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

Author

Listed:
  • Shaul K. Bar-Lev

    (Holon Institute of technology)

  • Gérard Letac

    (Institut de Mathématiques de Toulouse, Université Paul Sabatier)

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.

Suggested Citation

  • Shaul K. Bar-Lev & Gérard Letac, 2023. "A note on the discretization of natural exponential families on the real line," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 86(1), pages 83-90, January.
    • Handle: RePEc:spr:metrik:v:86:y:2023:i:1:d:10.1007_s00184-022-00863-4
    DOI: 10.1007/s00184-022-00863-4
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    References listed on IDEAS

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    1. Kokonendji, Célestin C. & Zocchi, Silvio S., 2010. "Extensions of discrete triangular distributions and boundary bias in kernel estimation for discrete functions," Statistics & Probability Letters, Elsevier, vol. 80(21-22), pages 1655-1662, November.
    2. Hagmark, Per-Erik, 2008. "On construction and simulation of count data models," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 77(1), pages 72-80.
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