On some compound distributions with Borel summands

H. Finner, P. Kern and M. Scheer

Insurance: Mathematics and Economics, 2015, vol. 62, issue C, 234-244

Abstract: The generalized Poisson distribution is well known to be a compound Poisson distribution with Borel summands. As a generalization we present closed formulas for compound Bartlett and Delaporte distributions with Borel summands and a recursive structure for certain compound shifted Delaporte mixtures with Borel summands. Our models are introduced in an actuarial context as claim number distributions and are derived only with probabilistic arguments and elementary combinatorial identities. In the actuarial context related compound distributions are of importance as models for the total size of insurance claims for which we present simple recursion formulas of Panjer type.

Keywords: Generalized Poisson distribution; Delaporte distribution; Claim number distribution; Lagrangian probability distribution; Recursive evaluation; Aggregate claim distribution; Panjer recursion; Multinomial Abel identity (search for similar items in EconPapers)
Date: 2015
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Persistent link: https://EconPapers.repec.org/RePEc:eee:insuma:v:62:y:2015:i:c:p:234-244

DOI: 10.1016/j.insmatheco.2015.03.012

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