Extreme order statistics in an equally correlated Gaussian array

Mateusz Wiśniewski

Applicationes Mathematicae (1994)

  • Volume: 22, Issue: 2, page 193-200
  • ISSN: 1233-7234

Abstract

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This paper contains the results concerning the weak convergence of d-dimensional extreme order statistics in a Gaussian, equally correlated array. Three types of limit distributions are found and sufficient conditions for the existence of these distributions are given.

How to cite

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Wiśniewski, Mateusz. "Extreme order statistics in an equally correlated Gaussian array." Applicationes Mathematicae 22.2 (1994): 193-200. <http://eudml.org/doc/219091>.

@article{Wiśniewski1994,
abstract = {This paper contains the results concerning the weak convergence of d-dimensional extreme order statistics in a Gaussian, equally correlated array. Three types of limit distributions are found and sufficient conditions for the existence of these distributions are given.},
author = {Wiśniewski, Mateusz},
journal = {Applicationes Mathematicae},
keywords = {equally correlated; Gaussian array; extreme order statistics; limit distributions; triangular array of Gaussian, equally correlated random vectors; limiting distributions},
language = {eng},
number = {2},
pages = {193-200},
title = {Extreme order statistics in an equally correlated Gaussian array},
url = {http://eudml.org/doc/219091},
volume = {22},
year = {1994},
}

TY - JOUR
AU - Wiśniewski, Mateusz
TI - Extreme order statistics in an equally correlated Gaussian array
JO - Applicationes Mathematicae
PY - 1994
VL - 22
IS - 2
SP - 193
EP - 200
AB - This paper contains the results concerning the weak convergence of d-dimensional extreme order statistics in a Gaussian, equally correlated array. Three types of limit distributions are found and sufficient conditions for the existence of these distributions are given.
LA - eng
KW - equally correlated; Gaussian array; extreme order statistics; limit distributions; triangular array of Gaussian, equally correlated random vectors; limiting distributions
UR - http://eudml.org/doc/219091
ER -

References

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  1. [1] S. M. Berman, Equally correlated random variables, Sankhyā A 24 (1962), 155-156. Zbl0105.33101
  2. [2] J. Galambos, The Asymptotic Theory of Extreme Order Statistics, Wiley, New York, 1978. Zbl0381.62039
  3. [3] M. R. Leadbetter, G. Lindgren and H. Rootzén, Extremes and Related Properties of Random Sequences and Processes, Springer, New York, 1983. Zbl0518.60021
  4. [4] Y. Mittal and D. Ylvisaker, Limit distributions for the maxima of stationary Gaussian processes, Stochastic Process. Appl. 3 (1975), 1-18. 
  5. [5] J. Pickands III, Maxima of stationary Gaussian processes, Z. Wahrsch. Verw. Gebiete 7 (1967), 190-223. Zbl0158.16702
  6. [6] W. Rudin, Real and Complex Analysis, McGraw-Hill, New York, 1974. 
  7. [7] M. Wiśniewski, Multidimensional point processes of extreme order statistics, Demonstratio Math., to appear. Zbl0843.60052

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