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We have previously shown how survival models based around the force of mortality, μx, have the ability to use more of your data. We have also seen that attempting to use fractional years of exposure in a qx model can lead to potential mistakes. However, the Poisson distribution also uses μx, so why don't we use a Poisson model for the grouped count of deaths in each cell?
An early bath for the bathtub model
My last posting looked at why actuaries fitted survival models differently to statisticians, even though the conceptual framework for survival models is common to both disciplines.
Actuarial exceptionalism
In an earlier posting I listed some actuarial terms and their statistical equivalents (and later a short list of statistical terms and their equivalents in other fields). Using different expressions for the same concept is an unfortunate barrier to understanding across disciplines.
Why use survival models?
We and our clients much prefer to analyse mortality continuously, rather than in yearly intervals like actuaries used to do in previous centuries. Actuaries normally use μx to denote the continuous force of mortality at age x, and qx to denote the yearly rate of mortality. For any statisticians reading this, μx is the continuous-time hazard rate.
Survival models for actuarial work
The CMI recently asked for an overview note on survival models. Since this subject is of wider actuarial interest, we wanted to make this publically available. An electronic copy can be downloaded from the link on the right.
Business benefits of statistical models
In a recent meeting I was asked by a reinsurer what the advantages were of using statistical models in his business. The reinsurer knew about the greater analytical power of survival models, but he wanted more.
How much data do you need?
We have written before about how survival models make better use of available data.
Lost in translation
Actuaries have a long-standing habit of using different terminology to statisticians. This page lists some common terms used by actuaries in mortality work and their "translation" for a non-actuarial audience. The terms and notation are those used by actuaries in the UK, but in every country I have visited the local actuaries have used similar notation.
Table 1. Common actuarial terms and their definition for statisticians.
Out for the count
In an earlier post we described a problem when fitting GLMs for qx over multiple years. The key mistake is to divide up the period over which the individual was observed in a model for individual mortality.
Postcode pricing in 15 minutes!
Just a short post to announce we've revised our overview videos for both Longevitas and mortalityrating.com.