Loss Models, 5th Edition

18Empirical Bayes Parameter Estimation

18.1 Introduction

In Chapter 17, a modeling methodology was proposed that suggests the use of either the Bayesian or the credibility premium as a way to incorporate past data into the prospective rate. There is a practical problem associated with the use of these models that has not yet been addressed.

In the examples seen so far, we have been able to obtain numerical values for the quantities of interest because the input distributions and have been assumed to be known. These examples, while useful for illustration of the methodology, can hardly be expected to accurately represent the business of an insurance portfolio. More practical models of necessity involve the use of parameters that must be chosen to ensure a close agreement between the model and reality. Examples of this include: the Poisson–gamma model (Example 17.1), where the gamma parameters and need to be selected; or the Bühlmann or Bühlmann–Straub parameters , and a. The assignment ...