dc.contributor.author
Gasull, Armengol
dc.contributor.author
Jolis Giménez, Maria
dc.contributor.author
Utzet, Frederic
dc.identifier
https://ddd.uab.cat/record/145349
dc.identifier
urn:10.1016/j.jmaa.2014.08.025
dc.identifier
urn:oai:ddd.uab.cat:145349
dc.identifier
urn:gsduab:3626
dc.identifier
urn:scopus_id:85028104382
dc.identifier
urn:wos_id:000349938500020
dc.identifier
urn:oai:egreta.uab.cat:publications/ce279672-d476-478b-9029-847a12dd1807
dc.identifier
urn:articleid:10960813v422p376
dc.description.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.
dc.format
application/pdf
dc.relation
Ministerio de Economía y Competitividad MTM2012-33937
dc.relation
Ministerio de Economía y Competitividad MTM2009-08869
dc.relation
Ministerio de Economía y Competitividad MTM2008-03437
dc.relation
Agència de Gestió d'Ajuts Universitaris i de Recerca 2009/SGR-410
dc.relation
Journal of mathematical analysis and applications ; Vol. 422 (2015), p. 376-396
dc.rights
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dc.rights
https://rightsstatements.org/vocab/InC/1.0/
dc.subject
Extreme value theory
dc.subject
Lambert W function
dc.title
On the norming constants for normal maxima
