Orderings of extremes among dependent extended Weibull random variables
In this work, we consider two sets of dependent variables $\{X_{1},\ldots,X_{n}\}$ and $\{Y_{1},\ldots,Y_{n}\}$ , where $X_{i}\sim EW(\alpha_{i},\lambda_{i},k_{i})$ and $Y_{i}\sim EW(\beta_{i},\mu_{i},l_{i})$ , for $i=1,\ldots, n$ , which are coupled by Archimedean copulas having different generator...
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| Published in: | Probability in the engineering and informational sciences Vol. 38; no. 4; pp. 705 - 732 |
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| Main Authors: | , , |
| Format: | Journal Article |
| Language: | English |
| Published: |
Cambridge
Cambridge University Press
01.10.2024
|
| Subjects: | |
| ISSN: | 0269-9648, 1469-8951 |
| Online Access: | Get full text |
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| Summary: | In this work, we consider two sets of dependent variables
$\{X_{1},\ldots,X_{n}\}$
and
$\{Y_{1},\ldots,Y_{n}\}$
, where
$X_{i}\sim EW(\alpha_{i},\lambda_{i},k_{i})$
and
$Y_{i}\sim EW(\beta_{i},\mu_{i},l_{i})$
, for
$i=1,\ldots, n$
, which are coupled by Archimedean copulas having different generators. We then establish different inequalities between two extremes, namely,
$X_{1:n}$
and
$Y_{1:n}$
and
$X_{n:n}$
and
$Y_{n:n}$
, in terms of the usual stochastic, star, Lorenz, hazard rate, reversed hazard rate and dispersive orders. Several examples and counterexamples are presented for illustrating all the results established here. Some of the results here extend the existing results of [5] (Barmalzan, G., Ayat, S.M., Balakrishnan, N., & Roozegar, R. (2020). Stochastic comparisons of series and parallel systems with dependent heterogeneous extended exponential components under Archimedean copula.
Journal of Computational and Applied Mathematics
380
: Article No. 112965). |
|---|---|
| Bibliography: | ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14 |
| ISSN: | 0269-9648 1469-8951 |
| DOI: | 10.1017/S026996482400007X |