Description: This paper is from Transactions of Society of Actuaries 1955 Volume 7, Number 17. The author notes that in mortality studies the ‘natural’ unit for exposures and deaths is number of lives, but often more insight is gained by use of other weights, such as face amount. In this paper, the author develops a method which, ‘by a combination of exposed to risk formulas, provides a comparatively simple procedure to permit consideration of weights which vary during the observation period.’

Description: This paper is from Transactions of Society of Actuaries 1955 Volume 7, Number 17. The author notes that recent advances in calculating equipment make possible producing graduations much more elaborate than any done previously. The paper confines itself to the problem of graduating a single column of rates, such as an ultimate column, using a Whittaker-Henderson B graduation of the fourth order. The author provides a detailed description of the process with significant mathematical theory.