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Some Applications of the Poisson Distribution in Mortality Studies

Published online by Cambridge University Press:  03 October 2014

W. F. Scott
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Abstract

Let θx, denote the number of deaths (from all causes or a certain cause) at age x last birthday arising from the central exposed to risk Ecx. We show that, under certain conditions, θx, has approximately a Poisson distribution with parameter

where μy denotes the force of mortality at age y. This result is applied to find confidence intervals for the true central death rate, to estimate the distribution of the cost of claims and the expected death strain.

The frequently-used actuarial formula

where A is the actual deaths and E the expected deaths, is found to hold in large investigations, as is the alternative (but generally less accurate) formula

Type
Research Article
Information
Transactions of the Faculty of Actuaries , Volume 38 , 1981 , pp. 255 - 263
Copyright
Copyright © Institute and Faculty of Actuaries 1981

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