Chapter 1: Introduction

It is in human nature to try and understand the physical and natural phenomena that occur around us. For example, all of us know that death is a certainty and that it is only the time of death that is not known beforehand. People have tried to understand the time of death as much as possible, by quantifying the chances of this event at various ages. In the mid-nineteenth century, William Guy published a series of articles (see e.g. Guy, 1859) on comparative studies of the duration of life among persons of different professions. Figure 1.1 depicts a part of the age-at-death data published by him, where the deceased person’s profession has been classified into eight categories: ‘historians’, ‘poets’, ‘painters’, ‘musicians’, ‘mathematicians and astronomers’, ‘chemists and natural philosophers’, ‘naturalists’ and ‘engineers, architects and surveyors’. Despite the variation in ages at death within each category, it would be interesting to know whether people in these various professions generally live for the same duration. For instance, do mathematicians live significantly longer than poets or historians? This is not merely a matter of casual curiosity. Today actuaries routinely classify potential customers for life insurance by various characteristics that are perceived to have a bearing on the hazard of death. Since it is very difficult to identify a large group of people exactly matching the profile of a specific customer, we look for a broader picture. We seek to describe the probable lifetimes of individuals through a mathematical model that is applicable for the entire set of data, covering all the categories and other relevant characteristics that might affect a lifetime…