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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| Vydané v: | Probability in the engineering and informational sciences Ročník 38; číslo 4; s. 705 - 732 |
|---|---|
| Hlavní autori: | , , |
| Médium: | Journal Article |
| Jazyk: | English |
| Vydavateľské údaje: |
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01.10.2024
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| ISSN: | 0269-9648, 1469-8951 |
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| Abstract | 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). |
|---|---|
| AbstractList | 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). 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). |
| Author | Das, Sangita Balakrishnan, N. Samanta, Ramkrishna Jyoti |
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| Cites_doi | 10.1016/j.cam.2020.112965 10.1093/biomet/84.3.641 10.2307/3213414 10.1016/j.spl.2013.03.012 10.1016/j.jmva.2014.09.016 10.1080/02331888.2016.1230859 10.1007/978-0-387-68276-1 10.1080/03610926.2015.1099671 10.1007/s10035-004-0180-z 10.1080/01621459.1996.10476725 10.1186/1029-242X-2014-190 10.1016/j.jkss.2017.10.003 10.1016/j.jkss.2014.05.004 10.1016/j.jspi.2004.12.013 10.1109/24.229504 10.1239/jap/1429282609 10.1214/07-AOS556 10.1007/978-0-387-34675-5 |
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| References | Balakrishnan (S026996482400007X_ref3) 1998; 16 Balakrishnan (S026996482400007X_ref4) 1998; 17 S026996482400007X_ref19 S026996482400007X_ref14 S026996482400007X_ref13 S026996482400007X_ref12 Nelsen (S026996482400007X_ref17) 2006 S026996482400007X_ref22 S026996482400007X_ref11 S026996482400007X_ref18 S026996482400007X_ref16 S026996482400007X_ref15 Arnold (S026996482400007X_ref1) 1992 S026996482400007X_ref2 S026996482400007X_ref10 S026996482400007X_ref21 S026996482400007X_ref20 S026996482400007X_ref5 S026996482400007X_ref6 S026996482400007X_ref7 S026996482400007X_ref8 S026996482400007X_ref9 |
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| Snippet | 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... 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... |
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| SubjectTerms | Applications of mathematics Applied mathematics Dependent variables Euclidean space Flexibility Random variables |
| Title | Orderings of extremes among dependent extended Weibull random variables |
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