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2011•Anales del Instituto de Actuarios EspañolesOpen access

Panjer Class United: one formula for the probabilities of the Poisson, Binomial, and Negative Binomial distribution

Michael Flacker

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Abstract

This paper gives a formula representing all discrete loss distributions of the Panjer class (Poisson, Binomial, and Negative Binomial) in one. Further it provides an overview of the many Negative Binomial variants used by actuaries.

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What this paper is about

This paper gives a formula representing all discrete loss distributions of the Panjer class (Poisson, Binomial, and Negative Binomial) in one. Further it provides an overview of the many Negative Binomial variants used by actuaries.

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OpenAlex reports 5 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available abstract

This paper gives a formula representing all discrete loss distributions of the Panjer class (Poisson, Binomial, and Negative Binomial) in one. Further it provides an overview of the many Negative Binomial variants used by actuaries.

Key concepts: Negative multinomial distribution, Negative binomial distribution, Poisson binomial distribution, Continuity correction, Binomial distribution, Mathematics, Poisson distribution, Count data

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