/*
* 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.math4.distribution;
import org.apache.commons.math4.exception.NumberIsTooLargeException;
import org.apache.commons.math4.exception.OutOfRangeException;
import org.apache.commons.rng.UniformRandomProvider;
/**
* 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);
/**
* 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}
*
* @since 4.0, was previously named cumulativeProbability
*/
double probability(double x0, double x1) throws NumberIsTooLargeException;
/**
* 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);
/**
* Returns the natural logarithm of 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. Note that
* due to the floating point precision and under/overflow issues, this method will
* for some distributions be more precise and faster than computing the logarithm of
* {@link #density(double)}.
*
* @param x the point at which the PDF is evaluated
* @return the logarithm of the value of the probability density function at point {@code x}
* @since 4.0
*/
double logDensity(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);
/**
* 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}} for {@code 0 < p <= 1},</li>
* <li>{@code inf{x in R | P(X<=x) > 0}} 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}}.</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}}.</p>
*
* @return upper bound of the support (might be
* {@code Double.POSITIVE_INFINITY})
*/
double getSupportUpperBound();
/**
* 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();
/**
* Creates a sampler.
*
* @param rng Generator of uniformly distributed numbers.
* @return a sampler that produces random numbers according this
* distribution.
*/
Sampler createSampler(UniformRandomProvider rng);
/**
* Sampling functionality.
*/
interface Sampler {
/**
* Generates a random value sampled from this distribution.
*
* @return a random value.
*/
double sample();
}
}