Stochastic comparisons of order statistics from heterogeneous random variables with Archimedean copula. (English) Zbl 1416.62271
The paper discusses several ordering properties of order statistics from heterogeneous random variables with an Archimedean copula. In this sense, the study indicates conditions for determining hazard rate order, reversed hazard rate order and the likelihood ratio order.
Reviewer: Catalin Stoean (Craiova)
MSC:
| 62G30 | Order statistics; empirical distribution functions |
| 62H05 | Characterization and structure theory for multivariate probability distributions; copulas |
| 60E15 | Inequalities; stochastic orderings |
Keywords:
order statistics; Archimedean copula; hazard rate order; reversed hazard rate order; likelihood ratio orderReferences:
| [1] | Amini-Seresht E, Qiao J, Zhang Y, Zhao P (2016) On the skewness of order statistics in multiple-outlier PHR models. Metrika 79:817-836 · Zbl 1345.62079 · doi:10.1007/s00184-016-0579-7 |
| [2] | Arnold BC, Balakrishnan N, Nagaraja HN (1992) A first course in order statistics. Wiley, New York · Zbl 0850.62008 |
| [3] | Balakrishnan N, Rao CR (1998) Handbook of statistics 16: order statistics: theory and methods. Elsevier, New York · Zbl 0894.00024 |
| [4] | Balakrishnan N, Rao CR (1998) Handbook of statistics 17: order statistics: applications. Elsevier, New York · Zbl 0897.00016 |
| [5] | Balakrishnan N, Zhao P (2013) Hazard rate comparison of parallel systems with heterogeneous gamma components. J Multivar Anal 113:153-160 · Zbl 1253.60022 · doi:10.1016/j.jmva.2011.05.001 |
| [6] | Balakrishnan N, Zhao P (2013) Ordering properties of order statistics from heterogeneous populations: a review with an emphasis on some recent developments. Probab Eng Inf Sci 27:403-444 · Zbl 1288.60023 · doi:10.1017/S0269964813000156 |
| [7] | Dykstra R, Kochar SC, Rojo J (1997) Stochastic comparisons of parallel systems of heterogeneous exponential components. J Stat Plan Inference 65:203-211 · Zbl 0915.62044 · doi:10.1016/S0378-3758(97)00058-X |
| [8] | Fang L, Zhang X (2012) New results on stochastic comparison of order statistics from heterogeneous Weibull populations. J Korean Stat Soc 41:13-16 · Zbl 1296.62106 · doi:10.1016/j.jkss.2011.05.004 |
| [9] | Khaledi B, Kochar SC (2000) Some new results on stochastic comparisons of parallel systems. J Appl Probab 37:1123-1128 · Zbl 0995.62104 · doi:10.1017/S0021900200018301 |
| [10] | Kochar SC, Rojo J (1996) Some new results on stochastic comparisons of spacings from heterogeneous exponential distributions. J Multivar Anal 59:272-281 · Zbl 0864.62033 · doi:10.1006/jmva.1996.0065 |
| [11] | Li X, Fang R (2015) Ordering properties of order statistics from random variables of Archimedean copulas with applications. J Multivar Anal 133:304-320 · Zbl 1327.60051 · doi:10.1016/j.jmva.2014.09.016 |
| [12] | McNeil A, Nešlehovà J (2009) Multivariate Archimedean copulas, \[d\] d-monotone functions and \[l_1\] l1-norm symmetric distributions. Ann Stat 37:3059-3097 · Zbl 1173.62044 · doi:10.1214/07-AOS556 |
| [13] | Nelsen RB (2006) An Introduction to Copulas, 2nd edn. Springer, New York · Zbl 1152.62030 |
| [14] | Rezapour M, Alamatsaz M (2014) Stochastic comparison of lifetimes of two \[(n - k + 1)\](n-k+1)-out-of-\[n\] n systems with heterogeneous dependent components. J Multivar Anal 130:240-251 · Zbl 1360.62498 · doi:10.1016/j.jmva.2014.05.009 |
| [15] | Shaked M, Shantikumar JG (2007) Stochastic orders. Springer, New York · Zbl 1111.62016 · doi:10.1007/978-0-387-34675-5 |
| [16] | Stoyan D (1991) Comparison methods for queues and other stochastic models. Wiley, New York |
| [17] | Zhao P, Balakrishnan N (2014) A stochastic inequality for the largest order statistics from heterogeneous gamma variables. J Multivar Anal 129:145-150 · Zbl 1293.60027 · doi:10.1016/j.jmva.2014.04.003 |
| [18] | Zhao P, Balakrishnan N (2009) Characterization of MRL order of fail-safe systems with heterogeneous exponential components. J Stat Plan Inference 139:3027-3037 · Zbl 1181.62171 · doi:10.1016/j.jspi.2009.02.006 |
| [19] | Zhao P, Zhang Y (2014) On the maxima of heterogeneous gamma variables with different shape and scale parameters. Metrika 77:811-836 · Zbl 1304.60028 · doi:10.1007/s00184-013-0466-4 |
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