## 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.

Original language | English |
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Journal | Metrika |

DOIs | |

State | Accepted/In press - 2022 |

Externally published | Yes |

### Bibliographical note

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

## Keywords

- Discretization
- General exponential family
- Natural exponential family

## ASJC Scopus subject areas

- Statistics and Probability
- Statistics, Probability and Uncertainty