On the asymptotics of numbers of observations in random regions determined by order statistics

  • Authors:

  • Anna Dembińska;George Iliopoulos

  • Affiliations:

  • Faculty of Mathematics and Information Science, Warsaw University of Technology, Pl. Politechniki 1, 00-661 Warsaw, Poland;Department of Statistics and Insurance Science, University of Piraeus, 80 Karaoli & Dimitriou str., 18534 Piraeus, Greece

  • Venue:
  • Journal of Multivariate Analysis
  • Year:
  • 2012

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Abstract

In this paper, we consider random variables counting numbers of observations that fall into regions determined by extreme order statistics and Borel sets. We study multivariate asymptotic behavior of these random variables and express their joint limiting law in terms of independent multinomial and negative multinomial laws. First, we give our results for samples with deterministic size; next we explain how to generalize them to the case of randomly indexed samples.