Hostname: page-component-586b7cd67f-l7hp2 Total loading time: 0 Render date: 2024-11-28T10:47:45.087Z Has data issue: false hasContentIssue false
  • English
  • Français

Weak limits of sample range

Published online by Cambridge University Press:  14 July 2016

Laurens De Haan
Laurens De Haan*
Affiliation:
Erasmus University Rotterdam
Get access Rights & Permissions [Opens in a new window]

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 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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