smile.stat.distribution.ExponentialFamily Maven / Gradle / Ivy
/******************************************************************************
* Confidential Proprietary *
* (c) Copyright Haifeng Li 2011, All Rights Reserved *
******************************************************************************/
package smile.stat.distribution;
/**
* The exponential family is a class of probability distributions sharing
* a certain form. The normal, exponential, gamma, chi-square, beta, Weibull
* (if the shape parameter is known), Dirichlet, Bernoulli, binomial,
* multinomial, Poisson, negative binomial, and geometric distributions
* are all exponential families. The family of Pareto distributions with
* a fixed minimum bound form an exponential family.
*
* The Cauchy, Laplace, and uniform families of distributions are not
* exponential families. The Weibull distribution is not an exponential
* family unless the shape parameter is known.
*
* The purpose of this interface is mainly to define the method M that is
* the Maximization step in the EM algorithm. Note that distributuions of exponential
* family has the close-form solutions in the EM algorithm. With this interface,
* we may allow the mixture contains distributions of different form as long as
* it is from exponential family.
*
* @see ExponentialFamilyMixture
* @see DiscreteExponentialFamily
* @see DiscreteExponentialFamilyMixture
*
* @author Haifeng Li
*/
public interface ExponentialFamily {
/**
* The M step in the EM algorithm, which depends the specific distribution.
*
* @param x the input data for estimation
* @param posteriori the posteriori probability.
* @return the (unnormalized) weight of this distribution in the mixture.
*/
public Mixture.Component M(double[] x , double[] posteriori);
}