# Multiplication of Hazard in Gompertz-Makeham Distributions

Multiplication of Hazard in Gompertz-Makeham Distributions

There are frequently no published survival tables for particular subsets of a population. What actuaries will then sometimes do in order to obtain needed figures such as net single premiums or reserves is to assume that the hazard faced by that subset is, for all periods in a person's lifetime, a constant multiple of the hazard published in an accepted table. Thus, an actuary might assume (or have data showing) that the hazard for male diabetic smokers is 2.3 times the hazard for males published in the 2001 Commissioners Standard Ordinary (CSO) mortality table.

This Demonstration permits you to construct a baseline mortality table from the Gompertz–Makeham family by specifying the mean and standard deviation of life expectancy at birth. You then create a modified distribution by selecting an inception age—a point in time such as the purchase of a life insurance policy at which you know the individual is alive—and changing the hazard multiple. You then choose various visualizations (such as survival functions and probability density functions) of the resulting statistical distribution. The Demonstration likewise computes the new mean life expectancy both from birth and from some inception point (such as the purchase of a life insurance policy) at which we know the individual is alive.