Splitting models for multivariate count data

We investigate the class of splitting distributions as composition a singular multivariate distribution and univariate distribution. It will be shown that most common parametric count (multinomial, negative multinomial, hypergeometric, …) can written with separate parameters for both components, thus facilitating their interpretation, inference, study probabilistic characteristics extensions to regression models. highlight many properties deriving from compound aspect underlying algebraic properties. Parameter inference model selection are reduced two problems, preserving time space complexity base Based on this principle, we introduce several new distributions. In case multinomial distributions, conditional independence asymptotic normality estimators obtained. Mixtures models used mango tree dataset in order analyze patchiness.