The extended Conway-Maxwell-Poisson distribution is a three-parameter laws family recently introduced as an alternative to the Poisson model for the statistical analysis of count data. It is a class of laws which generalizes at the same time the basic Katz’s model and the Conway-Maxwell-Poisson family, characterized by a dispersion index greater than, equal to or smaller than one. This property allows it to describe overdispersed and underdispersed data. In this paper, we are interested in this distribution estimation of parameters and a simulation study is made. Some numerical examples of illustration are presented.

count data, maximum likelihood, least-squares, overdispersion, underdispersion.