The cascade model of mortality

(Apr 25, 2016)

It is often instructive to look at mortality models where the parameters have an underlying meaning in a process. One interesting example of this is the cascade model of mortality, described by Izsak & Gavrilov (1995). Under the cascade model an individual in state \(n\) can do one of two things:

  1. Move to state \(n+1\) with intensity \(\lambda_0+n\lambda\), or
  2. Move to the dead state with intensity \(\mu_0+n\mu\).

where \(\lambda_0>0\) is the background rate of transition from one state to the next, \(\lambda>0\) is the additional rate of transition, \(\mu_0>0\) is the background rate of mortality and \(\mu>0\) is the additional rate of mortality.  This is illustrated in Figure 1.

Figure…

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Tags: cascade process, Makeham-Beard model, multi-state model

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