Tahmasebi, S.; Jafari, A. A.; Ahsanullah, M. Properties on concomitants of generalized order statistics from a bivariate Rayleigh distribution. (English) Zbl 06835872 Bull. Malays. Math. Sci. Soc. (2) 41, No. 1, 355-370 (2018). Summary: The concept of generalized order statistics (gos) has been introduced as a unified models of ordered random variables. In this paper, we find some properties on concomitants of gos in Morgenstern type bivariate Rayleigh distribution (MTBRD). Recurrence relations between moments of concomitants are also obtained. Some properties of joint distributions for concomitants of gos are presented. Finally, we have derived the best linear unbiased estimator based on concomitants of record values for a parameter involved in MTBRD. Cited in 1 Document MSC: 62E15 Exact distribution theory in statistics 62G30 Order statistics; empirical distribution functions Keywords:concomitant; generalized order statistics; Rayleigh distribution; record values PDFBibTeX XMLCite \textit{S. Tahmasebi} et al., Bull. Malays. Math. Sci. Soc. (2) 41, No. 1, 355--370 (2018; Zbl 06835872) Full Text: DOI References: [1] Ahsanullah, M.: Generalized order statistics from exponential distribution. J. Stat. Plan. Inference 85, 85-91 (2000) · Zbl 0968.62016 · doi:10.1016/S0378-3758(99)00068-3 [2] Ahsanullah, M., Beg, M.I.: Concomitant of generalized order statistics in gumbel’s bivariate exponential distribution. J. Stat. Theory Appl. 6(2), 118-132 (2006) [3] Ahsanullah, M., Nevzorov, B.V., Shakil, M.: An Introduction to Order Statistics. Springer, New York (2013) · Zbl 1276.62029 · doi:10.2991/978-94-91216-83-1 [4] Arslan, G.: On a characterization of the uniform distribution by generalized order statistics. J. Comput. Appl. Math. 235(16), 4532-4536 (2011) · Zbl 1430.62035 · doi:10.1016/j.cam.2010.02.040 [5] Barakat, H.M., Nigm, E.M., Elsawah, A.M.: Asymptotic distributions of the generalized and the dual generalized extremal quotient. Bull. Malays. Math. Sci. Soc. 36(3), 657-670 (2013) · Zbl 1272.62021 [6] Beg, M.I., Ahsanullah, M.: Concomitants of generalized order statistics from Farlie-Gumbel-Morgenstern distributions. Stat. Methodol. 5(1), 1-20 (2008) · Zbl 1248.62076 · doi:10.1016/j.stamet.2007.04.001 [7] BuHamra, S., Ahsanullah, M.: Fisher Information in concomitants of generalized order statistics in Farlie-Gubmel-Morgenstern distributions. J. Stat. Theory Appl. 4(4), 387-399 (2005) [8] BuHamra, S., Ahsanullah, M.: On Concomitants of bivariate Farlie-Gubmel-Morgenstern distributions. Pak. J. Stat. 29(4), 453-466 (2013) · Zbl 1509.62235 [9] David, H.A., Nagaraja, H.: Order Statistics. Wiley, New York (2003) · Zbl 1053.62060 · doi:10.1002/0471722162 [10] Kamps, U.: A Concept of Generalized Order Statistics. B.G. Teubner, Stuttgart (1995) · Zbl 0851.62035 · doi:10.1007/978-3-663-09196-7 [11] Morgenstern, D.: Einfache beispiele zweidimensionaler verteilungen. Mitteilingsblatt für Math. Stat. 8(1), 234-235 (1956) · Zbl 0070.36202 [12] Tahmasebi, S., Behboodian, J.: Shannon information for concomitants of generalized order statistics in Farlie-Gumbel-Morgenstern (FGM) family. Bull. Malays. Math. Sci. Soc. 35(4), 975-981 (2012) · Zbl 1318.62015 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.