### The age pattern of mortality

#### (Feb 1, 2016)

Heligman and Pollard published a famous paper in 1980 with the title "The age pattern of mortality".  In their paper they proposed an additive, three-component model of mortality:

$q_x/p_x = f_I(x) + f_S(x) + f_A(x)$

where $$f_I(x)$$ describes infant and child mortality, $$f_S(x)$$ is underlying mortality (senescence) for the whole of life and $$f_A(x)$$ is the "accident hump'".  Here $$q_x$$ is the probability of dying within one year for a person aged $$x$$ exactly, $$p_x = 1 - q_x$$.  These three components reflect almost universal patterns in human mortality and, on the log scale, Heligman and Pollard's components are:

1. $$\log f_I(x) = A(x+B)^C$$, i.e. a power of $$x$$,
2. $$\log f_S(x) = G + Hx$$, i.e.…