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Panjer class revisited: one formula for the distributions of the Panjer (a,b,n) class

Published online by Cambridge University Press:  26 September 2022

Michael Fackler Open the ORCID record for Michael Fackler [Opens in a new window]
Michael Fackler*
Affiliation:
Actuary (DAV), Munich, Germany
*
E-mail: michael_fackler@web.de
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Abstract

The loss count distributions whose probabilities ultimately satisfy Panjer’s recursion were classified between 1981 and 2002; they split into six types, which look quite diverse. Yet, the distributions are closely related – we show that their probabilities emerge out of one formula: the binomial series. We propose a parameter change that leads to a unified, practical and intuitive, representation of the Panjer distributions and their parameter space. We determine the subsets of the parameter space where the probabilities are continuous functions of the parameters. Finally, we give an inventory of parameterisations used for Panjer distributions.

Keywords

Panjer classUnified representationDiscrete loss distributionBinomial series
Type
Original Research Paper
Information
Annals of Actuarial Science , Volume 17 , Issue 1 , March 2023 , pp. 145 - 169
Copyright
© The Author(s), 2022. Published by Cambridge University Press on behalf of Institute and Faculty of Actuaries

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