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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Bibliographic Details
Published in:Probability in the engineering and informational sciences Vol. 38; no. 4; pp. 705 - 732
Main Authors: Samanta, Ramkrishna Jyoti, Das, Sangita, Balakrishnan, N.
Format: Journal Article
Language:English
Published: Cambridge Cambridge University Press 01.10.2024
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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).
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ISSN:0269-9648
1469-8951
DOI:10.1017/S026996482400007X