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.