R Programming for Actuarial Science

18 Assessing the Suitability of Mortality Models: Statistical Tests

Peter McQuire

18.1 Introduction

library(stats4)
library(tseries)

In the previous chapter we undertook the process of determining a best-fitting, smooth function which represented our mortality rates given a particular set of mortality data. The objective of this chapter is to test these proposed rates to assess whether they are suitable, that is, do they represent the true mortality rates of the population from which the mortality data is obtained? We analyse each proposal using a series of statistical tests and thus decide on their suitability. We then consider which set of rates, out of all those which have “passed” our tests, is the most suitable.

Therefore, this chapter continues from the previous one where we fitted potentially suitable parametric models, such as the Gompertz model, to our mortality data. Here, we assess the suitability of the proposed model, and compare it with others (see Section 18.6).

We will be assessing proposed mortality rates produced from two graduation methods in this chapter:

• adjusting a standard mortality table which has previously been independently tested and verified;
• determine a suitable parametric model (this methodology was the subject of Chapter 17).

In reality, however, the actuary is first likely to adopt a different approach by testing the suitability of various standard mortality rate tables which currently exist in the literature, thus potentially saving us ...