Everything points to Poisson

(Jan 16, 2018)

One recurring theme in our forthcoming book, Modelling Mortality with Actuarial Applications, is the all-pervading role of likelihoods that suggest the lurking presence of a Poisson distribution.  A popular assumption in modelling hazard rates is that the number of deaths observed at any given age is a Poisson random variable, so perhaps that might explain it?  Surprisingly, it is the other way round - it is the very nature of the data in a survival model that leads inexorably to the Poisson distribution, even if we assume no such thing.

Stripped back to basics, we observe \(n\) individuals and record our observations as:

  • The length of time \(E_i\) that the \(i\)th person was observed and alive; and
  • An indicator…

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Tags: survival data, Poisson distribution

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