Abstract
In this paper, we investigate sufficient conditions for preservation property of the dispersive order for the smallest and largest order statistics of homogeneous dependent random vectors. Moreover, we establish sufficient conditions for ordering with the dispersive order the largest order statistics from dependent homogeneous samples of different sizes.
References
[1] Balakrishnan N. and C.R. Rao (1998). Order Statistics: Theory and Methods. Elsevier, New York.Search in Google Scholar
[2] Balakrishnan N. and C.R. Rao (1998). Order Statistics: Applications. Elsevier, New York.Search in Google Scholar
[3] David H.A. and H.N. Nagaraja (2003). Order Statistics. Third edition. Wiley, New York.10.1002/0471722162Search in Google Scholar
[4] Boland P.J., E. El-Neweihi and F. Proschan (1994). Applications of the hazard rate ordering in reliability and order statistics. J. Appl. Probab. 31(1), 180–192.10.2307/3215245Search in Google Scholar
[5] J. Appl. Probab. Raqab M.Z. and W.A. Amin (1996). Some ordering results on order statistics and record values. IAPQR Transactions 21, 1–8.Search in Google Scholar
[6] S. C. Kochar (1996). Dispersive ordering of order statistics. Statist. Probab. Lett. 27(3), 271–274.10.1016/0167-7152(95)00083-6Search in Google Scholar
[7] Khaledi B.-E.and S. C. Kochar (2000). On dispersive ordering between order statistics in one-sample and two-sample problems. Statist. Probab. Lett. 46(3), 257–261.10.1016/S0167-7152(99)00110-8Search in Google Scholar
[8] S. C. Kochar (2012). Stochastic comparisons of order statistics and spacings: a review. ISRN Probab. Statist. 2012, Article ID 839473, 47 pages.10.5402/2012/839473Search in Google Scholar
[9] Balakrishnan N. and P. Zhao (2013). Ordering properties of order statistics from heterogeneous populations: a review with an emphasis on some recent developments. Probab. Eng. Inf. Sci. 27(4), 403–443.10.1017/S0269964813000156Search in Google Scholar
[10] Dykstra R., S. C. Kochar and J. Rojo (1997). Stochastic comparisons of parallel systems of heterogeneous exponential components. J. Statist. Plann. Inference 65(2), 203–211.10.1016/S0378-3758(97)00058-XSearch in Google Scholar
[11] Khaledi B.-E. and S. C. Kochar (2000). Some new results on stochastic comparisons of parallel systems. J. Appl. Probab. 37(4), 1123–1128.10.1239/jap/1014843091Search in Google Scholar
[12] Fang L. and X. Zhang (2013). Stochastic comparisons of series systems with heterogeneous Weibull components. Statist. Probab. Lett. 83(7), 1649–1653.10.1016/j.spl.2013.03.012Search in Google Scholar
[13] Li X. and, R. Fang (2015). Ordering properties of order statistics from random variables of Archimedean copula with applications. J. Multivariate Anal. 133, 304–320.Search in Google Scholar
[14] Li C. and X. Li (2015). Likelihood ratio order of sample minimum from heterogeneous Weibull random variables. Statist. Probab. Lett. 97, 46–53.Search in Google Scholar
[15] Fang R., X. Li and C. Li (2016). Stochastic comparisons on sample extremes of dependent and heterogenous observations. Statistics 50(4), 930-955.10.1080/02331888.2015.1119151Search in Google Scholar
[16] Li C., R. Fang and X. Li (2016). Stochastic comparisons of order statistics from scaled and interdependent random variables. Metrika 79, 553-578.Search in Google Scholar
[17] Shaked M. and J. G. Shanthikumar (2007). Stochastic Orders. Springer, New York.10.1007/978-0-387-34675-5Search in Google Scholar
[18] McNeil A.J. and J. Nešlehová (2009). Multivariate Archimedean copulas, D-monotone functions and l1-norm symmetric distributions. Ann. Statist. 37(5B), 3059-3097.Search in Google Scholar
[19] Bagnoli, M. and T. Bergstrom (2005). Log-concave probability and its applications. Econom. Theory 26, 445-469.10.1007/s00199-004-0514-4Search in Google Scholar
[20] Li X. and R. Fang (2015). Ordering properties of order statistics from random variables of Archimedean copulas with applications. J. Multivariate Anal. 133, 304-320.Search in Google Scholar
[21] Mesfioui M., M. Kayid and S. Izadkhah (2017). Stochastic comparisons of order statistics from heterogeneous random variables with Archimedean copula. Metrika 80, 749-760.Search in Google Scholar
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