BulDML at Institute of Mathematics and Informatics >
IMI Periodicals >
Pliska Studia Mathematica Bulgarica >
2011 Volume 20 >

Please use this identifier to cite or link to this item:

Title: Nonlinear Normalization in Limit Theorems for Extremes
Authors: I. Pancheva, E.
V. Mitov, K.
Nadarajah, S.
Keywords: Extreme values
Nonlinear normalization
Limit theorems
Domain of attraction
Issue Date: 2011
Publisher: Institute of Mathematics and Informatics Bulgarian Academy of Sciences
Citation: Pliska Studia Mathematica Bulgarica, Vol. 20, No 1, (2011), 169p-186p
Abstract: It is well known that under linear normalization the maxima of iid random variables converges in distribution to one of the three types of max-stable laws: Frechet, Gumbel and Weibull. During the last two decades the first author and her collaborators worked out a limit theory for extremes and extremal processes under non-linear but monotone normalizing mappings. In this model there is only one type of max-stable distributions and all continuous and strictly increasing df's belong to it. In a recent paper on General max-stable laws, Sreehari points out two "confusing" results in Pancheva (1984). They concern the explicit form of a max-stable df with respect to a continuous one-parameter group of max-automorphisms, and domain of attraction conditions. In the present paper the first claim is answered by a detailed explanation of the explicit form, while for the second we give a revised proof. The rate of convergence is also discussed.
Description: 2000 Mathematics Subject Classification: 60G70, 60F05.
ISSN: 0204-9805
Appears in Collections:2011 Volume 20

Files in This Item:

File Description SizeFormat
Pliska-20-2011-169-186.pdf1.16 MBAdobe PDFView/Open


Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.


Valid XHTML 1.0!   Creative Commons License