On distributions of order statistics for absolutely continuous copulas with applications to reliability

Piotr Jaworski; Tomasz Rychlik

Kybernetika (2008)

  • Volume: 44, Issue: 6, page 757-776
  • ISSN: 0023-5954

Abstract

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Performance of coherent reliability systems is strongly connected with distributions of order statistics of failure times of components. A crucial assumption here is that the distributions of possibly mutually dependent lifetimes of components are exchangeable and jointly absolutely continuous. Assuming absolute continuity of marginals, we focus on properties of respective copulas and characterize the marginal distribution functions of order statistics that may correspond to absolute continuous and possibly exchangeable copulas. One characterization is based on the vector of distribution functions of all order statistics, and the other concerns the distribution of a single order statistic.

How to cite

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Jaworski, Piotr, and Rychlik, Tomasz. "On distributions of order statistics for absolutely continuous copulas with applications to reliability." Kybernetika 44.6 (2008): 757-776. <http://eudml.org/doc/33963>.

@article{Jaworski2008,
abstract = {Performance of coherent reliability systems is strongly connected with distributions of order statistics of failure times of components. A crucial assumption here is that the distributions of possibly mutually dependent lifetimes of components are exchangeable and jointly absolutely continuous. Assuming absolute continuity of marginals, we focus on properties of respective copulas and characterize the marginal distribution functions of order statistics that may correspond to absolute continuous and possibly exchangeable copulas. One characterization is based on the vector of distribution functions of all order statistics, and the other concerns the distribution of a single order statistic.},
author = {Jaworski, Piotr, Rychlik, Tomasz},
journal = {Kybernetika},
keywords = {coherent system; order statistic; copula; exchangeable distribution; absolute continuous distribution; absolute continuous copula; coherent system; order statistic; copula; exchangeable distribution; absolute continuous distribution; absolute continuous copula},
language = {eng},
number = {6},
pages = {757-776},
publisher = {Institute of Information Theory and Automation AS CR},
title = {On distributions of order statistics for absolutely continuous copulas with applications to reliability},
url = {http://eudml.org/doc/33963},
volume = {44},
year = {2008},
}

TY - JOUR
AU - Jaworski, Piotr
AU - Rychlik, Tomasz
TI - On distributions of order statistics for absolutely continuous copulas with applications to reliability
JO - Kybernetika
PY - 2008
PB - Institute of Information Theory and Automation AS CR
VL - 44
IS - 6
SP - 757
EP - 776
AB - Performance of coherent reliability systems is strongly connected with distributions of order statistics of failure times of components. A crucial assumption here is that the distributions of possibly mutually dependent lifetimes of components are exchangeable and jointly absolutely continuous. Assuming absolute continuity of marginals, we focus on properties of respective copulas and characterize the marginal distribution functions of order statistics that may correspond to absolute continuous and possibly exchangeable copulas. One characterization is based on the vector of distribution functions of all order statistics, and the other concerns the distribution of a single order statistic.
LA - eng
KW - coherent system; order statistic; copula; exchangeable distribution; absolute continuous distribution; absolute continuous copula; coherent system; order statistic; copula; exchangeable distribution; absolute continuous distribution; absolute continuous copula
UR - http://eudml.org/doc/33963
ER -

References

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