Information Matrix

In a previous posting I looked at how using a well founded statistical model can improve the accuracy of estimated mortality rates. We saw how the relative uncertainty for the estimate of \(\log \mu_{75.5}\) could be reduced from 20.5% to 3.9% by using a simple two-parameter Gompertz model:

\(\log \mu_x = \alpha + \beta x\qquad (1)\)

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.