Joint modelling of the total amount and the number of claims by conditionals
Sarabia, José María
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 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.
Classical collective model Hierarchical model Conditionally specified distributions Tweedie's distribution
In order to set up a list of libraries that you have access to,
you must first login
or sign up.
Then set up a personal list of libraries from your profile page by
clicking on your user name at the top right of any screen.