A JUSTIFICATION OF SOME COMMON LAWS OF MORTALITY

Abstract

Tm~ objectives of this paper are twofold. The first one is to introduce the modem concepts and definitions of the statistical subject of life testing and to tie them in with the corresponding concepts of actuarial science. The second half of the paper presents a justification of some common laws of mortality (Gompertz's, Makeham's I, Makeham's II), and also gives a very general form of a mortality law that may prove useful. Let F(x) be a life cumulative distribution function for some element under consideration. F(x) is thus the probability that this element fails before reaching age x. Associated with F(x) is a life density function, f(x) = dF(x)/dx and a failure rate at age x, #(x) = f(x)/[1 -- F(x)]. From the equation, [1 -F (x) ] ~,(x),ax = f (x)ZXx, (1)

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