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Approximations to extreme tail probabilities for sampling without replacement

Published online by Cambridge University Press:  24 October 2008

M. Stone
M. Stone
Affiliation:
University College London
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Extract

Introduction and summary: In the distribution of the sum of n random variables

for which we suppose , the tail probability will be called an extreme tail probability if the normal approximation

is poor, when is asymptotically normal and n is large. This paper concerns the specialization of (1.1) in which

with a random permutation of nλ ones and n − nλ zeros, that is, in which T is the total for a simple random sample from the population with sampling fraction λ. In this case, we will always write T as Tλ. For brevity, we may write {c1,…, cn} for .

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 66 , Issue 3 , November 1969 , pp. 587 - 606
Copyright
Copyright © Cambridge Philosophical Society 1969

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References

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