Loss Models, 5th Edition

14Construction of Empirical Models

14.1 The Empirical Distribution

The material presented here has traditionally been presented under the heading of “survival models,” with the accompanying notion that the techniques are useful only when studying lifetime distributions. Standard texts on the subject, such as Klein and Moeschberger [70] and Lawless [77], contain examples that are exclusively oriented in that direction. However, the same problems that occur when modeling lifetime occur when modeling payment amounts. The examples we present are of both types. However, the latter sections focus on special considerations when constructing decrement models. Only a handful of references are presented, most of the results being well developed in the survival models literature. If you want more detail and proofs, consult a text dedicated to the subject, such as the ones just mentioned.

In Chapter 4, models were divided into two types – data-dependent and parametric. The definitions are repeated here.

Definition 14.1

A data-dependent distribution is at least as complex as the data or knowledge that produced it, and the number of “parameters” increases as the number of data points or amount of knowledge increases.

Definition 14.2

A parametric distribution is a set of distribution functions, each member of which is determined by specifying one or more values called parameters. The number of parameters is fixed and finite.

This chapter will focus on data-dependent distributions ...