Dealing with dates in actuarial mortality investigations
When we first wrote our survival-modelling software in late 2005, we had to decide how to represent dates for the purpose of calculating exposure times. We decided to adopt a real-valued approach, e.g. 14th March 1968 would be represented as 1968.177596 (the fractional part is \(\frac{31+29+14}{366}\), since 1968 is a leap year).
I recently discovered that this approach has a long pedigree. Figure 1 shows a specimen policy from Downes (1862):
Figure 1. Sample record in Downes (1862, page 8).
where the dates of entry and exit are then decimalised in Figure 2:
Figure 2. Decimalised dates in Downes (1862, page 9).
A historical review is given by Lidstone (1946), where it is noted that the results of the process described by Downes (1862) were actually published in Downes (1857). Thus, the decimalisation of dates in actuarial investigations is probably at least 168 years old at the time of writing.
However, modern actuaries should note that decimalisation should only be done after data validation, for which the actual dates themselves are invaluable. Macdonald et al (2018, Chapter 2) detail the sorts of data-quality checks made possible with dates on individual records.
References:
Downes, J. J. (1857) Rate of Mortality experienced in the Economic Life Assurance Society, The Assurance Magazine and Journal of the Institute of Actuaries, Volume 7(2), pages 78-80, doi:10.1017/S2046165800023339.
Downes, J. J. (1862) An Account of the Processes employed in getting out the Mortality Experience of the Economic Life Assurance Society.
Lidstone, G. J. (1946) The origins of the card system, Journal of the Institute of Actuaries, 72(2), pages 229-233, doi:10.1017/S0020268100035150.
Macdonald, A. S., Richards. S. J. and Currie, I. D. (2018). Modelling Mortality with Actuarial Applications. Cambridge University Press, Cambridge.
Thanks to David Raymont, Librarian at the Institute and Faculty of Actuaries, for sourcing a copy of Downes (1862).
Dates, durations and ages in Longevitas
Dates are input into Longevitas for detailed validation and checking, as described in Macdonald et al (2018). However, these dates are converted to real-valued exposure times and ages for the purposes of model-fitting.
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