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

References


Al-Omari, A.I. (2021). Maximum likelihood estimation in location-scale families using

varied L ranked set sampling. RAIRO Operations Research, 55, 2759{2771.

Al-Omari, A.I. and Abdallah, M.S. (2021). Estimation of the distribution function using

moving extreme and minimax ranked set sampling. Communications in Statistics-

Simulation and Computation.

Al-Omari, A.I. and Almanjahie, I.M. (2021). New improved ranked set sampling design

with an application to real data. Computers, Materials and Continua.

Beg, M.I. and Ahsanullah, M. (2008). Concomitants of generalized order statistics from

FarlieGumbelMorgenstern distributions. Statistical Methodology, 5(1): 1-20.

Benchiha, S. and Al-Omari, A.I. (2021). Generalized quasi Lindley distribution: theoretical

properties, estimation methods and applications. Electronic Journal of Applied

Statistical Analysis, 14(1), 167-196.

David, H.A. and Nagaraja, H.N. (2003). Order Statistics. Third edition. John Wiley and

Sons, New York..

Jemain, A.A., Al-Omari, A.I. and Ibrahim, K. (2007). Multistage median ranked set

sampling for estimating the population median. Journal of Mathematics and Statistics,

(2): 58-64.

Al-Omari, A.I. and Haq, A. (2019). A new sampling method for estimating the population mean. Journal of Statistical Computation and Simulation, 89(11): 1973-1985.

Electronic Journal of Applied Statistical Analysis 15

Johnson N.L. and Kotz, S. (1977). On some generalized Farlie-Gumbel-Morgenstern

distributions-II: Regression, correlation and further generalizations.Communications

in Statistics-Theory and Methods, 6, 485-496.

Maya, R., Irshad, M.R. and Shibu, D.S. (2018). Concomitants of record values arising

from the Morgenstern type bivariate Lindley distribution. Afrika Statistika, 13(4),

-1875.

Maya, R., Irshad, M.R. and Arun, S.P. (2021). Farlie-Gumbel-Morgenstern bivariate

Bilal Distribution and its inferential aspects using concomitants of order statistics.

Journal of Probability and Statistical Science, 19(1), 1-20.

McIntyre, G.A. (1952). A method for unbiased selective sampling using ranked sets.

Australian Journal of Agricultural Research 3, 385-390.

Morgenstern, D. (1956). Einfache beispiele zweidimensionaler verteilungen. Mittelings-

blatt fur Mathematische Statistik, 8, 234-235.

Philip, A. (2011). Concomitants of order statistics from an extended Farlie-Gumbel-

Morgenstern distribution. Journal of the Kerala Statistical Association, 22, 5-20.

Irshad, M.R., Maya, R. and Arun S.P. (2019). Estimation of a parameter of Morgenstern

type bivariate Lindley distribution by ranked set sampling. iSTATISTIK: Journal of

the Turkish Statistical Association, 12(1-2), 25-34.

Scaria, J. and Nair, N.U. (1999). On concomitants of order statistics from Morgenstern

family. Biometrical Journal, 41: 483-489.

Stokes, S.L. (1977). Ranked set sampling with concomitant variables. Communications

in Statistics-Theory and Methods, 6, 1207-1211.

Al-Omari, A.I. (2011). Estimation of mean based on modied robust extreme ranked set

sampling. Journal of Statistical Computation and Simulation, 81(8), 1055-1066.

Zamanzade, E. and Al-Omari, A.I. (2016). New ranked set sampling for estimating

the population mean and variance. Hacettepe Journal of Mathematics and Statistics,

(6), 1891-1905.

Haq, A., Brown, J., Moltchanova, E. and Al-Omari, A.I. (2015). Varied L ranked set

sampling scheme. Journal of Statistical Theory and Practice, 9(4), 741-767.

Takahasi, K. and Wakimoto, K. (1968). On the unbiased estimates of the population

mean based on the sample stratied by means of ordering. Annals of the Institute of

Statistical Mathematics, 20, 1-31.


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