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A remark on the asymptotic theory of sums with random size

Published online by Cambridge University Press:  24 October 2008

Janos Galambos
Affiliation:
Temple University, Philadelphia, U.S.A.

Extract

The aim of the present note is to point to a strange fact, through an example, in connexion with the asymptotic distribution of sums of a random number of independent and identically distributed (i.i.d.) random variables. We shall formulate our conclusion after the introduction of some notations.

Type
Research Article
Copyright
Copyright © Cambridge Philosophical Society 1976

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References

REFERENCES

(1)Anscombe, F. J.Large sample theory of sequential estimation. Proc. Cambridge Philos. Soc. 48 (1952), 600607.CrossRefGoogle Scholar
(2)Foster, F. G. and Stuart, A.Distribution free tests in time series based on the breaking of records. J. Roy. Stat. Soc., Ser. B 16 (1954), 113.Google Scholar
(3)Tata, M. M.On outstanding values in a sequence of random variables. Z. Wahrscheinlichkeitstheorie verw. Gebiete 12 (1969), 920.CrossRefGoogle Scholar
(4)Zacks, S.The theory of statistical inference. (New York: John Wiley, 1971.)Google Scholar