Families of power series distributions,with particular reference to the Lerch family

The paper revisits the concept of a power series distribution by defining its series function, its power parameter, and hence its probability generating function. Realization that the series function for a particular distribution is a special case of a recognized mathematical function enables distributions to be classified into families. Examples are the generalized hypergeometric family and the q-series family, both of which contain generalizations of the geometric distribution. The Lerch function (a third generalization of the geometric series) is the series function for the Lerch family. A list of distributions belonging to the Lerch family is provided.