A class of Poisson--multiplication distributions for modeling count data with over-dispersion
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：Guoliang Tian (Southern University of Science Technology)
： 2025-11-21 09:00
：Conference Room S207 at Experiment Building at Haiyun Campus
Speaker：Guoliang Tian (Southern University of Science and Technology)
Time：2025-11-21 9:00
Location：Conference Room S207 at Experiment Building at Haiyun Campus
Abstract:
Count data with over-dispersion widely appears in natural sciences (e.g., biology and physics), social sciences and economics, medicine and health sciences, engineering and technology. Although the gamma-Poisson (mixture), generalized Poisson and double Poisson distributions were developed to address the issue of over-dispersion in count data, the number of existing discrete distributions is insufficient to meet the needs of fitting such complex count data. By decomposing the variance parameter in the Poisson distribution, in this paper, we propose a class of Poisson-multiplication (PM) distributions or a general Poisson-multiplication (Ge-PM) distribution with a natural statistical interpretation. We provide five specific PM distributions that can be used to model count data with over-dispersion. In the Ge-PM framework, we also develop five PM mean regression models for analyzing count data with covariates. We apply the normalized expectation-maximization (N-EM) algorithm aided by the upper--crossing/solution (US) algorithm to calculate maximum likelihood estimates of parameters. Simulation studies on model comparisons showed that the proposed five PM models extend the application scope of existing models, and a German health care demand data set is analyzed to illustrate the proposed methods.
