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.

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Tags: Heligman-Pollard model, accident hump, shape penalty, smoothness penalty

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