NEW MATHEMATICAL LAWS OF SELECT AND ULTIMATE MORTALITY

Abstract

The objectives of this paper are (1) to show why scientific laws of mortality are preferable to the continued use of graduation techniques on mortality tables; (2) to develop a new theory leading to a new mathematical law of mortality that reduces to Gompertz's law as a first approximation, and to detail the biological justification for such laws; (3) to demonstrate an understanding of select mortality and produce a simple formula that is reasonably consistent with it; (4) to develop methods to test this and other similar formulas on various bodies of data to establish their validity and usefulness; (5) to discuss the meaning of the results produced above and provide some examples of the use of the formula for purposes other than graduation; and (6) to discuss extensions of the models. The authors believe that the final formula is simple, easy to use, and considerably more useful than traditional graduation processes. The second-named author developed the models and wrote the sections dealing with their development and justification. The first-named author developed the techniques of regression analysis for testing and fitting the models and wrote the corresponding sections of this paper.