A reappraisal of the principle underlying the conventional actuarial estimator of qx

This paper considers the principle underlying the conventional actuarial estimator of qx. A new rationale of this estimation method is described, providing an alternative to the rationale set out by Cantelli (1914), from time to time the focus of controversy. It is pointed out that the product limit estimator also conforms to this new rationale. Discussion of the new rationale identifies an instructive analogy between the conventional actuarial estimator and a money-weighted rate of return in a financial transaction, and between the product limit estimator and a time-weighted rate of return.