Maxima of Gamma random variables and other Weibull like distributions and the Lambert W function
Gasull, Armengol (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
López Salcedo, José Antonio (Universitat Autònoma de Barcelona. Departament de Telecomunicació i Enginyeria de Sistemes)
Utzet i Civit, Frederic (Universitat Autònoma de Barcelona. Departament de Matemàtiques)

Date:	2015
Abstract:	In some applied problems of signal processing, the maximum of a sample of _2(m) random variables is computed and compared with a threshold to assess certain properties. It is well known that this maximum, conveniently normalized, converges in law to a Gumbel random variable; however, numerical and simulation studies show that the norming constants that are usually suggested are inaccurate for moderate or even large sample sizes. In this paper, we propose, for Gamma laws (in particular, for a _2(m) law) and other Weibull-like distributions, other norming constants computed with the asymptotics of the Lambert W function that significantly improve the accuracy of the approximation to the Gumbel law.
Grants:	Ministerio de Economía y Competitividad MTM2013-40998-P Ministerio de Economía y Competitividad MTM2012-33937 Agència de Gestió d'Ajuts Universitaris i de Recerca 2014/SGR-568 Agència de Gestió d'Ajuts Universitaris i de Recerca 2014/SGR-422 Agència de Gestió d'Ajuts Universitaris i de Recerca 2014/SGR-1586
Note:	Agraïments: The second author by the European Space Agency (ESA) through the DINGPOS contract AO/1-5328/06/NL/GLC, and by the Spanish Government and Generalitat de Catalunya through grants TEC2011-28219
Rights:	Tots els drets reservats.
Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	Extreme value theory ; Gamma distributions ; Lambert function ; Weibull-like distributions
Published in:	TEST, Vol. 24 Núm. 4 (2015) , p. 714-733, ISSN 1863-8260

DOI: 10.1007/s11749-015-0431-9

Postprint 29 p, 1.3 MB

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Research literature > UAB research groups literature > Research Centres and Groups (research output) > Experimental sciences > GSD (Dynamical systems)
Articles > Research articles
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