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Effective dimension

Actuaries often need to smooth mortality rates. Gompertz (1825) smoothed mortality rates by age and his famous law was a landmark in this area. Figure 1 shows the Gompertz model fitted to CMI assured lives data for ages 20–90 in the year 2002. The Gompertz Law usually breaks down below about age 40 and a more general smooth curve would be appropriate. However, a more general smooth curve would obviously require more parameters than the two for the simple Gompertz model.

Written by: Iain CurrieTags: effective dimension, splines, P-splines

Boundless confidence?

We've talked repeatedly about a key advantage of statistical models over deterministic ones — specifically, that they provide confidence intervals in addition to a best estimate.
Written by: Gavin RitchieTags: mortality, longevity, data quality

S2 mortality tables

The CMI has released the long-awaited S2 series of mortality tables based on pension-scheme data.  These are the first new tables since the CMI changed its status (the S2 series is only available to paying subscribers, unlike prior CMI tables). 
Written by: Stephen RichardsTags: S2 Series, S1 Series, CMI, mortality improvements

The perils of parameter interpretation

With some notable exceptions, such as the Kaplan-Meier estimator, most mortality models contain parameters. In a statistical model these parameters need to be estimated, and it is a natural thing for people to want to place interpretations on those parameter estimates. However, this can be tricky, as parameters in a multi-parameter model are dependent on each other.

Written by: Stephen RichardsTags: Lee-Carter, parameterisation

Mind the gap!

Recognising and quantifying mortality differentials is what experience analysis is all about. Whether you calculate traditional A/E ratios, graduate raw rates by formula (Forfar et al. 1988), or fit a statistical model (Richards 2012), the aim is always to find risk factors influencing the level of mortality.

Written by: Kai KaufholdTags: mortality convergence, survival models

Spotting hidden data-quality issues

The growing market for longevity risk-transfer means that takers of the risk are keenly interested in the mortality characteristics of the portfolio concerned. The first thing requested by the risk-taker is therefore detailed data on the portfolio's recent mortality experience.  This is ideally data extracted on a policy-by-policy basis.
Written by: Stephen RichardsTags: data validation, Kaplan-Meier

Reducing uncertainty

The motto of the old UK Institute of Actuaries was certum ex incertis, i.e. certainty from uncertainty. I never particularly liked this motto — it implied that certainty can be obtained from uncertainty, whereas uncertainty is all-too-often overlooked.
Written by: Stephen RichardsTags: estimation error, survival models

A tale of three cities

Given my birthplace, I have a more than casual interest in the causes of excess mortality experienced by Scots beyond that explicable by deprivation alone.
Written by: Gavin RitchieTags: mortality, longevity, Scotland, Glasgow

Out of line

Regular readers of this blog will be in no doubt of the advantages of survival models over models for the annual mortality rate, qx. However, what if an analyst wants to stick to the historical actuarial tradition of modelling annualised mortality rates?
Written by: Stephen RichardsTags: GLM, linearity, survival models

Longevitas input format

We have made available an Excel spreadsheet describing how to create input files for uploading into Longevitas.
Written by: Helena BuckmayerTags: Longevitas, data format, CSV