A note on the discretization of natural exponential families on the real line

Shaul K. Bar-Lev, Gérard Letac

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish
Pages (from-to)83-90
Number of pages8
Issue number1
StatePublished - Jan 2023
Externally publishedYes

Bibliographical note

Publisher Copyright:
© 2022, The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.


  • Discretization
  • General exponential family
  • Natural exponential family

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


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