The Estimation of Finite Population Variance Under Stratified Sampling Technique

  • Uzma Yasmeen Department of Statistics and Actuarial Sciences, University of Waterloo, Canada and Institute of Molecular Biology and Biotechnology/Centre for Research in Molecular Medicine, The University of Lahore, Pakistan
  • Muhammad Noor-ul-Amin Department of Statistics, COMSATS University Islamabad, Lahore Campus, Pakistan
Keywords: exponential estimator, stratified sampling, auxiliary variables, relative efficiency,

Abstract

The efficiency of the study variable can be improved by incorporating the information from the known auxiliary variables. Usually two techniques ratio and regression estimation are used with the help of auxiliary information in different approaches to acquire the high precision of the estimators. Considering the very heterogeneous population to get the size of the sample it may be originating impossible to get a sufficiently accurate and precise estimate by taking the simple random sampling technique from the complete population. Occasionally taking sample issue may differ significantly in different part of the entire population. For example, under study population consists of people living in apartments, own homes, hospitals and prisons or people living in plain regions and hill regions so in such situations the stratified sampling is one of the most commonly used approach to get a representative sample in survey sampling from different cross units of the population. The present study is set out on the recommendation of generalized variance estimators for finite population variance incorporating stratified sampling scheme with the information of single and two transformed auxiliary variables. The expressions of bias and mean square error (MSE) are obtained for the advised exponential type estimators. The conditions are obtained for which the anticipated estimators are better than the usual estimator. An empirical and simulation study is conducted to prove the superiority of the recommended estimator.

Downloads

Download data is not yet available.

Author Biographies

Uzma Yasmeen, Department of Statistics and Actuarial Sciences, University of Waterloo, Canada and Institute of Molecular Biology and Biotechnology/Centre for Research in Molecular Medicine, The University of Lahore, Pakistan

Uzma Yasmeen is a Ph.D. from the National College of Business Administration & Economics, Lahore, Pakistan. She has worked at the University of Waterloo, Canada and COMSATS University Islamabad. Currently, she is working as an Assistant professor at the University of Lahore, Lahore Campus. Her research interest is sampling Techniques, Bio Statistics. She is an HEC approved supervisor.

Muhammad Noor-ul-Amin, Department of Statistics, COMSATS University Islamabad, Lahore Campus, Pakistan

Muhammad Noor-ul-Amin received his Ph.D. degree from NCBA&E, Lahore, Pakistan. He has working experience in various universities for teaching and research that includes the Virtual University of Pakistan, University of Sargodha, Pakistan, and the University of Burgundy, France. He is currently working as an Assistant professor at COMSATS University Islamabad-Lahore Campus. His research interests include sampling techniques and control charting techniques. He is an HEC approved supervisor.

References

Dalabehara, M., and Sahoo, L. N. (1997). A class of estimators in stratified sampling with two auxiliary variables. Journal Into Society Agriculture Statistics, 50(2), pp. 144–149.

Dalabehara, M., Sahoo, L. N. (1999). A new estimator with two auxiliary variables for stratified sampling, Statistica, 59(1), pp. 101–107.

Shabbir, J., Gupta, S. (2005). Improved ratio estimators in stratified sampling, American Journal of Mathematical & Management Sciences, 25, pp. 293–311.

Diana, G. (1993). A class of estimators of the population mean in stratified random sampling, Statistica, 53(1), pp. 59–66.

Singh, M. P. (1965). On the estimation of ratio and product of the population parameters, Sankhyā The Indian Journal of Statistics, Series B, pp. 321–328.

Singh, H. P., Tailor, R., Singh, S., Kim, J. M. (2008). A modified estimator of population mean using power transformation, Statistica, 49, pp. 37–58.

Khoshnevisan M., Singh R., Chauhan P., Sawan, N., Smarandache, F. (2007). A general family of estimators for estimating population mean using known value of some population parameter(s), Far East Journal of Theoretical Statistics, 22, pp. 181–191.

Kadilar, C., Cingi, H. (2003). Ratio estimators in stratified random sampling, Biometrical Journal, 45: 218–225.

Kadilar, C., and Cingi, H. (2003). Ratio estimators in stratified random sampling, Biometrical Journal: Journal of Mathematical Methods in Biosciences, 45(2), pp. 218–225.

Kadilar, C. and Cingi, H. (2006). An improvement in estimating the population mean by using the correlation co-efficient, Hacettepe Journal of Mathematics and Statistics, 35 (1), pp. 103–109.

Chandra, P., Singh H. P. (2005) A family of estimators for population variance using knowledge of kurtosis of an auxiliary variable in sample survey, Statistics in Transition, 37 pp. 7–27.

Gupta, S., Shabbir, J. (2007). On the use of transformed auxiliary variables in estimating population mean, Journal of Statistical Planning and Inference, 137(5), pp. 1606–1611.

Gupta, S., Shabbir, J. (2008). On improvement in estimating the population mean in simple random sampling. Journal of Applied Statistics, 35(5), pp. 559–566.

Isaki, C. T. (1983). Variance estimation using auxiliary information, Journal of the American Statistical Association, 78, pp. 117–123.

Parsad, B., Singh, H. P. (1990). Some improved ratio-type estimators of finite population variance using auxiliary information in sample surveys, Communication in Statistics – Theory and Methods, 19(3), pp. 1127–1139.

Parsad, B., Singh, H. P. (1992). Unbiased estimators of finite population variance using auxiliary information in sample survey, Communication in Statistics – Theory and Methods, 21(5), pp. 1367–1376.

Singh, H. P., Vishvakarama, G. K. (2010). A general procedure for estimating the population mean in stratified random sampling using auxiliary information, Metron, 68(1), pp. 47–65.

Subramani, J. and Kumarapandiyan, G. (2012a). A class of almost unbiased modified ratio estimators for population mean with known population parameters, Elixir Statistics, 44, pp. 7411–7415.

Subramani, J. and Kumarapandiyan, G. (2012b). Estimation of population mean using known median and co-efficient of skewness, American Journal of Mathematics and Statistics, 2(5), pp. 101–107.

Subramani, J. and Kumarapandiyan, G. (2012c). Estimation of population mean using co-efficient of variation and median of an auxiliary variable, International Journal of Probability and Statistics, 1(4), pp. 111–118.

Yadav, S. K., Kadilar, C., Shabbir, J., Gupta, S. (2015). Improved family of estimators of population variance in Simple Random Sampling, Journal of Statistical Theory and Practice, 9(2), pp. 219–226.

Yasmeen, U., Noor ul Amin, M., Hanif, M. (2015). Generalized exponential estimators of finite population mean using transformed auxiliary variables. International Journal of Applied Computational Mathematics, 1(2), pp. 1–10.

Yasmeen U, Noor ul Amin M, Hanif M. (2016). Exponential ratio and product type estimators of finite population mean. Journal of statistics and management systems 19: 55–71.

Yasmeen, U., Noor ul Amin, M., Hanif M. (2018). Exponential Estimators of Finite Population Variance Using Transformed Auxiliary Variables. Proceedings of the National Academy of Sciences, India Section A: Physical Sciences.

Noor ul Amin, M., Yasmeen, U., Hanif M. (2018). Generalized Variance Estimators In Adaptive Cluster Sampling Using Single Auxiliary Variable. Journal of Statistics and Management Sciences.

Yasmeen, U., Noor ul Amin, M., Hanif M. (2018) Estimation of finite population variance under systematic sampling using auxiliary information. Statistics and Applications.

Gupta, S., and Shabbir, J. (2010). Estimating variance of stratified random sample mean in two phase sampling using two auxiliary variables. American Journal of Mathematical and Management Sciences, 30(3–4), 347–364.

Shabbir, J., and Gupta, S. (2010). Some estimators of finite population variance of stratified sample mean. Communications in Statistics—Theory and Methods, 39(16), 3001–3008.

Published
2021-11-20
Section
Articles