Abstract:
e Poisson regression model is a commonly used statistical
method for analyzing the count response variable [1]. One
disadvantage of this model is that it is an overdispersion
issue that is common in the real-world applications of actuarial,
engineering, biomedical, and economic sciences. e
overdispersion occurs when the conditional variance of the
count response variable exceeds the conditional mean of the
count response variable. In this context, the index of dispersion
(variance-to-mean ratio) is greater than one. To
tackle this issue in the Poisson regression model, researchers
have proposed several mixed Poisson regression models. e
standard mixed Poisson distribution is obviously the negative
binomial (NB)/Poisson-gamma regression model introduced
by Greenwood and Yule [2]. However, the NB
distribution fails to t well for a count data with a higher
value of the index of dispersion and long right-tail behavior.
en, the regression model based on NB is not a good choice
for such a count response variable. As an alternative to the
NB regression model, several mixed Poisson regression
models are in the literature. However, most of the probability
mass functions (pmfs) of these mixed Poisson distributions
are not in an explicit form. Some notable
examples of such regression models are the Poisson-Inverse
Gaussian regression model [3] and the Poisson-Inverse
gamma regression model [4]. is algebraic intractability in
such distributions leads to computational complexity, and
their regression models are limited in practice.
