Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5076534 | Insurance: Mathematics and Economics | 2015 | 27 Pages |
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.
Related Topics
Physical Sciences and Engineering
Mathematics
Statistics and Probability
Authors
H. Finner, P. Kern, M. Scheer,