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Weak limits of sample range

Published online by Cambridge University Press:  14 July 2016

Laurens De Haan
Laurens De Haan*
Affiliation:
Erasmus University Rotterdam
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Abstract

Necessary and sufficient conditions are obtained for the weak convergence of the sample range of i.i.d. random variables as the number of observations tends to infinity.

Keywords

SAMPLE RANGEORDER STATISTICSWEAK CONVERGENCE
Type
Short Communications
Information
Journal of Applied Probability , Volume 11 , Issue 4 , December 1974 , pp. 836 - 841
Copyright
Copyright © Applied Probability Trust 1974 

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References

Balkema, A. A. and Haan, L. De (1972) On R. von Mises' condition for the domain of attraction of exp (–e–x). Ann. Math. Statist. 43, 1352–1354.Google Scholar
Feller, W. (1966) An Introduction to Probability Theory and its Applications. Vol. II. Wiley, New York.Google Scholar
Gnedenko, B. V. (1943) Sur la distribution limite du terme maximum d'une série aléatoire. Ann. Math. 44, 423–453.Google Scholar
Haan, L. De (1970) On Regular Variation and its Application to the weak Convergence of Sample Extremes. Mathematisch Centrum, Amsterdam.Google Scholar
Lukacs, E. and Laha, R. G. (1964) Applications of Characteristic Functions. Griffin, London.Google Scholar
Mises, R. Von (1936) La distribution de la plus grande de n valeurs. Selected Papers II. 271–294. Amer. Math. Soc.Google Scholar
Resnick, S. I. (1971) Tail equivalence and applications. J. Appl. Prob. 8, 136–156.Google Scholar