Parameter estimation in credibility theory and a statistical approach

Credibility theory which is used to determine the premium in the non-life branches of insurance is a calculation method which used for weigted estimation to make balanced allocation between past period data and recent period data. In recent years, some well known statistical models are being applied to credibility theory. One of such statistical models is ?mixed effects model? which presents itself in a wide range of applications. In line with the logical basis of credibility, the Bühlmann model being one of the classical credibility models exhibits a Bayesian approach to credibility theory. The Bühlmann-Straub model on the other hand is indeed a generalized form of the Bühlmann model. In this study, it was aimed to examine and reveal theoretically the relations between the Bühlmann-Straub model and the random effects model for the one-way classification which is a special form of the mixed effects model. Furthermore, using the real data set belonging to three groups of insureds and fifteen time periods, a loss modelling was carried out for both Bühlmann-Straub credibility model and the random effect model for the one-way classification, whereby estimations of premiums for both models were calculated. For the case of the random effect model for the one-way classification, by employing maximum likelihood and restricted maximum likelihood methods, parameter estimations were obtained and the results were comperatively interpreted. In addition, Premium values estimations were estimated by simulation method for both vii Bühlmann-Straub model and random effect model for the one-way classification by using different insured groups and different time periods and also by assuming different distributions and different distribution parameters.