On the nature of Phase-Type Poisson distributions

TL;DR

This paper introduces Phase-type Poisson distributions as a nonnegative matrix generalization of Panjer distributions, providing a physical interpretation and an EM algorithm for parameter estimation.

Contribution

It defines the restricted family of Phase-type Poisson distributions with a physical interpretation and develops an EM algorithm for their estimation.

Findings

Phase-type Poisson distributions extend PH distributions with nonnegative matrix representations.

The paper provides an EM algorithm for parameter estimation of these distributions.

The interpretation links these distributions to physical processes.

Abstract

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.