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

Shaul K. Bar-Lev () and Gérard Letac ()
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Shaul K. Bar-Lev: Holon Institute of technology
Gérard Letac: Institut de Mathématiques de Toulouse, Université Paul Sabatier

Metrika: International Journal for Theoretical and Applied Statistics, 2023, vol. 86, issue 1, No 4, 83-90

Abstract: Abstract 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.

Keywords: Discretization; Natural exponential family; General exponential family; 62E10 (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s00184-022-00863-4

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