The exponentiated exponential Poisson distribution revisited

The main aim of this article is to characterize and investigate the three parameter exponentiated exponential Poisson probability distribution EEP(α, β, λ) by giving explicit closed form expressions for its characteristic function φξ(t) and moment generating function Mξ(t), and finally, to show that the existing series and integral form expressions for positive integer order moments Eξ , ν ∈ N are in fact valid for all ν > 1− α, α > 0.