Some Probability Results for Mortality Rates based on Insurance Data

Abstract

It is not usual in mortality investigations of insurance data to associate exactly one unit with each life. It is easier to use policies or sums assured or some variation of policies and sums assured. But a proper statistical test of graduated rates of mortality derived from such an investigation cannot be made unless the effect of the variable number of units associated with each life is known. Beard and Perks (1949, J.I.A. lxxv, 75) gave, for four different sampling processes, formulae for the variance of the distribution of deaths for a mortality study based on policies, and Daw (1951, J.I.A. lxxvii, 261) illustrated the formulae by numerical examples on various hypotheses. In particular, he showed that the sampling process employed had little effect on the numerical results, but that the frequency distribution of the number of policies held was very important. The formulae derived by Beard and Perks assumed that the frequency distribution of the universe of number of policies held was known.