Stephen Richards

The CMI is the part of the UK actuarial profession which collates mortality data from UK life offices and pension consultants. Amongst its many outputs is an Excel spreadsheet used for setting deterministic mortality forecasts. This spreadsheet is in widespread use throughout the UK at the time of writing, not least for the published reserves for most insurers and pension schemes.

I wrote earlier that deviance residuals were better than Pearson residuals when examining a model fit for Poisson counts. It is worth expanding on why this is, since it also neatly illustrates why there are limits to models based on grouped counts.

When fitting a model for Poisson counts, an important step is to check the goodness of fit using the following statistic:

\[\tilde{\chi}^2 = \sum_{i=1}^n r_i^2\]

The survivor function from age \(x\) to age \(x+t\), denoted \({}_tp_x\) by actuaries, is a useful tool in mortality work. As mentioned in one of our earliest blogs, a basic feature is that the expected time lived is the area under the survival curve, i.e. the integral of \({}_tp_x\). This is easy to express in visual terms, but it often requires numerical integration if there is no closed-form expression for the integral of the survival curve.

In a previous blogs I have looked at seasonal fluctuations in mortality, usually with lower mortality in summer and higher mortality in winter.  The subject of excess winter deaths is back in the news, as the UK experienced heavy mortality in the winter of 2014/15, as demonstrated in Figure 1.