On the norming constants for normal maxima
Gasull, Armengol (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Jolis Giménez, Maria (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Utzet, Frederic (Universitat Autònoma de Barcelona. Departament de Matemàtiques)

Date:	2015
Abstract:	In a remarkable paper, Peter Hall [On the rate of convergence of normal extremes, J. App. Prob, 16 (1979) 433-439] proved that the supremum norm distance between the distribution function of the normalized maximum of n independent standard normal random variables and the distribution function of the Gumbel law is bounded by 3/ log n. In the present paper we prove that choosing a different set of norming constants that bound can be reduced to 1/ log n. As a consequence, using the asymptotic expansion of a Lambert W type function, we propose new explicit constants for the maxima of normal random variables.
Grants:	Ministerio de Economía y Competitividad MTM2012-33937 Ministerio de Economía y Competitividad MTM2009-08869 Ministerio de Economía y Competitividad MTM2008-03437 Agència de Gestió d'Ajuts Universitaris i de Recerca 2009/SGR-410
Rights:	Tots els drets reservats.
Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	Gaussian law ; Extreme value theory ; Lambert W function
Published in:	Journal of mathematical analysis and applications, Vol. 422 (2015) , p. 376-396, ISSN 1096-0813

DOI: 10.1016/j.jmaa.2014.08.025

Postprint 21 p, 373.9 KB

The record appears in these collections:
Research literature > UAB research groups literature > Research Centres and Groups (research output) > Experimental sciences > GSD (Dynamical systems)
Articles > Research articles
Articles > Published articles