Description: In this paper two theorems concerning the optimality of the perfect-fit and perfect-smoothness graduations are proved. Two examples are presented and some difficulties with regard to computational feasibility are reviewed. A discussion of the paper follows. From Transactions of Society of Actuaries 1978, Vol. 30.

Description: This paper defines a general model for arbitrary units and gives formulas for computing the variance and mean squared error of decrement estimators. It is observed that, in small studies, the mean squared error is reduced by counting lives, even if the probability of death depends somewhat on the amount of insurance. From Transactions of Society of Actuaries 1981, Vol. 33.