Ordering results of second order statistics from random and non-random number of random variables with Archimedean copulas
Bin Lu,Rongfang Yan +1 more
- Vol. 6, Iss: 6, pp 6390-6405
TLDR
In this article, the second largest order statistics of homogeneous samples coupled by Archimedean copula were investigated, and the reversed hazard rate and likelihood ratio orders were established.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.read more
References
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Book
An Introduction to Copulas
TL;DR: This book discusses the fundamental properties of copulas and some of their primary applications, which include the study of dependence and measures of association, and the construction of families of bivariate distributions.
Journal ArticleDOI
Statistical Theory of Reliability and Life Testing Probability Models
Book
Statistical Theory of Reliability and Life Testing: Probability Models
Richard E. Barlow,Frank Proschan +1 more
TL;DR: A number of new classes of life distributions arising naturally in reliability models are treated systematically and each provides a realistic probabilistic description of a physical property occurring in the reliability context, thus permitting more realistic modeling of commonly occurring reliability situations.
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Stochastic Ageing and Dependence for Reliability
TL;DR: A panoramic view of theory and applications of Ageing and dependence in the use of mathematical methods in reliability and survival analysis is provided in this paper, which serves as a reference for professors and researchers involved in reliability analysis.
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