The index of the outstanding observation among n independent ones

L. de Haan and I. Weissman

Stochastic Processes and their Applications, 1987, vol. 27, 317-329

Abstract: Let X1, X2,... be independent random variables with distribution functions F1, F2,... respectively, Mn = max {X1,..., Xn} and Ln = min {k [less-than-or-equals, slant] n: Xk = Mn}. Assume that there exist constants an > 0 and bn such that (Mn - bn)/an converges in distribution to a non-degenerate random variable. It is easy to show that if for all t in (0,1) (M[nt] - bn)/an converges in distribution, so does Ln/n. We study the converse problem, namely, is it true that the convergence of Ln/n to a non-degenerate random variable implies the convergence in distribution of (M[nt] - bn)/an for all t[epsilon](0, 1)?

Keywords: extreme; values; limit; laws (search for similar items in EconPapers)
Date: 1987
References: Add references at CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/0304-4149(87)90045-7
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:27:y:1987:i::p:317-329

Ordering information: This journal article can be ordered from
http://http://www.elsevier.com/wps/find/supportfaq.cws_home/regional
https://shop.elsevie ... _01_ooc_1&version=01

Access Statistics for this article

Stochastic Processes and their Applications is currently edited by T. Mikosch

More articles in Stochastic Processes and their Applications from Elsevier
Bibliographic data for series maintained by Catherine Liu ().