Generalized modified ratio-cum-product kind exponentially estimator of the populations mean in stratified ranked set sample

Document Type : Research Paper


1 Department of Statistics and Informatics, Mosul University, Iraq

2 Department of Statistics, Baghdad University, Baghdad, Iraq


In this study, we present a proposal aimed at estimating the finite population's mean of the main variable by stratification rank set sample \(S_{t}\text{RSS}\) through the modification made to generalized ratio-cum-product type exponential estimator. The relative bias \(\text{PRB}\), Mean Squared Error \(\text{Mse}\) and percentage relative efficiencies \(\text{PRE}\) of the proposed modified estimator is obtained to the first degree of approximation. Conditions under which the proposed estimator is more efficient than the usual unbiased estimator, ratio, product type estimators, and some other estimators are obtained. Finally, the estimators' abilities are evaluated through the use of simulations, as showed that the proposed modified estimator is more efficient as compared to several other estimators.


[1] B. C. Arnold, N. Balakrishnan and H. Nagaraja, A First Course in Order Statistics, Siam, 1992.
[2] A.E. Cetin and N. Koyuncn, Estimation of population mean under different stratified ranked set sampling designs
with simulation study application to BMI data, Commun. Factulty Sci. Univer. Ankara Ser. A Math. Stat. 69 (1)
2020 560-575[3] T.R. Dell and J.L. Clutter, Ranked set sampling theory with order statistics background, Biometrics (1972)
[4] L. Khan and J. Shabbir, Hartley-Ross type unbiased estimators using ranked set sampling and stratified ranked
set sampling, North Carolina J. Math. Stat. 2 (2016) 10–22.
[5] L. Khan and J. Shabbir, Generalized exponential-type ratio-cum ratio estimators of population mean in ranked
set and stratified ranked set sampling, J.Stat. Manag. Syst. 20 (1) 2017 133–151.
[6] N. Koyuncu, Calibration estimator of population mean under stratified ranked set sampling design, Commun.
Stat. Theory Meth. 47(23) (2017) 5845–5853.
[7] K. H. A. N. Lakhkar, J. Shabbir and S. Gupta, Unbiased ratio estimators of the mean in stratified ranked set
sampling, Hacettepe J. Math. Stat. 46(6) (2016) 1151–1158.
[8] D.F. Linder, H. Samawi, L.Yu, A. Chatterjee, Y. Huang and R. Vogel, On stratified bivariate ranked set sampling
for regression estimators, J. Appl. Stat. 42(12) (2015) 2571–2583.
[9] H.A. Lone, R. Tailor and H.P. Singh,Generalized ratio-cum-product type exponential estimator in stratified random
sampling, Communi. Stat. Theory Meth. 45(11) (2016) 3302–3309.
[10] V. L. Mandowara and N. Mehta, Modified ratio estimators using stratified ranked set sampling, Hacettepe J.
Math. Stat. 43(3) (2014) 461–471.
[11] G.A. McIntyre, A method for unbiased selective sampling, using ranked ets, Aust. J. Agricul. Res. 3(4) (1952)
[12] N. Mehta and V. Manbowara, Advanced estimator in stratified ranked set sampling using auxiliary information,
Int. J. Appl. Math. 5(4) (2016) 37–46.
[13] M. Saini and A. Kumar, Ratio estimators using stratified random sampling and stratified ranked set sampling,
Life Cycle Reliab. Safety Engin. 8(1) (2019) 85–89.
[14] H.M. Samawi, Stratified Ranked Set Sample, Cambridge Scholars Publishing, 2010.
[15] H.M. Samawi and M.I. Siam, Ratio estimation using stratified ranked set sample, Metron 61(1) (2003) 75–90.
[16] H.M. Samawi and H.A. Muttlak, Estimation of ratio using rank set smpling, Biomet. J. 38(6) (1996) 753–764.
[17] H.P. Singh, V. Mehta and S.K. Pal, Dual to ratio and product type estimators using stratified ranked set sampling,
J. Basic Appl. Engin. Res. 1(13) (2014) 7–12.
[18] S. Stokes, Ranked set sampling with concomitant variables, Commun. Stat. Theory Meth. 6(12) (1977) 1207–1211.
[19] K. Takahasi and K. Wakimoto, On unbiased estimates of the population mean based on the sample stratified by
means of ordering, Ann. Instit. Stat. Math. 20(1) (1968) 1–31.
Volume 13, Issue 1
March 2022
Pages 1137-1149
  • Receive Date: 15 March 2021
  • Revise Date: 27 April 2021
  • Accept Date: 04 May 2021
  • First Publish Date: 15 October 2021