2021

DOI: 10.2139/ssrn.3813246

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

Michael Fackler¹

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“…The large Table 3 below extends and enhances similar tables given in Fackler (2011) and (the better-known non-refereed version) Fackler (2009), where the parameterisations are discussed and the first all-in-one model is introduced.…”

Section: Tablesupporting

confidence: 69%

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

2022

Ann. actuar. sci.

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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.

“…The large Table 3 below extends and enhances similar tables given in Fackler (2011) and (the better-known non-refereed version) Fackler (2009), where the parameterisations are discussed and the first all-in-one model is introduced.…”

Section: Tablesupporting

confidence: 69%

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

2022

Ann. actuar. sci.

View full text Add to dashboard Cite

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.

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