Joint modelling of the total amount and the number of claims by conditionals
In the risk theory context, let us consider the classical collective model. The aim of this paper is to obtain a flexible bivariate joint distribution for modelling the couple (S,N), where N is a count variable and S=X1+...+XN is the total claim amount. A generalization of the classical hierarchical model, where now we assume that the conditional distributions of SN and NS belong to some prescribed parametric families, is presented. A basic theorem of compatibility in conditional distributions of the type S given N and N given S is stated. Using a known theorem for exponential families and results from functional equations new models are obtained. We describe in detail the extension of two classical collective models, which now we call PoissonGamma and the PoissonBinomial conditionals models. Other conditionals models are proposed, including the PoissonLognormal conditionals distribution, the GeometricGamma conditionals model and a model with inverse Gaussian conditionals. Further developments of collective risk modelling are given.
Year of publication: 
2008


Authors:  Sarabia, José María ; Guillén, Montserrat 
Published in: 
Insurance: Mathematics and Economics.  Elsevier, ISSN 01676687.  Vol. 43.2008, 3, p. 466473

Publisher: 
Elsevier 
Keywords:  Classical collective model Hierarchical model Conditionally specified distributions Tweedie's distribution 
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