Ordering results of second order statistics from random and non-random number of random variables with Archimedean copulas

Bin Lu; Rongfang Yan; Bin Lu; Rongfang Yan

doi:10.3934/math.2021375

AIMS Mathematics

2021, Volume 6, Issue 6: 6390-6405. doi: 10.3934/math.2021375

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Research article

Ordering results of second order statistics from random and non-random number of random variables with Archimedean copulas

Bin Lu ,
Rongfang Yan ^,

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

Received: 10 January 2021 Accepted: 31 March 2021 Published: 12 April 2021
MSC : 60E15, 60K10, 90B25

In this paper, we investigate stochastic comparisons of the second largest order statistics of homogeneous samples coupled by Archimedean copula, and we establish the reversed hazard rate and likelihood ratio orders, and we further generalize the corresponding results to the case of random sample size. Also, we derive some results for relative ageing between parallel systems and $ 2 $-out-of-$ n $/$ 2 $-out-of-$ (n+1) $ systems. Finally, some examples are given to illustrate the obtained results.
- stochastic orders,
- archimedean copula,
- order statistics,
- random sample size,
- relative ageing
Citation: Bin Lu, Rongfang Yan. Ordering results of second order statistics from random and non-random number of random variables with Archimedean copulas[J]. AIMS Mathematics, 2021, 6(6): 6390-6405. doi: 10.3934/math.2021375

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Abstract

In this paper, we investigate stochastic comparisons of the second largest order statistics of homogeneous samples coupled by Archimedean copula, and we establish the reversed hazard rate and likelihood ratio orders, and we further generalize the corresponding results to the case of random sample size. Also, we derive some results for relative ageing between parallel systems and $ 2 $-out-of-$ n $/$ 2 $-out-of-$ (n+1) $ systems. Finally, some examples are given to illustrate the obtained results.

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