Some Applications of the Poisson Distribution in Mortality Studies
- 1 January 1981
- journal article
- research article
- Published by Cambridge University Press (CUP) in Transactions of the Faculty of Actuaries
- Vol. 38, 255-263
- https://doi.org/10.1017/s0071368600008855
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) formulaKeywords
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