Normal–Poisson distribution as a lifetime of a series system

In this paper, we introduce a new three parameter skewed distribution. This new class which is obtained by compounding the normal and Poisson distributions, is presented as an alternative to the class of skew-normal and normal distributions, among others. Different properties of this new distribution have been investigated. The density and distribution functions of proposed distribution, are given by a closed expression which allows us to easily compute probabilities, moments and related measurements. Estimation of the parameters of this new model using maximum likelihood method via an EM-algorithm is given. Finally, some applications of this new distribution to real data are given