Reading notes on Vaupel, Manton, Stallard 1979, Demography, The impact of heterogeneity in individual frailty on the dynamics of mortality.
This is really a classic paper to study the effect of heterogeneity on aging.
VMS79 defined frailty $z$ as $\mu(z) = z \mu$, where $mu$ is the mortality rate (termed force of mortality in the paper).
VMS79 used a gamma distribution to model frailty. They found that frailty among the survivors at age $x$ is gamma distributed with the same shape parameter $k$ at birth. The second parameter is
$\lamda(x) = \lambda + H(x)$.
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