In this paper the mixed Poisson regression model is discussed and a Poisson Birnbaum-Saunders regression model is introduced consider the over-dispersion. The Birnbaum-Saunders distribution is the mixture of two the generalized inverse Gaussian distributions, therefore it can be considered as an extension of traditional models. Our proposed model has less dimensional parameter space than the Poisson- generalized inverse Gaussian regression model. We also show that the proposed model has a closed form for likelihood function and we obtain its moments. The EM algorithm is used to estimate the parameters and its efficiency is compared with conventional models by a simulation study. An analysis of a real data is provided for more illustration.

This paper presents a new extension of Birnbaum-Saunders distribution based on skew Laplace distribution. Some properties of the new distribution are studied and the EM-type estimators of the parameters with their standard errors are obtained. Finally, we conduct a simulation study and illustrate our distribution by considering two real data example.