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 is a discussion of the paper, New Possibilities in Graduation by Kingsland Camp. From Transactions of Society of Actuaries 1955, Vol. 7, No. 19.

Description: In this paper, the coefficients of the minimum-Rz moving-weighted-average formulas are derived using matrix algebra and the method of Lagrange multipliers. Reviewer's note: This mathematics can be useful in the graduation process of mortality and morbidity table construction

Description: The use of Gompertz's law to describe mortality between the ages of 30 and 90 is discussed in this paper. A further use of Gompertz's law, as a tool in comparing mortality tables, is presented for thirty-three modern tables. From Transactions of Society of Actuaries 1981, Vol. 33.