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Title: Bayesian robustness of the compound Poisson distribution under bidimensional prior: an application to the collective risk model
Authors: Hernandez Bastida, Agustin
Gomez Deniz, Emilio
Perez Sanchez, Jose Maria 
UNESCO Clasification: 1208 Probabilidad
1209 Estadística
Keywords: Estadística
Bayesian Robustness
Class Of Distributions
Issue Date: 2009
Publisher: 0266-4763
Journal: Journal of Applied Statistics 
Abstract: The distribution of the aggregate claims in one year plays an important role in Actuarial Statistics for computing, for example, insurance premiums when both the number and size of the claims must be implemented into the model. When the number of claims follows a Poisson distribution the aggregated distribution is called the compound Poisson distribution. In this article we assume that the claim size follows an exponential distribution and later we make an extensive study of this model by assuming a bidimensional prior distribution for the parameters of the Poisson and exponential distribution with marginal gamma.This study carries us to obtain expressions for net premiums, marginal and posterior distributions in terms of some well-known special functions used in statistics. Later, a Bayesian robustness study of this model is made. Bayesian robustness on bidimensional models was deeply treated in the 1990s, producing numerous results, but few applications dealing with this problem can be found in the literature.
ISSN: 0266-4763
DOI: 10.1080/02664760802510059
Source: Journal Of Applied Statistics[ISSN 0266-4763],v. 36 (8), p. 853-869, (2009)
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