Find the survival functions for the Gompertz–Makeham andWeibull laws in Example 3.1-6.

Example 3.1-6.

Over the years, there has been a great deal of interest in finding analytical representations for survival functions of “real” people. Such attempts were based on the belief that the duration of human life is subject to some universal laws. These laws, if any, have not been found yet, but some good approximations of real survival functions were suggested, and these approximations were given in terms of forces of mortality.

The first approximation is referred to as the Gompertz–Makeham law and consists in the presentation μ_GM(x) =Be^αx+A, where A, B, and α are parameters which may be estimated basing on statistical data.