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Statistical distributions library (in statu nascendi)
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/*
* Copyright 2013 SPZ
*
* Licensed 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 math.stats.distribution;
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 #cdf(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 pdf(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 cdf(double x);
/**
* 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
*/
double[] sample(int sampleSize);
/**
* Use this method to get the the mean of this distribution.
*
* @return the mean or {@code Double.NaN} if it is not defined
*/
double mean();
/**
* Use this method to get the variance of this distribution.
*
* @return the variance (possibly {@code Double.POSITIVE_INFINITY} as for
* certain cases in {@link StudentT}) or {@code Double.NaN} if it is
* not defined
*/
double variance();
/**
* For a random variable {@code X} whose values are distributed according to
* this distribution, this method returns {@code P(x0 < X <= x1)}.
*
* @param x0
* Lower bound (excluded).
* @param x1
* Upper bound (included).
* @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}.
*
* The default implementation uses the identity
* {@code P(x0 < X <= x1) = P(X <= x1) - P(X <= x0)}
*/
double probability(double x0, double x1);
}
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