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On the nature of Phase-type Poisson distributions

Published online by Cambridge University Press:  05 November 2013

Sophie Hautphenne ,
Guy Latouche  and
Giang T. Nguyen
Sophie Hautphenne
Affiliation:
The University of Melbourne, Department of Mathematics and Statistics, Victoria 3010, Australia
Guy Latouche
Affiliation:
Université libre de Bruxelles, Département d'Informatique, CP 212, Boulevard du Triomphe, 1050 Bruxelles, Belgium
Giang T. Nguyen*
Affiliation:
The University of Adelaide, School of Mathematical Sciences, SA 5005, Australia
*
*Correspondence to: Giang T. Nguyen, The University of Adelaide, School of Mathematical Sciences, SA 5005, Australia. E-mail: giang.nguyen@adelaide.edu.au
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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.

Keywords

91B30secondary 65Q3062P05.Panjer's algorithmgeneralized Panjer distributionscompound distributionsEM algorithmminimal variancePH-Poisson.
Type
Papers
Information
Annals of Actuarial Science , Volume 8 , Issue 1 , March 2014 , pp. 79 - 98
Copyright
Copyright © Institute and Faculty of Actuaries 2013 

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