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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. */
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><code>inf{x in Z | P(X<=x) > 0}</code> for {@code p = 0}.
* </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>.
*
* @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>.
*
* @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);
}
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