Business benefits of statistical models

(Mar 25, 2011)

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. One reason I gave is that because survival models are built at the level of the individual, it is often easier to spot data problems which would otherwise be invisible to an actuary using traditional methods.

As it happened, a good example of this cropped up the following week. A pension scheme was looking at the feasibility of a longevity swap. During the quotation process an updated extract of the pensioner data was provided, ostensibly to give an up-to-date picture of the annual pension amounts. A cursory…

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Tags: data validation, residual, survival models

Residual concerns

(Jun 5, 2009)

One of the most important means of checking a model's fit is to look at the residuals, i.e. the standardised differences between the actual data observed and what the model predicts.  One common definition, known as the Pearson residual, is as follows:

Definition of Pearson residual

where r is the residual, D is the observed number of deaths and E is the expected number of deaths. This definition is quick and easy to apply, and works well where there are relatively large numbers of observed and expected deaths.  If the underlying model used to generate the expected values in E is correct, the residuals should have an approximate N(0, 1) distribution.  The sum of the r2 values can be compared with the appropriate point of a χ2 (chi-squared)…

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Tags: residual, deviance residual, Pearson residual

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