulative probability can not be
    79       *            computed due to convergence or other numerical errors.
    80       * @throws IllegalArgumentException if p is not between 0 and 1 (inclusive)
    81       */
    82      int inverseCumulativeProbability(double p) throws MathException;
    83  }