The extended Farlie-Gumbel-Morgenstern bivariate Lindley distribution: Concomitants of order statistics and estimation


Abstract


The ranked set sampling (RSS) is a new sampling method alternative tothe simple random sampling (SRS). In this work, we develop the theory ofconcomitant of order statistics (COS) ascending from the extended Farlie-Gumbel-Morgenstern bivariate Lindley distribution (EFGMBLD). Also, wehave discussed the problem of estimating the parameters related with thedistribution of the variable interest, Y , based on the RSS dened by orderingthe marginal observations on an auxiliary variable X, provided that (X; Y )follows an EFGMBLD. When the association parameters corresponding to Yare known, we have derived two estimators, viz., an unbiased estimator basedon Stoke's RSS and the best linear unbiased estimator (BLUE) based on theStoke's RSS. The BLUE and the unbiased estimators are also compared basedon simulation study.

DOI Code: 10.1285/i20705948v14n2p373

Keywords: Concomitants of order statistics; Ranked set sampling; Extended Farlie- Gumbel-Morgenstern bivariate Lindley distribution

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