On the maximum of periodic integer-valued sequences with exponential type tails via max-semistable laws |
| |
Authors: | Andreia Hall,Maria da Graç a Temido |
| |
Affiliation: | 1. Center for Research and Development in Mathematics and Applications, Departamento de Matemática, Universidade de Aveiro, 3810-193 Aveiro, Portugal;2. CMUC, Departamento de Matemática, Universidade de Coimbra, 3001-454 Coimbra, Portugal |
| |
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. |
| |
Keywords: | Integer-valued sequences Extremal index Periodic sequences Binomial thinning |
本文献已被 ScienceDirect 等数据库收录! |
|