Journal of Statistics: Advances in Theory and ApplicationsAuthor's: Emilio Gómez-Déniz and Enrique Calderín-Ojeda
Pages: [53] - [70]
Received Date: August 26, 2009
Submitted by:
Premium computation in a Bayesian context requires the use of a prior
distribution that the unknown risk parameter of the likelihood follows
in the heterogeneous population. Sometimes, the Bayes premium is
expressed as a weighted sum of the sample mean and the collective
premium, known in the literature as credibility formula.
In this paper, some connections between credibility theory and
identifiability problems are reviewed and modestly extended by
identifying the prior distribution under different likelihoods by the
form of the Bayes premium, which results under appropriate likelihood
and prior distribution a credibility formula. Results under the net
premium principle for Poisson, binomial, and negative binomial
likelihood functions and under the Esscher premium principle for
Poisson likelihood function are shown. The methodology is applied to
generate a wide spectrum of discrete distributions when
non-credibility formulae appear.
Bayes, credibility, discrete distributions, identification.
