Main Article Content

Abstract

Until now, various types of estimators have been used for estimating the population variance in simple random sampling studies, including ratio, product, regression and exponential-type estimators. In this article, we propose a family of -type estimators for the first time in the simple random sampling and show that they are more efficient than the other types of estimators under certain conditions obtained theoretically. Numerical illustrations and a simulation study support our findings in theory. In addition, it has been shown how to determine the optimal points in order to reach the minimum MSE values with the properties of the ln-type estimators in the different data sets.

Keywords

Simple Random Sampling Variance Estimator ln-type Estimator Efficiency

Article Details

Author Biographies

Hatice Oncel Cekim, Hacettepe University

Department of Statistics

Cem Kadilar, Hacettepe University, Turkey

Department of Statistics

How to Cite
Oncel Cekim, H., & Kadilar, C. (2020). ln-Type Variance Estimators in Simple Random Sampling. Pakistan Journal of Statistics and Operation Research, 16(4), 689-696. https://doi.org/10.18187/pjsor.v16i4.3072

References

  1. Adichwal, N. K., Sharma, P., Verma, H. K., & Singh, R. (2016). Generalized class of estimators for population variance using auxiliary attribute. International Journal of Applied and Computational Mathematics, 2(4), 499-508.
  2. Asghar, A. & Sanaullah, A. & Hanif, M. (2014). Generalized exponential type estimator for population variance in survey sampling. Revista Colombiana de Estadistica, 37(1), 213-224.
  3. Asghar, A., Sanaullah, A. & Hanif, M. (2017). A multivariate regression-cum-exponential estimator for population variance vector in two phase sampling. Journal of King Saud University-Science, 30(2), 223-228.
  4. Bahl, S. & Tuteja, R. K. (1991). Ratio and product type exponential estimator. Information Optimiz. Sci., 12, 159-163.
  5. Cekim, H. O., & Kadilar, C. (2020). In-type estimators for the population variance in stratified random sampling. Communications in Statistics-Simulation and Computation, 49(7), 1665-1677.
  6. Diana, G. & Tommasi, C. (2004). Estimation for finite population variance in double sampling. METRON – International Journal of Statistics, 62(2), 223-232.
  7. Hassan, Y., Ismail, M., Murray, W., & Shahbaz, M. Q. (2020). Efficient estimation combining exponential and ln functions under two phase sampling. AIMS Mathematics, 5(6), 7605.
  8. Isaki, C. T. (1983). Variance estimation using auxiliary information. Journal of American Statistical Association, 78, 117-123.
  9. Kadilar, C. & Cekim, H. O. (2017, July). Hartley-Ross type variance estimators in simple random sampling. In AIP Conference Proceedings (Vol. 1863, No. 1, p. 560008). AIP Publishing.
  10. Kadilar, C. & Cingi, H. (2006). Ratio estimators for population variance in simple and stratified sampling. Applied Mathematics and Computation, 173, 1047-1058.
  11. Kadilar, C. & Cingi, H. (2007). Improvement in variance estimation in simple random sampling. Communications in Statistics-Theory and Methods, 36(11), 2075-2081.
  12. Khan, M. (2015). An improved exponential-type estimator for finite population variance using transformation of variables. Journal of Statistics Applications & Probability, 4(1), 31-35.
  13. Shabbir, J. & Gupta, S. (2014). An improved generalized difference-cum-ratio-type estimator for the population variance in two-phase sampling using two auxiliary variables. Communications in Statistics-Simulation and Computation, 43(10), 2540-2550.
  14. Singh, H. P., Solanki, R. S. & Singh, A. K. (2016). A generalized ratio-cum-product estimator for estimating the finite population mean in survey sampling”, Communications in Statistics—Theory and Methods, 45(1), 158-172.
  15. Singh, H. P. & Solanki, R. S. (2014). An efficient class of estimators for the population mean using auxiliary information. Communications in Statistics—Theory and Methods, 43(16), 3380-3401.
  16. Singh, H. P., Pal, S. K. & Yadav, A. (2017). A Study on the chain ratio-ratio-type exponential estimator for finite population variance. Communications in Statistics-Theory and Methods, 47(6), 1442-1458.
  17. Singh, H. P. & Solanki, R. S. (2013). A new procedure for variance estimation in simple random sampling using auxiliary information. Statistical Papers, 54(2), 479-497.
  18. Singh, H. P. & Solanki, R. S. (2013). A new procedure for variance estimation in simple random sampling using auxiliary information. Statistical Papers, 54(2), 479-497.
  19. Solanki, R. S., Singh, H. P. & Pal, S. K. (2015). Improved ratio-type estimators of finite population variance using quartiles. Hacettepe Journal of Mathematics and Statistics, 44(3), 747-754.
  20. Subramani, J. & Kumarapandiyan, G. (2015). A class of modified ratio estimators for estimation of population variance. Journal of Applied Mathematics Statistics and Informatics, 11(1), 91-114.
  21. Upadhyaya, L. N. & Singh, H. P. (1999). An estimator of population variance that utilizes the kurtosis of an auxiliary variable in sample surveys. Vikram Mathematics Journal, 19, 14-17.
  22. 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), 219-226.
  23. Yadav, S. K., & Kadilar, C. (2013). Improved exponential type ratio estimator of population variance. Revista Colombiana de Estadistica, 36(1), 145-152.
  24. Yadav, S. K., Mishra, S. S., Shukla, A. K. & Tiwari, V. (2015). Improvement of estimator for population variance using correlation coefficient and quartiles of the auxiliary variable. Journal of Statistics Applications & Probability, 4(2), 259-263.
  25. Yadav, S. K., Mishra, S. S., Shukla, A. K. & Tiwari, V. (2015). Improvement of estimator for population variance using correlation coefficient and quartiles of the auxiliary variable. Journal of Statistics Applications & Probability, 4(2), 259-263.
  26. Yadav, R., Upadhyaya, L. N., Singh, H. P. & Chatterjee, S. (2013). A generalized family of transformed ratio-product estimators for variance in sample surveys. Communications in Statistics-Theory and Methods, 42(10), 1839-1850.