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On the Discretization of Continuous Probability Distributions Using a Probabilistic Rounding Mechanism

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  • Chénangnon Frédéric Tovissodé

    (Laboratoire de Biomathématiques et d’Estimations Forestières, Université d’Abomey-Calavi, Abomey-Calavi, Benin)

  • Sèwanou Hermann Honfo

    (Laboratoire de Biomathématiques et d’Estimations Forestières, Université d’Abomey-Calavi, Abomey-Calavi, Benin
    These authors contributed equally to this work.)

  • Jonas Têlé Doumatè

    (Laboratoire de Biomathématiques et d’Estimations Forestières, Université d’Abomey-Calavi, Abomey-Calavi, Benin
    Faculté des Sciences et Techniques, Université d’Abomey-Calavi, Abomey-Calavi, Benin
    These authors contributed equally to this work.)

  • Romain Glèlè Kakaï

    (Laboratoire de Biomathématiques et d’Estimations Forestières, Université d’Abomey-Calavi, Abomey-Calavi, Benin)

Abstract

Most existing flexible count distributions allow only approximate inference when used in a regression context. This work proposes a new framework to provide an exact and flexible alternative for modeling and simulating count data with various types of dispersion (equi-, under-, and over-dispersion). The new method, referred to as “balanced discretization”, consists of discretizing continuous probability distributions while preserving expectations. It is easy to generate pseudo random variates from the resulting balanced discrete distribution since it has a simple stochastic representation (probabilistic rounding) in terms of the continuous distribution. For illustrative purposes, we develop the family of balanced discrete gamma distributions that can model equi-, under-, and over-dispersed count data. This family of count distributions is appropriate for building flexible count regression models because the expectation of the distribution has a simple expression in terms of the parameters of the distribution. Using the Jensen–Shannon divergence measure, we show that under the equidispersion restriction, the family of balanced discrete gamma distributions is similar to the Poisson distribution. Based on this, we conjecture that while covering all types of dispersions, a count regression model based on the balanced discrete gamma distribution will allow recovering a near Poisson distribution model fit when the data are Poisson distributed.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:5:p:555-:d:511924
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    References listed on IDEAS

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