Stochastic comparisons of extreme order statistic from dependent and heterogeneous lower-truncated Weibull variables under Archimedean copula

Xiao Zhang; Rongfang Yan; Xiao Zhang; Rongfang Yan

doi:10.3934/math.2022381

AIMS Mathematics

2022, Volume 7, Issue 4: 6852-6875. doi: 10.3934/math.2022381

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Research article

Stochastic comparisons of extreme order statistic from dependent and heterogeneous lower-truncated Weibull variables under Archimedean copula

Xiao Zhang ,
Rongfang Yan ^,

College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, China

Received: 13 October 2021 Revised: 31 December 2021 Accepted: 09 January 2022 Published: 26 January 2022
MSC : Primary 90B25; Secondary 60E15, 60K10

This article studies the stochastic comparisons of order statistics with dependent and heterogeneous lower-truncated Weibull samples under Archimedean copula. To begin, we obtain the usual stochastic and hazard rate orders of the largest and smallest order statistics from heterogeneous and dependent lower-truncated Weibull samples under Archimedean copula. Second, under Archimedean copula, we get the convex transform and the dispersive orders of the largest and smallest order statistics from dependent and heterogeneous lower-truncated Weibull samples. Finally, several numerical examples are given to demonstrate the theoretical conclusions.
- order statistic,
- Archimedean copula,
- majorization,
- lower-truncated Weibull,
- stochastic orders
Citation: Xiao Zhang, Rongfang Yan. Stochastic comparisons of extreme order statistic from dependent and heterogeneous lower-truncated Weibull variables under Archimedean copula[J]. AIMS Mathematics, 2022, 7(4): 6852-6875. doi: 10.3934/math.2022381

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Abstract

This article studies the stochastic comparisons of order statistics with dependent and heterogeneous lower-truncated Weibull samples under Archimedean copula. To begin, we obtain the usual stochastic and hazard rate orders of the largest and smallest order statistics from heterogeneous and dependent lower-truncated Weibull samples under Archimedean copula. Second, under Archimedean copula, we get the convex transform and the dispersive orders of the largest and smallest order statistics from dependent and heterogeneous lower-truncated Weibull samples. Finally, several numerical examples are given to demonstrate the theoretical conclusions.

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