ARTICLE
ABSTRACT
A multistage balanced groups ranked set samples (MBGRSS) method and its properties for estimating the population median is considered. The suggested estimator is compared to those obtained based on simple random sampling (SRS) and the ranked set sampling (RSS) methods. The MBGRSS estimator of the population median is found to be unbiased if the underlying distribution is symmetric and has a small bias if the underlying distribution is asymmetric, the bias is decreasing in r (r is the number of stage). It is found that, MBGRSS is as efficient as RSS when m = 3 and r = 1 , and it is more efficient than RSS for r > 1 . However, the efficiency of MBGRSS is increasing in r for specific value of the sample size whether the underlying distribution is symmetric or asymmetric. Real data is used to illustrate the method.
KEYWORDS
Ranked set sampling; simple random sampling; balanced groups ranked set samples, symmetric distribution; asymmetric distribution.
REFERENCES
AL-OMARI, A.I. (1999). Multistage ranked set sampling, Master Thesis, Department of Statistics, Yarmouk University, Jordan
AL-OMARI, A.I. and JABER, K. (2008). Percentile double ranked set sampling, Journal of Mathematics and Statistics. 4 (1): 60–64.
AL-SALEH, M. F. and AL-OMARI, A. I. (2002). Multistage ranked set sampling, Journal of Statistical Planning and Inference. 102(2): 273–286.
DELL, T. R. and CLUTTER, J. L. (1972). Ranked set sampling theory with order statistic background. Biometrics, 28: 545–553.
JEMAIN, A. A. and AL-OMARI, A. I. (2006). Multistage median ranked set samples for estimating the population mean. Pakistan Journal of Statistics. 22(3): 195–207.
JEMAIN, A. A., AL-OMARI, A. I., and IBRAHIM, K. (2007). Multistage extreme ranked set sampling for estimating the population mean. Journal of Statistical Theory and Applications. 6(4): 456–471.
MCINTYRE, G. A. (1952). A method for unbiased selective sampling using ranked sets, Australian Journal of Agricultural Research. 3: 385–390.
MUTTLAK, H. A. (2003a). Investigating the use of quartile ranked set samples for estimating the population mean. Journal of Applied Mathematics and Computation. 146: 437–443.
MUTTLAK, H. A. (2003b) Modified ranked set sampling methods. Pakistan Journal of Statistics. 19(3): 315–323.
MUTTLAK, H. A. (1997). Median ranked set sampling, Journal of Applied Statistical sciences. 6(4): 245–255.
OZTURK, O. and DESHPANDE, J.V. (2006). Ranked-set sample nonparametric quantile confidence intervals. Journal of Statistical Planning and Inference. 136, 570–577.
SAMAWI, H, ABU-DAYYEH, W and AHMED, S. (1996). Extreme ranked set sampling, The Biometrical Journal. 30: 577–586.
TAKAHASI, K. and WAKIMOTO, K. (1968). On unbiased estimates of the population mean based on the sample stratified by means of ordering, Annals of the Institute Statistical Mathematics. 20: 1–31.
ZHENG, G. and MODARRES, R. (2006). A robust estimate of the correlation coefficient for bivariate normal distribution using ranked set sampling. Journal of Statistical Planning and Inference. 136 (2006) 298–309
TIENSUWAN, M., SARIKAVANIJ, S. and SINHA, B.K. (2007). Nonnegative unbiased estimation of scale parameters and associated quantiles based on a ranked set sample. Communications in Statistics-Simulation and Computation, 36, 3–31.
TSENG, Y.L. and SHAO, S.W. (2007). Ranked-Set-Sample-Based Tests for Normal and Exponential Means. Communications in Statistics—Simulation and Computation, 36: 761–782.
