smile.stat.distribution

Interface ExponentialFamily

All Known Implementing Classes:

BetaDistribution, ChiSquareDistribution, ExponentialDistribution, GammaDistribution, GaussianDistribution

public interface ExponentialFamily

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 distributions 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 Also:

ExponentialFamilyMixture, DiscreteExponentialFamily, DiscreteExponentialFamilyMixture

Method Summary

Modifier and Type	Method and Description
Mixture.Component	M(double[] x, double[] posteriori) The M step in the EM algorithm, which depends the specific distribution.

Method Detail

M

Mixture.Component M(double[] x,
                    double[] posteriori)

The M step in the EM algorithm, which depends the specific distribution.

Parameters:

x - the input data for estimation

posteriori - the posteriori probability.

Returns:

the (unnormalized) weight of this distribution in the mixture.