A NEW CLASS OF EXPONENTIAL REGRESSION CUM RATIO ESTIMATOR IN TWO PHASE SAMPLING

Abstract

In this paper, we propose a new class of exponential regression cumratio estimator using the auxiliary variable for the estimation of thefinite population mean under two phase sampling scheme. The Biasand Mean Square Error (MSE) equations of the proposed estimatorare obtained and compared with the MSE equations of some existingestimators in two phase sampling. We find theoretically the proposedestimator is always more efficient than classical ratio and regression estimators, Singh and Vishwakarma [17] ratio type exponential estimatorin two phase sampling. In addition, theoric results are supported by anumerical example using original data sets.

Keywords

• Two phase sampling, Auxiliary variable, Exponential estimation, Efficiency.

A NEW CLASS OF EXPONENTIAL REGRESSION CUM RATIO ESTIMATOR IN TWO PHASE SAMPLING

Abstract

-

Keywords

• -

References

1. Ahmad, Z. Generalized Multivariate Ratio and Regression Estimators for Multi-phase Sampling (PhD thesis, National College of Business Administration and Economics, Lahore, Pakistan, 2008).
2. Bahl, S. and Tuteja, R.K. Ratio and product exponential estimators, Journal of Information and Optimization Sciences, 12 (1), 159-164, 1991.
3. Cingi, H., Kadilar, C. and Kocberber, G. Determination of the Opportunities of the Primary and the Secondary Schools in Turkey and Suggestions to Solve the Determined Problems (TUBITAK, SOBAG106K077.(in Turkish), 2007).
4. Cingi, H. and Kadilar, C. Advances in Sampling Theory-Ratio Method of Estimation (Bentham Science Publishers, 2009).
5. Das, A.K. and Tripathi, T.P. Use of auxiliary information in estimating the finite population variance, Sankhya C 40 (2): 139-148, 1978.
6. Grover, L.K. and Kaur, P. An improved estimator of the finite population mean in simple random sampling, Model Assisted Statistics and Applications 6 (1), 47-55, 2011.
7. Hanif, M., Shahbaz, M.Q. and Ahmad, Z. Some Improved Estimators in Multiphase Sampling, Pak. J. Statist. 26 (1), 195-202, 2010.
8. Kadilar, C. and Cingi, H. Ratio Estimators in Stratified Random Sampling, Biometrical Journal 45 (2), 218-225, 2003.

9. 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), 103109, 2006.
10. Keen, K. J. Two-Phase Sampling, Encyclopedia of Biostatistics, 2005.
11. Koyuncu, N. and Kadilar, C. On the family of estimators of population mean in stratified random sampling, Pak. Jour. Statist. 26 (2), 427-443, 2010.
12. Murthy, M.N. Sampling Theory and methods (Statistical Publishing Society, Calcutta, India, 1967).
13. Neyman, J. Contribution to the theory of sampling human populations, Journal of the American Statistical Association 33, 101-116, 1938.
14. Ozgul, N. Mean Estimators in Two Phase Sampling (MSc.Thesis (in Turkish), Department of Statistics, Hacettepe University, Ankara, Turkey, 2007).
15. Samiuddin, M. and Hanif, M. Estimation of population mean in single and two phase sampling with or without additional information, Pak. J. Stat. 23 (2), 99-118, 2007.
16. Singh, H.P. and Ruiz-Espejo, M. On linear regression and ratio-product estimation of a finite population mean, The Statistician 52 (1), 59-67, 2003.
17. Singh, H.P. and Vishwakarma, G.K. Modified exponential ratio and product estimators for finite population mean in two phase sampling, Austrian Journal of Statistics 36 (3), 217-225, 200 Singh, H.P., Tailor, R. and Tailor, R. On ratio and product methods with certain known population parameters of auxiliary variable in sample surveys, SORT 34 (2), 157-180, 2010. Singh, R., Chauhan, P., Sawan, N. and Smarandache, F. Improvement in estimating the population mean using exponential estimator in simple random sampling, Bulletin of Statistics and Economics 3 (9), 13-18, 2009.
18. Sukhatme, P.V. and Sukhatme, B.V. Sampling theory of surveys with applications (Second Edition) (Asia Publishing House, Bombay, India, 1970).