Hautphenne, S.Latouche, G.Nguyen, G.2017-01-172017-01-172014Annals of Actuarial Science, 2014; 8(1):79-981748-49951748-5002http://hdl.handle.net/2440/103297Matrix-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.en© Institute and Faculty of Actuaries 2013Panjer’s algorithm; generalized Panjer distributions; compound distributions; EM algorithm; minimal variance; PH-PoissonJournal article003000802310.1017/S174849951300012281524