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https://hdl.handle.net/10316/11287
Title: | On the maximum of periodic integer-valued sequences with exponential type tails via max-semistable laws | Authors: | Hall, A. Temido, M. G. |
Keywords: | Integer-valued periodic sequences; Max-semistable laws; Binomial thinning | Issue Date: | 2007 | Publisher: | Centro de Matemática da Universidade de Coimbra | Citation: | Pré-Publicações DMUC. 07-31 (2007) | Abstract: | In this work we study the limiting distribution of the maximum term of periodic integer-valued sequences with marginal distribution belonging to a particular class where the tail decays exponentially. This class does not belong to the domain of attraction of any max-stable distribution. Nevertheless, we prove that the limiting distribution is max-semistable when we consider the maximum of the first kn observations, for a suitable sequence {kn} increasing to infinity. We obtain an expression for calculating the extremal index of sequences satisfying certain local conditions similar to conditions D(m)(un), m ∈ N, defined by Chernick et al. (1991). We apply the results to a class of max-autoregressive sequences and a class of moving average models. The results generalize the ones obtained for the stationary case. | URI: | https://hdl.handle.net/10316/11287 | Rights: | openAccess |
Appears in Collections: | FCTUC Matemática - Vários |
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On the maximum of periodic integer-valued sequences.pdf | 242.21 kB | Adobe PDF | View/Open |
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