Diverse Exponential Type Estimators for Estimating Population Means in Simple Random Sampling

Sangeeta Malik¹ , Megha ²

Section:Research Paper, Product Type: Journal-Paper
Vol.9 , Issue.3 , pp.61-65, Jun-2022

Online published on Jun 30, 2022

Copyright © Sangeeta Malik, Megha . This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
 

View this paper at   Google Scholar | DPI Digital Library

XML View     PDF Download

How to Cite this Paper

Abstract :
Small area estimation techniques are used for estimating the population means to give good estimates in agriculture field like estimates of crop yield. This article advises fresh exponential type estimators for small area to appraise the mean of the finite population expending information on single auxiliary variable. The bias and mean square error of these estimators have been obtained. These estimators are compared for their precision with usual mean per unit, ratio estimator, product estimator and some of other existing estimators and are found to be more efficient in many practical situations. Further, it is shown that these estimators reduce to regression estimator. Numerical results of the efficiency of the proposed estimators as percent relative efficiencies (PRE) are displayed to confirm the cases of superiority of the proposed estimators with exciting estimators.

Key-Words / Index Term :
Small area, Estimators, Mean Square Error, PRE

References :
[1] Singh G, Singh RK, Kaur P. “Estimating Ratio of Proportions Using Auxiliary Information”. Biometrical J. 28: 637–643, 1986.
[2] Naik VD, Gupta PC. “A note on estimation of mean with known population proportion of an auxiliary character”. Journal Indian Soc Ag
[3] Bahl, S. and Tuteja, R.K. “Ratio and product type exponential estimators”. Information and Optimization Sciences, 12(1), 159-163, 1991.
[4] Singh, R. and N.S. Mangat. “Elements of Survey Sampling”, Kluwer Academic Publishers, Dordrecht, The Netherlands, 1996.
[5] 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, 2007.
[6] Singh, R., Kumar, M., Singh, R.D., and Chaudhary, M.K.(2008). “Exponential Ratio Type Estimators in Stratified Random Sampling”, Presented in International Symposium On Optimisation and Statistics (I.S.O.S), A.M.U., Aligarh, India, 29-31 Dec2008.
[7] Singh, R., Kumar, M., Chaudhary, M.K., Kadilar, C. “Improved Exponential Estimator in Stratified Random Sampling”, Pak. J. Stat. Oper. Res. 5(2), pp 67- 82, 2009.
[8] H. P. Singh , R. Tailor, and N. K. Jatwa, “Modified ratio and product estimators for population mean in systematic sampling,” Journal of Modern Applied Statistical Methods, vol. 10, no. 2, pp. 424–435, 2011.
[9] Singh, R., Chauhan, P., Sawan, N. and Smarandache, F. Improved Exponential Estimator for Population Variance Using Two Auxiliary Variables, Italian Journal of Pure and Applied Math, 28, 103-110, 2011.
[10] Kumar, Mukesh et al. “Exponential Ratio Method of Estimation in the Presence of Measurement Errors”. Int. J. Agri. Statist. Sci, 7(2): 457–461, 2011.
[11] Shabbir, J. and Gupta, S. (2011). On Estimating finite population mean in simple and stratified random sampling, Commun. Stat. Theory and Methods 40: 199-212, 2011
[12] Solanki RS, Singh HP. Improved estimation of population mean using population proportion of an auxiliary character. Chil J Stat. 2013; 4: 3–17
[13] Malik S, Singh R. An improved estimator using two auxiliary attributes. Appl Math Comput. 2013; 219: 10983–10986.
[14] Tailor Rajesh, Mishra Asha, “An Exponential Strategy for Estimation of Population Mean in Systematic Sampling” Vol.5 , Issue.3 , pp.73-78, Jun-2018
[15] Onyango R., Oduor B., Odundo F., “Enhanced Estimation of Population Mean in Presence of Errors on a Survey Variable in Stratified Two Phase Sampling”, International Journal of Scientific Research in Mathematical and Statistical Sciences Volume-9, Issue-1, pp.32-39, February 2022.
[16] Megha, Sangeeta Malik, (2022). Generalized Composite Regression with Ratio and Product Estimators in Double Sampling. International Journal of Scientific Research in Mathematical and Statistical Sciences, 9(2), 31-35, 2022.