A note on the discretization of natural exponential families on the real line View Full Text


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Article Info

DATE

2022-03-20

AUTHORS

Shaul K. Bar-Lev, Gérard Letac

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. More... »

PAGES

1-8

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Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/s00184-022-00863-4

DOI

http://dx.doi.org/10.1007/s00184-022-00863-4

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1146429453


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