On the nature of Phase-Type Poisson distributions
  Matrix-form Poisson probability distributions were recently introduced as one matrix generalization of Panjer distributions. We show in this paper that under the constraint that their representation is to be nonnegative, they have a physical interpretation as extensions of PH distributions, and we name this restricted family Phase-type Poisson. We use our physical interpretation to construct an EM algorithm-based estimation procedure. 
Sophie Hautphenne, Guy Latouche, Giang Nguyen
math.PR