/*
* 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;
/**
* Base interface for distributions on the reals.
*
* @since 3.0
*/
public interface RealDistribution {
/**
* 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 point {@code x}
*/
double probability(double x);
/**
* Returns the probability density function (PDF) of this distribution
* evaluated at the specified point {@code x}. In general, the PDF is
* the derivative of the {@link #cumulativeProbability(double) CDF}.
* If the derivative does not exist at {@code x}, then an appropriate
* replacement should be returned, e.g. {@code Double.POSITIVE_INFINITY},
* {@code Double.NaN}, or the limit inferior or limit superior of the
* difference quotient.
*
* @param x the point at which the PDF is evaluated
* @return the value of the probability density function at point {@code x}
*/
double density(double 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(double 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
* takes a value between {@code x0} and {@code x1},
* excluding the lower and including the upper endpoint
* @throws NumberIsTooLargeException if {@code x0 > x1}
*
* @deprecated As of 3.1. In 4.0, this method will be renamed
* {@code probability(double x0, double x1)}.
*/
@Deprecated
double cumulativeProbability(double x0, double 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 R | P(X<=x) >= p}</code> for {@code 0 < p <= 1},</li>
* <li><code>inf{x in R | P(X<=x) > 0}</code> for {@code p = 0}.</li>
* </ul>
*
* @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}
*/
double 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} as
* for certain cases in {@link TDistribution}) 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 R | P(X <= x) > 0}</code>.</p>
*
* @return lower bound of the support (might be
* {@code Double.NEGATIVE_INFINITY})
*/
double 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>.</p>
*
* @return upper bound of the support (might be
* {@code Double.POSITIVE_INFINITY})
*/
double getSupportUpperBound();
/**
* Whether or not the lower bound of support is in the domain of the density
* function. Returns true iff {@code getSupporLowerBound()} is finite and
* {@code density(getSupportLowerBound())} returns a non-NaN, non-infinite
* value.
*
* @return true if the lower bound of support is finite and the density
* function returns a non-NaN, non-infinite value there
* @deprecated to be removed in 4.0
*/
@Deprecated
boolean isSupportLowerBoundInclusive();
/**
* Whether or not the upper bound of support is in the domain of the density
* function. Returns true iff {@code getSupportUpperBound()} is finite and
* {@code density(getSupportUpperBound())} returns a non-NaN, non-infinite
* value.
*
* @return true if the upper bound of support is finite and the density
* function returns a non-NaN, non-infinite value there
* @deprecated to be removed in 4.0
*/
@Deprecated
boolean isSupportUpperBoundInclusive();
/**
* Use this method to get information about whether the support is connected,
* i.e. whether all values 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
*/
void reseedRandomGenerator(long seed);
/**
* Generate a random value sampled from this distribution.
*
* @return a random value.
*/
double 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
*/
double[] sample(int sampleSize);
}