Chapter Preview. This chapter introduces the reader to credibility and related regression modeling. The first section provides a brief overview of credibility theory and regression-type credibility, and it discusses historical developments. The next section shows how some well-known credibility models can be embedded within the linear mixed model framework. Specific procedures on how such models can be used for prediction and standard ratemaking are given as well. Further, in Section 9.3, a step-by-step numerical example, based on the widely studied Hachemeister's data, is developed to illustrate the methodology. All computations are done using the statistical software package R. The fourth section identifies some practical issues with the standard methodology, in particular, its lack of robustness against various types of outliers. It also discusses possible solutions that have been proposed in the statistical and actuarial literatures. Performance of the most effective proposals is illustrated on the Hachemeister's dataset and compared to that of the standard methods. Suggestions for further reading are made in Section 9.5.

Introduction

9.1.1 Early Developments

Credibility theory is one of the oldest but still most common premium ratemaking techniques in insurance industry. The earliest works in credibility theory date back to the beginning of the 20th century, when Mowbray (1914) and Whitney (1918) laid the foundation for limited fluctuation credibility theory.