Loss Models, 5th Edition

10Introduction to Mathematical Statistics

10.1 Introduction and Four Data Sets

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 you have 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 13. Bayesian methodology also provides the basis for the credibility methods covered in Chapter 16.

To see the need for methods of statistical inference, consider the case where your supervisor needs a model for basic dental payments. One option is to simply announce the model. You proclaim that it is the lognormal distribution with and . (The many decimal places are designed to give your proclamation an aura of precision.) When your supervisor, 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 ...