Difference-type-exponential estimators based on dual auxiliary information under simple random sampling

Document Type : Article

Authors

1 Department of Statistics, Government College University, Faisalabad, Pakistan

2 - Department of Statistics, Government College University, Faisalabad, Pakistan. - Department of Mathematics, Institute of Statistics Zhejiang University, Hangzhou 310027, China

Abstract

Auxiliary information plays a vital role at the selection and/or estimation stage to achieve the efficient estimates of the unknown population parameters. Dual use of auxiliary information, one the original and second the ranks of the auxiliary variable help to increase the efficiency of the estimators. In this article, we proposed and evaluated the performance of difference-type-exponential estimators based on dual auxiliary information for population mean under simple random sampling. Mathematical expressions for the bias and the mean squared error of the proposed estimators are obtained. Three real-life data sets and Monte Carlo simulation studies are carried out for illustration. The results of the empirical and the simulation studies, in terms of mean square errors and percentage relative efficiencies indicate that the proposed estimators perform better as compared to their counterparts.

Keywords

References

References:
1. Haq, A., Khan, M., and Hussain, Z. A new estimator of finite population mean based on the dual use of the auxiliary information", Communications in Statistics- Theory and Methods, 46(9), pp. 4425-4436 (2017).
2. Kadilar, C. and Cingi, H. "Ratio estimators in simple random sampling", Applied Mathematics and Computation, 151, pp. 893-902 (2004).
3. Kadilar, C. and Cingi, H. "Improvement in estimating the population mean in simple random sampling", Applied Mathematics Letters, 19, pp. 75-79 (2006a).
4. Gupta, S. and Shabbir, J. "On improvement in estimating the population mean in simple random sampling", Journal of Applied Statistics, 35(5), pp. 559- 566 (2008).
5. 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), pp. 47-55 (2011).
6. Grover, L.K. and Kaur, P. "A generalized class of ratio type exponential estimators of population mean under linear transformation of auxiliary variable", Communications in Statistics- Simulation and Computation, 43, pp. 1552-1574 (2014).
7. Singh, H.P. and Solanki, R.S. "An efficient class of estimators for the population mean using auxiliary information",
Communications in Statistics-Theory and Methods, 42, pp. 145-163 (2013).
8. Haq, A. and Shabbir, J. "Improved exponential type estimators of finite population mean under complete and partial auxiliary information", Hacettepe Journal of Mathematics and Statistics, 43(6), pp. 1079-1093 (2014).
9. Shabbir, J., Haq, A., and Gupta, S. "A new differencecum- exponential type estimator of finite population mean in simple random sampling", Revista Colombiana de Estadistica, 37(1), pp. 199-211 (2014).
10. Ekpenyong, E.J. and Enang, E.I. "Efficient exponential ratio estimator for estimating the population mean in simple random sampling", Hacettepe Journal of Mathematics and Statistics, 44(3), pp. 689-705 (2015).
11. Khan, S.A., Ali, H., Manzoor, S., et al. "A class of transformed efficient ratio estimators of finite population mean", Pakistan Journal of Statistics, 31(4), pp. 353-362 (2015).
12. Solanki, R.S. and Singh, H.P. "The improvement over regression method of estimation of finite population mean in survey sampling", Journal of Advanced Computing, 4(3), pp. 101-111 (2015).
13. Srisodaphol, W., Kingphai, K., and Tanjai, N. "New ratio estimators of a population mean using one auxiliary variable in simple random sampling", Chiang Mai Journal of Science, 42(2), pp. 523-527 (2015).
14. Singh, H.P. and Pal, S.K. "A class of exponential-type ratio estimators of a general parameter", Communications in Statistics- Theory and Methods, 46(8), pp. 3957-3984 (2017).
15. Singh, H.P., Pal, S.K., and Solanki, R.S. "A new class of estimators of finite population mean in sample surveys", Communications in Statistics-Theory and Methods, 46(6), pp. 2630-2637 (2017).
16. Irfan, M., Javed, M., and Lin, Z. "Improved estimation of population mean through known conventional and non-conventional measures of auxiliary variable", Iranian Journal of Science and Technology, Transactions A: Science, 43(4), pp. 1851-1862 (2019).
17. Irfan, M., Javed, M., and Lin, Z. "Efficient ratiotype estimators of finite population mean based on correlation coefficient", Scientia Iranica: Transactions on Industrial Engineering (E), 25(4), pp. 2361-2372 (2018).
18. Javed, M., Irfan, M., and Pang, T. "Hartley-Ross type unbiased estimators of population mean using two auxiliary variables", Scientia Iranica: Transactions on Industrial Engineering (E), 26(6), pp. 3835-3845 (2019).
19. Bahl, S. and Tuteja, R.K. "Ratio and product type exponential estimator", Information and Optimization Sciences, XII(1), pp. 159-163 (1991).
20. Shabbir, J. and Gupta, S. "On estimating finite population mean in simple and stratified random sampling", Communications in Statistics- Theory and Methods, 40(2), pp. 199-212 (2011).
21. Singh, R.K. and Singh, G. "A class of estimators with estimated optimum values in sample surveys", Statistics and Probability Letters, 2, pp. 319-321 (1984).
22. Vishwakarmar, G.K. and Kumar, M. "A general family of dual to ratio-cum-product estimators of population mean in simple random sampling", Chilean Journal of Statistics, 6(2), pp. 69-79 (2015).
23. Rao, J.N.K., Kovar, J.G., and Mantel, H.J. "On estimating distribution function and quantiles from survey data using auxiliary information", Biometrika, 77, pp. 365-375 (1990).
24. Silva, N.P.L.D. and Skinner, C.J. "Estimating distribution functions with auxiliary information using poststratification", Journal of Official Statistics, 11, pp. 277-294 (1995).
25. Nidhi, B.V.S., Sisodia, Singh, S., and Singh, S.K. "Calibration approach estimation of the mean in stratified sampling and stratified double sampling", Communications in Statistics-Theory and Methods, 46(10), pp. 4932-4942 (2017).
26. Singh, R. and Mangat, N.S. "Elements of survey sampling", Norwell, MA: Kluwer Academic Publishers (1996).
27. Kadilar, C. and Cingi, H. "Ratio estimators for the population variance in simple and stratified random sampling", Applied Mathematics and Computation, 173(2), pp. 1047-1059 (2006b).
Scientia Iranica
Volume 29, Issue 1
Transactions on Industrial Engineering (E)
January and February 2022
Pages 343-354

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History

  • Receive Date: 21 May 2019
  • Revise Date: 27 January 2020
  • Accept Date: 20 April 2020

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