Bayesian and Bühlman Credibility in Collective Distributions

Credibility theory is a statistical tool for calculating the next period premium based on the insured’s historical experience. Each contract is defined based on a risk parameter. In this paper, a risk parameter for each policyholder is assumed and a model for calculating credibility premium and bayesian premium based on both frequency and serevity of losses is examined. The distribution of total severities of claims based on frequency, is an infinite mixed distribution. Finally, by considering prior gamma distribution for risk parameter, the credibility and Bayesian premium are calculated.