Refinement of a zero-one law for maxima

R. J. Tomkins

Statistics & Probability Letters, 1996, vol. 27, issue 1, 67-69

Abstract: Let X1, X2, ... be any sequence of random variables, and define Mn = max(X1, ..., Xn), n [greater-or-equal, slanted] 1. Let {bn} be a real sequence such that bn --> [infinity]. If {bn} is non-decreasing, it is well-known that P[Mn > bn i.o.] = P[Xn > bn i.o.]. This paper shows that this equality need not hold when {bn} is not monotone, even if X1, X2, ... are i.i.d. Moreover, it is established that P[Mn > bn i.o.] = P[Xn > bn* i.o.], where bn* = infm[greater-or-equal, slanted]nbm, n[greater-or-equal, slanted] 1.

Keywords: Zero-one; law; Almost; sure; stability; Sample; maxima (search for similar items in EconPapers)
Date: 1996
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/0167-7152(95)00045-3
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:stapro:v:27:y:1996:i:1:p:67-69

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

Access Statistics for this article

Statistics & Probability Letters is currently edited by Somnath Datta and Hira L. Koul

More articles in Statistics & Probability Letters from Elsevier
Bibliographic data for series maintained by Catherine Liu ().