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

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AuteurTOVISSODE, FREDERIC CHENANGNON
AuteurHONFO, SEWANOU HERMANN
AuteurDOUMATE, TELE JONAS
AuteurGLELE KAKAI, ROMAIN LUCAS
Date d'ajout2026-06-02T16:06:57Z
Date de disponibilite2026-06-02T16:06:57Z
Date de publication2021
ResumeMost 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 overdispersion). 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.
DOI10.3390/math9050555
Autre identifiantBECDB-11202
URIhttps://dspace.uac.bj/handle/123456789/9858
Languefr
Fait partie deMultidisciplinary Digital Publishing Institute/Mathematics
Sujetflexible count models
Sujetbalanced gamma distribution
SujetJensen–Shannon divergence
Sujetlatent
Sujetequidispersion
TitreOn the Discretization of Continuous Probability Distributions Using a Probabilistic Rounding Mechanism
TypeArticle

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