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Unbiased ratio estimators of the mean in stratified ranked set sampling

Yıl 2017, Cilt: 46 Sayı: 6, 1151 - 1158, 01.12.2017

Öz

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).

Kaynakça

  • 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, 610007-1􀀀610007-4; 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.
Yıl 2017, Cilt: 46 Sayı: 6, 1151 - 1158, 01.12.2017

Öz

Kaynakça

  • 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, 610007-1􀀀610007-4; 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.
Toplam 22 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm İstatistik
Yazarlar

Lakhkar Khan

Javid Shabbir

Sat Gupta

Yayımlanma Tarihi 1 Aralık 2017
Yayımlandığı Sayı Yıl 2017 Cilt: 46 Sayı: 6

Kaynak Göster

APA Khan, L., Shabbir, J., & Gupta, S. (2017). Unbiased ratio estimators of the mean in stratified ranked set sampling. Hacettepe Journal of Mathematics and Statistics, 46(6), 1151-1158.
AMA Khan L, Shabbir J, Gupta S. Unbiased ratio estimators of the mean in stratified ranked set sampling. Hacettepe Journal of Mathematics and Statistics. Aralık 2017;46(6):1151-1158.
Chicago Khan, Lakhkar, Javid Shabbir, ve Sat Gupta. “Unbiased Ratio Estimators of the Mean in Stratified Ranked Set Sampling”. Hacettepe Journal of Mathematics and Statistics 46, sy. 6 (Aralık 2017): 1151-58.
EndNote Khan L, Shabbir J, Gupta S (01 Aralık 2017) Unbiased ratio estimators of the mean in stratified ranked set sampling. Hacettepe Journal of Mathematics and Statistics 46 6 1151–1158.
IEEE L. Khan, J. Shabbir, ve S. Gupta, “Unbiased ratio estimators of the mean in stratified ranked set sampling”, Hacettepe Journal of Mathematics and Statistics, c. 46, sy. 6, ss. 1151–1158, 2017.
ISNAD Khan, Lakhkar vd. “Unbiased Ratio Estimators of the Mean in Stratified Ranked Set Sampling”. Hacettepe Journal of Mathematics and Statistics 46/6 (Aralık 2017), 1151-1158.
JAMA Khan L, Shabbir J, Gupta S. Unbiased ratio estimators of the mean in stratified ranked set sampling. Hacettepe Journal of Mathematics and Statistics. 2017;46:1151–1158.
MLA Khan, Lakhkar vd. “Unbiased Ratio Estimators of the Mean in Stratified Ranked Set Sampling”. Hacettepe Journal of Mathematics and Statistics, c. 46, sy. 6, 2017, ss. 1151-8.
Vancouver Khan L, Shabbir J, Gupta S. Unbiased ratio estimators of the mean in stratified ranked set sampling. Hacettepe Journal of Mathematics and Statistics. 2017;46(6):1151-8.