Estimation, Evaluation, and Selection of Actuarial Models

2 CHAPTER 1. INTRODUCTION
Exercises are scattered throughout this Note. Those marked with (*) have appeared on either a
past Part 4 Examination (from those given in May and November 2000 and May 2001) or Part 160
Examination of the Society of Actuaries. Solutions to these exercises can be found in Appendix A.
When named parametric distributions are used, the parameterizations used are those from
Appendices A and B of Loss Models. TheywillbereferredtoasLMA and LMB in this Note.
In order to solve many of the problems in this Note, it will be necessary to either solve equations
(either one equation with one unknown, or two equations with two unknowns) or maximize functions
of several variables. At the examination, you can count on being given problems that can be solved
on the calculator. In real life, that is not always the case. Some of the examples and exercises
cannot be done in any reasonable amount of time by hand. For those, solutions were obtained
by using features of Microsoft Excel TM . Appendix B provides information about using Excel for
solving equations and for maximization.
Because maximization programs have different degrees of accuracy, you may obtain answers
to the examples and exercises that differ slightly from those produced by the author. Do not be
concerned. Also, when the author was calculating answers, he often entered rounded answers from
intermediate answers and then used them to get the final answer. Your answers may differ slightly
if you carry more digits in your intermediate work.
The author is grateful to the many people who reviewed earlier drafts of this Note. Special
thanks to Clive Keatinge who, in addition to providing general and specific guidance, checked every
calculation and problem solution. I remain responsible for what errors may still exist. Comments,
suggestions, or corrections can be e-mailed to me at stuart.klugman@drake.edu