کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
5077321 | 1374125 | 2008 | 8 صفحه PDF | دانلود رایگان |
![عکس صفحه اول مقاله: Joint modelling of the total amount and the number of claims by conditionals Joint modelling of the total amount and the number of claims by conditionals](/preview/png/5077321.png)
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+â¯+XN is the total claim amount. A generalization of the classical hierarchical model, where now we assume that the conditional distributions of S|N and N|S 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 Poisson-Gamma and the Poisson-Binomial conditionals models. Other conditionals models are proposed, including the Poisson-Lognormal conditionals distribution, the Geometric-Gamma conditionals model and a model with inverse Gaussian conditionals. Further developments of collective risk modelling are given.
Journal: Insurance: Mathematics and Economics - Volume 43, Issue 3, December 2008, Pages 466-473