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* * This program and the accompanying materials are made available under the
* * terms of the Apache License, Version 2.0 which is available at
* * https://www.apache.org/licenses/LICENSE-2.0.
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* * See the NOTICE file distributed with this work for additional
* * information regarding copyright ownership.
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* * SPDX-License-Identifier: Apache-2.0
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package org.nd4j.linalg.api.rng.distribution;
import org.apache.commons.math3.exception.NumberIsTooLargeException;
import org.apache.commons.math3.exception.OutOfRangeException;
import org.nd4j.linalg.api.ndarray.INDArray;
/**
* A probability distribution
*
* @author Adam Gibson
*/
public interface Distribution {
/**
* 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
*
* inf{x in R | P(X<=x) >= p} for {@code 0 < p <= 1},inf{x in R | P(X<=x) > 0} for {@code p = 0}.
*
* @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 org.apache.commons.math3.distribution.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
* inf {x in R | P(X <= x) > 0}.
*
* @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
* inf {x in R | P(X <= x) = 1}.
*
* @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
*/
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
*/
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(long sampleSize);
/**
* Sample the given shape
*
* @param shape the given shape
* @return an ndarray with random samples
* from this distribution
*/
INDArray sample(int[] shape);
INDArray sample(long[] shape);
/**
* Fill the target array by sampling from the distribution
*
* @param target target array
* @return an ndarray with random samples from this distribution
*/
INDArray sample(INDArray target);
}