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On construction and simulation of count data models

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  • Hagmark, Per-Erik

Abstract

The mean–variance range and the shape flexibility are important measures of the applicability of a count data model. This paper develops a method for constructing nonnegative integer-valued random variables with any interval domain, any theoretically possible mean–variance pair, and different shapes. The basic tool is a simple mean-preserving discretization procedure for random variables. Two corresponding variate generation algorithms are derived, and shown to be comparable to the alias method. As an application, our method enables production of count data models with full under- and over-dispersion flexibility and desired shape.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:matcom:v:77:y:2008:i:1:p:72-80
    DOI: 10.1016/j.matcom.2007.01.037
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    References listed on IDEAS

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    1. Faddy, M. J., 1996. "Modelling and analysis of count data using a renewal process," Statistics & Probability Letters, Elsevier, vol. 31(2), pages 129-132, December.
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    Cited by:

    1. Chénangnon Frédéric Tovissodé & Sèwanou Hermann Honfo & Jonas Têlé Doumatè & Romain Glèlè Kakaï, 2021. "On the Discretization of Continuous Probability Distributions Using a Probabilistic Rounding Mechanism," Mathematics, MDPI, vol. 9(5), pages 1-17, March.
    2. Grzesiek, Aleksandra & Połoczański, Rafał & Kumar, Arun & Wyłomańska, Agnieszka, 2021. "Moment-based estimation for parameters of general inverse subordinator," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 575(C).
    3. 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.
    4. Hagmark, Per-Erik, 2009. "A new concept for count distributions," Statistics & Probability Letters, Elsevier, vol. 79(8), pages 1120-1124, April.

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