Electronic Thesis and Dissertation Repository


Doctor of Philosophy


Statistics and Actuarial Sciences


David Stanford

2nd Supervisor

Amin Hassan-Zadeh

Joint Supervisor


Credibility theory provides important guidelines for insurers in the practice of experience rating. It recognizes multiple sources of risk and proposes potential premium adjustments by considering individual experiences along with the class experiences. Two popular tools in credibility theory are Bayesian and Buhlmann premium estimators. This thesis develops both models assuming a phase-type distribution of losses, following a Bayesian inference approach. A family of conjugate priors is first established accordingly. The solutions for both Bayesian and Buhlmann estimators are then obtained in explicit forms. Simulation studies are performed to evaluate each estimator individually as well as to conduct comparisons where appropriate. Mean squared errors for each estimator are computed based on different prior choices and outcomes are compared against theoretical results.