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, Volume 21, Issue 1, pp 116–131 | Cite as

Limit laws for maxima of a stationary random sequence with random sample size

  • A. Freitas
  • J. HüslerEmail author
  • M. G. Temido
Original Paper

Abstract

Let {X n } be a stationary sequence and {k n } be a nondecreasing sequence such that k n+1/k n r≥1. Assume that the limit distribution G of \(M_{k_{n}}\) with an appropriate linear normalization exists. We consider the maxima M n =max {X i ,in} sampled at random times T n , where T n /k n converges in probability to a positive random variable D, and show that the limit distribution of \(M_{T_{n}}\) exists under weak mixing conditions. The limit distribution of \(M_{T_{n}}\) is a mixture of G and the distribution of D.

Keywords

Maximum Limit distribution Mixture Max-semistable laws Random sample size 

Mathematics Subject Classification (2000)

60G70 60F05 60G10 

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Copyright information

© Sociedad de Estadística e Investigación Operativa 2011

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of AveiroAveiroPortugal
  2. 2.Department of Mathematical StatisticsUniversity of BernBernSwitzerland
  3. 3.Department of MathematicsUniversity of CoimbraCoimbraPortugal

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