Description: This paper presents the general notion of a periodogram, following Elphinstone's approach. The paper then goes on to examine symmetric linear operators and their periodograms in preparation for the end discussion of periodograms of graduators.

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.’