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

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 si...

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Bibliographic Details
Published inAIMS mathematics Vol. 6; no. 6; pp. 6390 - 6405
Main Authors Lu, Bin, Yan, Rongfang
Format Journal Article
LanguageEnglish
Published AIMS Press 01.01.2021
Subjects
archimedean copula
order statistics
random sample size
relative ageing
stochastic orders
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Summary: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.
ISSN:2473-6988
2473-6988
DOI:10.3934/math.2021375