On some compound distributions with Borel summands
| Autor: | Peter Kern, M. Scheer, H. Finner |
|---|---|
| Rok vydání: | 2014 |
| Předmět: |
Statistics and Probability
Economics and Econometrics Generalization Probability (math.PR) Context (language use) Panjer recursion Type (model theory) Poisson distribution Combinatorics symbols.namesake Compound Poisson distribution Simple (abstract algebra) symbols Zero-inflated model FOS: Mathematics 60E05 Statistics Probability and Uncertainty Mathematics - Probability Mathematics |
| DOI: | 10.48550/arxiv.1409.3113 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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