Loss Models: From Data to Decisions, 4th Edition

10.1 Introduction

Before studying empirical models and then parametric models, we review some concepts from mathematical statistics. Mathematical statistics is a broad subject that includes many topics not covered in this chapter. For those topics that are covered, it is assumed that the reader has had some prior exposure. The topics of greatest importance for constructing actuarial models are estimation and hypothesis testing. Because the Bayesian approach to statistical inference is often either ignored or treated lightly in introductory mathematical statistics texts and courses, it receives more in-depth coverage in this text in Chapter 15. Bayesian methodology also provides the basis for the credibility methods covered in Chapter 17.

To see the need for methods of statistical inference, consider the case where your boss needs a model for basic dental payments. One option is to simply announce the model. You proclaim that it is the lognormal distribution with μ = 5.1239 and σ = 1.0345 (The many decimal places are designed to give your proclamation an aura of precision.). When your boss, or a regulator, or an attorney who has put you on the witness stand asks you how you know that to be so, it will likely not be sufficient to answer that “I just know these things” or “trust me, I am a trained statistician” or “it is too complicated, you wouldn’t understand.” It may not even be sufficient to announce that your friend at Gamma Dental uses that model.

An alternative is to collect ...