ContinuousDistribution.java
/*
* 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.statistics.distribution;
import java.util.stream.DoubleStream;
import org.apache.commons.rng.UniformRandomProvider;
/**
* Interface for distributions on the reals.
*/
public interface ContinuousDistribution {
/**
* 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. {@link Double#POSITIVE_INFINITY},
* {@link Double#NaN}, or the limit inferior or limit superior of the
* difference quotient.
*
* @param x Point at which the PDF is evaluated.
* @return the value of the probability density function at {@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(x0 < X <= x1)}.
* The default implementation uses the identity
* {@code P(x0 < X <= x1) = P(X <= x1) - P(X <= x0)}
*
* @param x0 Lower bound (exclusive).
* @param x1 Upper bound (inclusive).
* @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 IllegalArgumentException if {@code x0 > x1}.
*/
default double probability(double x0,
double x1) {
if (x0 > x1) {
throw new DistributionException(DistributionException.INVALID_RANGE_LOW_GT_HIGH, x0, x1);
}
return cumulativeProbability(x1) - cumulativeProbability(x0);
}
/**
* Returns the natural logarithm of the probability density function
* (PDF) of this distribution evaluated at the specified point {@code x}.
*
* @param x Point at which the PDF is evaluated.
* @return the logarithm of the value of the probability density function
* at {@code x}.
*/
default double logDensity(double x) {
return Math.log(density(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 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(X > x)}.
* In other words, this method represents the complementary cumulative
* distribution function.
*
* <p>By default, this is defined as {@code 1 - cumulativeProbability(x)}, but
* the specific implementation may be more accurate.
*
* @param x Point at which the survival function is evaluated.
* @return the probability that a random variable with this
* distribution takes a value greater than {@code x}.
*/
default double survivalProbability(double x) {
return 1.0 - cumulativeProbability(x);
}
/**
* Computes the quantile function of this distribution. For a random
* variable {@code X} distributed according to this distribution, the
* returned value is:
*
* <p>\[ x = \begin{cases}
* \inf \{ x \in \mathbb R : P(X \le x) \ge p\} & \text{for } 0 \lt p \le 1 \\
* \inf \{ x \in \mathbb R : P(X \le x) \gt 0 \} & \text{for } p = 0
* \end{cases} \]
*
* @param p Cumulative probability.
* @return the smallest {@code p}-quantile of this distribution
* (largest 0-quantile for {@code p = 0}).
* @throws IllegalArgumentException if {@code p < 0} or {@code p > 1}.
*/
double inverseCumulativeProbability(double p);
/**
* Computes the inverse survival probability function of this distribution. For a random
* variable {@code X} distributed according to this distribution, the
* returned value is:
*
* <p>\[ x = \begin{cases}
* \inf \{ x \in \mathbb R : P(X \ge x) \le p\} & \text{for } 0 \le p \lt 1 \\
* \inf \{ x \in \mathbb R : P(X \ge x) \lt 1 \} & \text{for } p = 1
* \end{cases} \]
*
* <p>By default, this is defined as {@code inverseCumulativeProbability(1 - p)}, but
* the specific implementation may be more accurate.
*
* @param p Survival probability.
* @return the smallest {@code (1-p)}-quantile of this distribution
* (largest 0-quantile for {@code p = 1}).
* @throws IllegalArgumentException if {@code p < 0} or {@code p > 1}.
*/
default double inverseSurvivalProbability(double p) {
return inverseCumulativeProbability(1 - p);
}
/**
* Gets the mean of this distribution.
*
* @return the mean.
*/
double getMean();
/**
* Gets the variance of this distribution.
*
* @return the variance.
*/
double getVariance();
/**
* Gets the lower bound of the support.
* It must return the same value as
* {@code inverseCumulativeProbability(0)}, i.e.
* \( \inf \{ x \in \mathbb R : P(X \le x) \gt 0 \} \).
*
* @return the lower bound of the support.
*/
double getSupportLowerBound();
/**
* Gets the upper bound of the support.
* It must return the same
* value as {@code inverseCumulativeProbability(1)}, i.e.
* \( \inf \{ x \in \mathbb R : P(X \le x) = 1 \} \).
*
* @return the upper bound of the support.
*/
double getSupportUpperBound();
/**
* Creates a sampler.
*
* @param rng Generator of uniformly distributed numbers.
* @return a sampler that produces random numbers according this
* distribution.
*/
Sampler createSampler(UniformRandomProvider rng);
/**
* Distribution sampling functionality.
*/
@FunctionalInterface
interface Sampler {
/**
* Generates a random value sampled from this distribution.
*
* @return a random value.
*/
double sample();
/**
* Returns an effectively unlimited stream of {@code double} sample values.
*
* <p>The default implementation produces a sequential stream that repeatedly
* calls {@link #sample sample}().
*
* @return a stream of {@code double} values.
*/
default DoubleStream samples() {
return DoubleStream.generate(this::sample).sequential();
}
/**
* Returns a stream producing the given {@code streamSize} number of {@code double}
* sample values.
*
* <p>The default implementation produces a sequential stream that repeatedly
* calls {@link #sample sample}(); the stream is limited to the given {@code streamSize}.
*
* @param streamSize Number of values to generate.
* @return a stream of {@code double} values.
*/
default DoubleStream samples(long streamSize) {
return samples().limit(streamSize);
}
}
}