### 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…