Global Journal of Science Frontier Research, F: Mathematics and Decision Science, Volume 21 Issue 4

improvement of the estimation of the median of a finite population of which the proposed estimator has bridged the gap. V. C onclusion This study was towards formulating an improved exponential-type estimator for population median using both simple random and two-phase sampling with two auxiliary variables. The bias and mean square error were obtained. From the theoretical derivations and numerical illustrations, it is evident to say that among the existing and proposed estimators, the proposed estimators under simple random sampling and two- phase sampling exhibit superior performance both in negligible bias and in gain in efficiency. It suffices to conclude that the proposed estimators perform better than existing estimators considered in this work in estimating population median when the population median of the auxiliary variables are known and positively correlated with the study variable. However, though the suggested estimator performed poorly with less efficiency in population V, probably because of the data type, it was still shown to have less bias compared to other estimators of its class. The idea of using separate ratio- product exponential-type estimator in this case has really paid off in improving on the efficiency of the median estimator under stratified random sampling. In addition, the proposed estimator will be suitable and highly recommended when the variable considered is from a distribution that is highly skewed. R eferences R éférences R eferencias 1. Aczel, A. D. & Sounderpandian, J. (2004). Complete Business Statistics. 5 th ed., McGraw Hill, New York. 2. Aladag, S. & Cingi, H. (2015). Improvement in estimating the population median in simplerandom sampling and stratified random sampling using auxiliary information. Communication in Statistics-Theory and Methods , 45(5), 1013-1032. 3. Bahl, S & Tuteja, R. K. (1991). Ratio and product type exponential estimator. Journal of Information and Optimization sciences, 12(1), 159-164. 4. Baig, A., Masood S. & Tarray, T. A. (2019). Improved class of difference-type estimators for population median in survey sampling. Communication in Statistics- Theory and Methods , DOI: 10.1080/03610926.2019.1622017 5. Enang, E. I., Etuk, S. I., Ekpenyong, E. J. & Akpan, V. M. (2016). An alternative Exponential estimator of population median. International Journal of Statistics and Economics, 17(3), 85-97. 6. Gross, T.S. (1980). Median estimation in sample surveys. in American Statistical Association Proceedings of Survey Research methodology Section , pp.181-184. 7. Iseh, M. J. (2020). Enhancing efficiency of ratio estimator of population median by calibration techniques. International Journal of Engineering Sciences & Research Technology, 9(8), 14-23. 8. Jhajj, H. S., Kaur, H. & Jhajj, P. (2016). Efficient family of estimators of median using two-phase sampling design. Communications in Statistics-Theory and Methods 45 (15):4325 – 31. DOI: 10.1080/03610926.2014.911912. 9. Kadilar, C. & Cingi, H. (2004). Ratio estimators in simple random sampling. Applied Mathematical Computations , 151, 893-902. 10. Kuk, A.Y.C. & Mak, T.K. (1989). Median estimation in the presence of auxiliary variable. Journal of Royal Statistical Society. Series B, 51,261-269. 11. MFA. 2004. Crops area production, Government of Pakistan, Ministry of Food, Agriculture and Livestocks. Islamabad, Pakistan: Economic Wing. Towards the Efficiency of the Ratio Estimator for Population Median in Survey Sampling © 2021 Global Journals 1 Global Journal of Science Frontier Research Volume XXI Issue IV Year 2021 48 ( F ) Version I N otes