The process of discretization of continuous distributions creates and provides a large set of discrete probabilistic models used in various statistical applications. The most common way of doing so is by considering the probability distribution of the integral part of a continuous random variable. In this note we explore the following problem related to the latter discretization process and pose the following question: If the family of distributions that is discretized is an exponential family on the real line, when the (integral) resulting discrete probability model also generates an exponential family? We give a complete answer to this question and provide necessary and sufficient conditions under which the discretized version of an exponential family is also an exponential family.
Bibliographical notePublisher Copyright:
© 2022, The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.
- General exponential family
- Natural exponential family
ASJC Scopus subject areas
- Statistics and Probability
- Statistics, Probability and Uncertainty