Unbiased ratio estimators of the mean in stratified ranked set sampling
Year 2017,
Volume: 46 Issue: 6, 1151 - 1158, 01.12.2017
Lakhkar Khan
,
Javid Shabbir
,
Sat Gupta
Abstract
Stratified ranked set sampling (StRSS) combines the advantages of stratification and ranked set sampling (RSS). In this paper, we propose several unbiased ratio type estimators using StRSS, when population mean of the auxiliary variable is known. The variances of the proposed
unbiased ratio-type estimators are obtained to first degree of approximation. In simulation study the proposed estimators are more efficient as compared to other competitor estimators using Percentage Relative Efficiency (PRE), Percentage Relative Bias (PRB) and Percentage Relative Root Mean Square Error (PRRMSE).
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mean using ranked set sampling, Hacettepe Journal of Mathematics and Statistics,
Doi:10.15672/HJMS.20156210579, 2015.
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Hacettepe Journal of Mathematics and Statistics, 43 (3), 461-471, 2014.
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Science, 3 (4), 385-390, 1952.
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Journal of Computational and Applied Mathematics, 232, 305-317, 2009.
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Journal, 38 (6), 753-764, 1996.
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61 (1), 75-90, 2003.
- Silva, P.L.D. and Skinner, C.J. Estimating distribution function with auxiliary information
using poststratification, Journal of Official Statistics, 11, 277-294, 1995.
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known parameters of auxiliary variate, Communications in Statistics-Theory and Methods,
43 (3), 547-565, 2014.
- Singh, H. P., Mehta, V. and Pal, S.K. Dual to ratio and product type estimators using
stratified ranked set sampling, Journal of Basic and Applied Engineering Research, 1 (13),
7-12, 2014.
- Takahasi, K. and Wakimoto, K. On unbiased estimates of the population mean based on the
sample stratified by means of ordering, Annals of the Institute of Statistical Mathematics,
20 (1), 1-31, 1968.
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finite population mean, Biometrical Journal, 41 (5), 627-636, 1999.
Year 2017,
Volume: 46 Issue: 6, 1151 - 1158, 01.12.2017
Lakhkar Khan
,
Javid Shabbir
,
Sat Gupta
References
- Arnold, B. C., Balakrishnan, N. and Nagaraja, H. N. A First Course in Order Statistics,
Vol. 54, Siam, 1992.
- Chambers, R.L. and Dunstan, R. Estimating the distribution function from survey data,
Biometrika, 73, 597-604, 1986.
- Harms, T and Duchesne, P. On calibration estimation for quantile, Survey Methodology,
32, 37-52, 2006.
- Hartley, H.O. and Ross, A. Unbiased ratio estimators, Nature, 174, 270-271, 1954.
- Kadilar, C and Cingi, H. A new ratio estimator in stratified random sampling, Communication
in Statistics: Theory and Methods, 34, 597-602, 2005.
- Kadilar, C and Cingi, H. New ratio estimators using correlation coefficient, Interstat, 1-11,
2006.
- Kadilar, C and Cingi, H. An improvement in estimating the population mean by using the
correlation coefficient, Hacettepe Journal of Mathematics and Statistics, 35 (1), 103-109,
2006.
- Kadilar, C , Candan, M. and Cingi, H. Ratio estimators using robust regression, Hacettepe
Journal of Mathematics and Statistics, 36 (2), 181-188, 2007.
- Kadilar, C and Cekim, H.O. Hartley-Ross type estimators in simple random sampling, Proceedings
of the International Conference on Numerical Analysis and Applied Mathematics,
AIP Conf.Proc. 1648, 610007-1610007-4; Doi:10.1063/1.4912849, 2014.
- Khan, L. and Shabbir, J. A class of Hartley-Ross type unbiased estimators for population
mean using ranked set sampling, Hacettepe Journal of Mathematics and Statistics,
Doi:10.15672/HJMS.20156210579, 2015.
- Mandowara, V. L. and Mehta, N. Modified ratio estimators using stratified ranked set sampling,
Hacettepe Journal of Mathematics and Statistics, 43 (3), 461-471, 2014.
- Mclntyre, G. A method for unbiased selective sampling using ranked sets, Crop and Pasture
Science, 3 (4), 385-390, 1952.
- Munoz, J. F. and Rueda, M. New imputation method for missing data using quantiles,
Journal of Computational and Applied Mathematics, 232, 305-317, 2009.
- Pascual, J. N. Unbiased ratio estimators in stratified sampling, Journal of the American
Statistical Association, 293 (56), 70-87, 1961.
- Rao, J.N.K. Kovar, J.G. and Mantel, H.J. On estimating distribution function and quantiles
from survey data using auxiliary information, Biometrika, 77, 365-375, 1990.
- Samawi, H. M. and Muttlak, H. A. Estimation of ratio using ranked set sampling, Biometrical
Journal, 38 (6), 753-764, 1996.
- Samawi, H. M. and Siam, M.I. Ratio estimation using stratified ranked set sample, Metron,
61 (1), 75-90, 2003.
- Silva, P.L.D. and Skinner, C.J. Estimating distribution function with auxiliary information
using poststratification, Journal of Official Statistics, 11, 277-294, 1995.
- Singh, H. P., Sharma, B. and Tailor, R. Hartley-Ross type estimators for population mean using
known parameters of auxiliary variate, Communications in Statistics-Theory and Methods,
43 (3), 547-565, 2014.
- Singh, H. P., Mehta, V. and Pal, S.K. Dual to ratio and product type estimators using
stratified ranked set sampling, Journal of Basic and Applied Engineering Research, 1 (13),
7-12, 2014.
- Takahasi, K. and Wakimoto, K. On unbiased estimates of the population mean based on the
sample stratified by means of ordering, Annals of the Institute of Statistical Mathematics,
20 (1), 1-31, 1968.
- Upadhyaya, L. N. and Singh, H. P. Use of transformed auxiliary variable in estimating the
finite population mean, Biometrical Journal, 41 (5), 627-636, 1999.