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On Waring's B-formula

Published online by Cambridge University Press:  27 November 2014

M. T. L. Bizley
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Extract

In the theory of Life Contingencies there arises the problem of determining the probability that exactly r lives shall survive a stated period of time out of n lives of different ages. This is of course a special case of a general question in Probability which may be stated thus: If there are n independent events whose individual probabilities of occurring at a single trial are p1,p2…pn, what in terms of p1,p2…pn is the probability that at a single trial of each exactly r of them shall occur?

The developments given in the text-books of King and Spurgeon are familiar to all, but these are not the only methods that have been evolved. Different proofs have appeared from time to time in various publications, most of them in foreign languages, and it is the object of the present paper to collect these together so that they may be easily accessible for reference and comparison. This would appear to be desirable because the question cited above is fundamental in Life Contingencies and in Probability, and also because some of the most satisfactory proofs are to be found only in foreign technical works and have not hitherto been published in English.

Type
Research Article
Information
Journal of the Staple Inn Actuarial Society , Volume 6 , Issue 3 , January 1947 , pp. 123 - 134
Copyright
Copyright © Institute of Actuaries Students' Society 1947

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References

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