The Poisson distribution is often used for modeling count data (McCullagh and Nelder [1989]): 194 ff.
The CMP distribution has quickly grown in popularity because of its ability to model count data in a flexible manner.
The sum-of-Conway-Maxwell-Poissons (sCMP) class of distributions is a flexible construct for modeling count data that captures several well-known distributions as special cases: the Poisson, negative binomial, binomial, geometric, Bernoulli, and Conway-Maxwell-Poisson (CMP).
Poisson processes are commonly used to model count data (data in which the observations can take only the non-negative integer values) [11, 54] in many domains, such as modeling rare incidents in psychiatric hospitals [45], and traffic analysis [52, 55].
The popularity of the NB distribution is due largely to its ability to model count data with varying degrees of overdispersion.
Negative binomial models, which allow for the variance to differ from the mean, are often used to model count data when the data is found to be overdispersed [17].
The Poisson distribution is commonly assumed when modeling count data.
The edgeR method was specifically developed to model count data dispersion and it is designed for overdispersed RNA-seq data.
Thus, although they are widely used to model count data, Poisson GLMMs may not well be suited to types of count outcomes from specific applications.
