The purpose of this thesis is to show how the theory and practice of credibility can bene t statistical modeling. The task was, fundamentally, to derive models that could provide the best estimate of the losses for any given class and also to assess the variability of the losses, both from a class perspective as well as from an aggregate perspective. The model tting and diagnostic tests will be carried out using standard statistical packages. A case study that predicts the number of deaths due to cancer is considered, utilizing data furnished by the Colorado Department of Public Health and Environment. Several credibility models are used, including Bayesian, B uhlmann and B uhlmann-Straub approaches, which are useful in a wide range of actuarial applications.

Credibility theory is widely used in insurance. It is included in the examination of the Society of Actuaries and in the construction and evaluation of actuarial models. In particular, the Buhlmann credibility model has played a fundamental role in both actuarial theory and practice. It provides a mathematical rigorous procedure for deciding how much credibility should be given to the actual experience rating of an individual risk relative to the manual rating common to a particular class of risks. However, for any selected risk, the Buhlmann model assumes that the outcome random variables in both experience periods and future periods are independent and identically distributed. In addition, the Buhlmann method uses sample mean-based estimators to insure the selected risk, which may be a poor estimator of future costs if only a few observations of past events (costs) are available. We present an extension of the Buhlmann model and propose a general method based on a linear combination of both robust and efficient estimators in a dependence framework. The performance of the proposed procedure is demonstrated by Monte Carlo simulations.