Estimation of population mean under different stratified ranked set sampling designs with simulation study application to BMI data

Abstract

In this article, we have compared the performance ratio-type estimators in some stratified ranked set sampling methods. These sampling methods are stratified random sampling, stratified ranked set sampling, stratified double ranked set sampling and stratified median ranked set sampling. In these methods, the ratio type estimators using auxiliary variable information such as coefficient of variation and kurtosis are examined. We have used a real data set to see the performance of estimators. We use the data concerning body mass index (BMI) as a study variable and the age and the weight as auxiliary variables for 800 people in Turkey in 2014. We stratified the data set using gender. A simulation study is carried out to see performance of the proposed ratio type estimators in these stratified ranked set sampling designs. The performances of these estimators are compared in terms of mean squared error (MSE) and percent relative efficiency (PRE). The importance of this study is that, a detail simulation study is done using a real data set and compare these stratified sampling designs in a study in the sampling literature.

Keywords

• Stratified sampling,Stratified ranked set sampling,Median ranked set sampling,Ratio-type estimators,Auxiliary variables,Mean squared error,Population mean,Efficiency,Body mass index

References

1. Al-Saleh, M.F. and Al-Kadiri, M.A., Double-ranked set sampling, Statistics and Probability Letters, 48(2) (2000), 205-212.
2. Al-Omari, A.I., Ratio estimation of the population mean using auxiliary information in simple random sampling and median ranked set sampling, Statistics and Probability Letters, 82 (2012), 1883-1890.
3. Dell, T. R. and Clutter, J.L., Ranked set sampling theory with order statistics background, Biometrics, 28 (1972), 545-555.
4. Hansen, M.H., Hurwitz, W.N., Gurney M., Problems and methods of the sample survey of business, Journal of American Statistical Association, 41(234) (1946), 173-189.
5. Ibrahim, K., Syam, M. and Al-Omari, A.I.,Estimating the population mean using stratified median ranked set sampling, Applied Mathematical Sciences, 4(47) (2010), 2341-2354.
6. Kadilar, C. and Cingi, H., Ratio estimators in stratified random sampling, Biometrical Journal, 4(2) (2003) 218-225.
7. Koyuncu, N., New difference-cum-ratio and exponential type estimators in median ranked set sampling, Hacettepe Journal of Mathematics and Statistics, 45(1) (2016), 207-225.
8. Khan, L., Shabbir J. and Kadilar C., Efficient classes of ratio-type estimators of population mean under stratified median ranked set sampling, Pakistan Journal of Statistics, 32(6) (2016), 475-496.

9. Khan, L., Shabbir, J. and Gupta, S., Improved ratio-type estimators using stratified double-ranked set sampling, Journal of Statistical Theory and Practice, 10(4) (2016) 755-767.
10. Mandowara, V. L. and Mehta, N., Modified ratio estimators using stratified ranked set sampling, Hacettepe Journal of Mathematics and Statistics, 43(3) (2014), 461-471.
11. Mc Intyre, G. A., A method for unbiased selective sampling, using ranked sets, Australian Journal of Agricultural Research, 3 (1952), 385-390.
12. Muttlak, H.A., Median ranked set sampling, Journal of Applied Statistical Science, 6 (1997), 245-255.
13. Samawi, H. M. and Muttlak, H.A., Estimation of ratio using rank set sampling, Biometrical Journal, 38 (1996), 753-764.
14. Samawi, H.M., Stratified ranked set sample, Pakistan Journal of Statistics, 12(1) (1996), 9-16.
15. Samawi, H.M. and Siam, M.I., Ratio estimation using stratified ranked set sample, Metron International Journal of Statistics, 61(1) (2003), 75-90.