Please use this identifier to cite or link to this item: http://hdl.handle.net/10525/2217

 Title: Nonlinear Normalization in Limit Theorems for Extremes Authors: I. Pancheva, E.V. Mitov, K.Nadarajah, S. Keywords: Extreme valuesNonlinear normalizationLimit theoremsDomain 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. URI: http://hdl.handle.net/10525/2217 ISSN: 0204-9805 Appears in Collections: 2011 Volume 20

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