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.