Title of article :
Bayesian robustness of the compound Poisson distribution under bidimensional prior: an application to the collective risk model
Author/Authors :
Agust?n Hern?ndez Bastidaa، نويسنده , , Emilio G?mez Dénizb* & José Mar?a Pérez S?ncheza، نويسنده ,
Issue Information :
روزنامه با شماره پیاپی سال 2009
Pages :
17
From page :
853
To page :
869
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.
Keywords :
Bayesian robustness , compound , net premium , generalized hypergeometric function , class of distributions , Bessel function
Journal title :
JOURNAL OF APPLIED STATISTICS
Serial Year :
2009
Journal title :
JOURNAL OF APPLIED STATISTICS
Record number :
712333
Link To Document :
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