An Improvement in Estimating the Population Mean Based on Family of Estimators with Different Application Areas

Yıl 2023, Cilt: 10 Sayı: 4, 402 - 416, 31.12.2023

Ceren Ünal , Cem Kadılar

https://doi.org/10.54287/gujsa.1333067

Öz

In a sampling study, the complete information for the necessary variables may not always be available in practice. Therefore, the non-response situation has been considered for estimating the unknown population parameters with different types of estimators. The families of estimators are proposed for the population mean in the case of non-response under two different cases with the approach of an exponential function. Their properties are derived in detail. We compare these estimators with the main estimators in the literature to present the efficiencies, theoretically. Moreover, the three different empirical studies are illustrated and, in that way, we found that the theoretical conclusion is supported by the obtained results numerically for each data set.

Anahtar Kelimeler

Population Mean, Family of Estimators, Auxiliary Information, Non-Response, Efficiency

Kaynakça

• Ahmad, S., Arslan, M., Khan, A., & Shabbir, J. (2021). A generalized exponential-type estimator for population mean using auxiliary attributes. Plos One, 16(5), e0246947. https://www.doi.org/10.1371/journal.pone.0246947
• Ahmad, S., Hussain, S., Aamir, M., Khan, F., Alshahrani, M. N., & Alqawba, M. (2022). Estimation of finite population mean using dual auxiliary variable for non-response using simple random sampling. Aims Mathematics, 793, 4592-4613. https://www.doi.org/10.3934/math.2022256
• Ahmadini, A. A. H., Yadav, T., Yadav, S. K., & Al Luhayb, A. S. M. (2022). Restructured searls family of estimators of population mean in the presence of nonresponse. Frontiers in Applied Mathematics and Statistics, 8, 969068. https://www.doi.org/10.3389/fams.2022.969068
• Anieting, A. E., Enang, E. I., & Onwukwe, C. E. (2020). Efficient estimator for Population mean in stratified double sampling in the presence of nonresponse using one auxiliary variable. Statistics, 4(2), 40-50. https://www.doi.org/10.52589/AJMSS-YF4V11QV
• Bahl, S., & Tuteja, R. K. (1991). Ratio and product type exponential estimators. Journal of Information and Optimization Sciences, 12(1), 159-164. https://www.doi.org/10.1080/02522667.1991.10699058
• Cochran, W. G. (1940). The estimation of the yields of the cereal experiments by sampling for the ratio of grain to total produce. The Journal of Agricultural Science, 30(2), 262-275. https://www.doi.org/10.1017/S0021859600048012
• Cochran, W. G. (1977) Sampling Techniques. John Wiley and Sons, New-York
• Dansawad, N. (2019). A class of exponential estimator to estimate the population mean in the presence of non-response. Naresuan University Journal: Science and Technology, 27(4), 20-26. https://www.doi.org/10.14456/nujst.2019.33
• Fatima, M., Shahbaz, S. H., Hanif, M., & Shahbaz, M. Q. (2022). A modified regression-cum-ratio estimator for finite population mean in presence of nonresponse using ranked set sampling. AIMS Mathematics, 7(4), 6478-6488. https://www.doi.org/10.3934/math.2022361
• Hansen, M. H., & Hurwitz, W. N. (1946). The problem of non-response in sample surveys. Journal of the American Statistical Association, 41(236), 517-529. https://www.doi.org/10.1080/01621459.1946.10501894
• Javed, M., Irfan, M., & Pang, T. (2019). Hartley-Ross type unbiased estimators of population mean using two auxiliary variables. Scientia Iranica, 26(6), 3835-3845. https://www.doi.org/10.24200/sci.2018.5648.1397
• Khare, B. B., & Sinha, R. R. (2009). On class of estimators for population mean using multi-auxiliary characters in the presence of non-response. Statistics in Transition, 10(1), 3-14.
• Khare, B. B., & Srivastava, S. (1993). Estimation of population mean using auxiliary character in presence of non-response. National Academy Science Letters, 16, 111-114.
• Khan, A., Ali, A., Ijaz, M., Azeem, M., & El-Morshedy, M. (2023). An exponential ratio type estimator of the population mean in the presence of non-response using double sampling. Journal of Statistics Applications and Probability, 12(1), 191-205. https://www.doi.org/10.18576/jsap/120118
• Khoshnevisan, M., Singh, R., Chauhan, P., Sawan, N., & Smarandache, F. (2007). A general family of estimators for estimating population mean using known value of some population parameter(s). Far East Journal of Theoretical Statistics, 22, 181-191.
• Kumar, S. (2013). Improved exponential estimator for estimating the population mean in the presence of non-response. Communications for Statistical Applications and Methods, 20(5), 357-366. https://www.doi.org/10.5351/CSAM.2013.20.5.357
• Kumar, S, & Bhougal, S. (2011). Estimation of the population mean in presence of non-response. Communications for Statistical Applications and Methods, 18(4), 537-548. https://www.doi.org/10.5351/CKSS.2011.18.4.537
• Kumar, K., & Kumar, M. (2017). Improved exponential ratio and product type estimators for population mean in the presence of nonresponse. Bulletin of Mathematics and Statistics Research, 5(2), 68-76.
• Mehta, P., & Tailor, R. (2020). Chain ratio type estimators using known parameters of auxiliary variates in double sampling. Journal of Reliability and Statistical Studies, 13(2-4), 243-252. https://www.doi.org/10.13052/jrss0974-8024.13242
• Oncel Cekim, H., & Kadilar, C. (2018). New families of unbiased estimators in stratified random sampling. Journal of Statistics and Management Systems, 21(8), 1481-1499. https://www.doi.org/10.1080/09720510.2018.1530176
• Oncel Cekim, H. (2022). Modified unbiased estimators for population variance: An application for COVID‐19 deaths in Russia. Concurrency and Computation: Practice and Experience, 34(22), e7169. https://www.doi.org/10.1002/cpe.7169
• Özel Kadilar, G. (2016). A new exponential type estimator for the population mean in simple random sampling. Journal of Modern Applied Statistical Methods, 15(2), 207-214. http://www.doi.org/10.22237/jmasm/1478002380
• Pal, S. K., & Singh, H. P. (2017). A class of ratio-cum-ratio-type exponential estimators for population mean with sub sampling the nonrespondents. Jordan Journal of Mathematics and Statistics, 10(1), 73-94.
• Pal, S. K., & Singh, H. P. (2018). Estimation of finite population mean using auxiliary information in presence of non-response. Communications in Statistics-Simulation and Computation, 47(1), 143-165. https://www.doi.org/10.1080/03610918.2017.1280161
• Rao, P. S. R. S. (1986). Ratio estimation with sub sampling the non-respondents. Survey Methodology, 12(2), 217-230.
• Rehman, S. A., & Shabbir, J. (2022). An efficient class of estimators for finite population mean in the presence of non-response under ranked set sampling (RSS). Plos One, 17(12), e0277232. https://www.doi.org/10.1371/journal.pone.0277232
• Sanaullah, A., Ehsan, I., & Noor-Ul-Amin, M. (2019). Estimation of mean for a finite population using sub-sampling of non-respondents. Journal of Statistics and Management Systems, 22(6), 1015-1035. https://www.doi.org/10.1080/09720510.2019.1572981
• Satici, E., & Kadilar, C. (2011). Ratio estimator for the population mean at the current occasion in the presence of non-response in successive sampling. Hacettepe Journal of Mathematics and Statistics, 40(1), 115-124.
• Shabbir, J., Haq, A., & Gupta, S. (2014). A new difference-cum-exponential type estimator of finite population mean in simple random sampling. Revista Colombiana de Estadística, 37(1), 199-211. https://www.doi.org/10.15446/rce.v37n1.44366
• Shabbir, J., & Onyango, R. (2022). Use of an efficient unbiased estimator for finite population mean. Plos One, 17(7), e0270277. https://www.doi.org/10.1371/journal.pone.0270277
• Sharma, P., Pal, S. K., & Singh, H. P. (2022). Improved estimators of population mean under nonresponse in successive sampling. Mathematical Problems in Engineering, 2022(1), 1-8. https://www.doi.org/10.1155/2022/1349689
• Singh, R., Chauhan, P., & Sawan, N. (2008). On linear combination of ratio and product type exponential estimator for estimating the finite population mean. Statistics in Transition - New Series, 9, 105-115.
• Singh, R., Kumar, M., Chaudhary, M. K., & Smarandache, F. (2010). Estimation of mean in presence of non-response using exponential estimator. Multispace & Multistructure Neutrosophic Transdisciplinarity (100 Collected Papers of Sciences), (vol IV, pp. 758-768). https://doi.org/10.48550/arXiv.0906.2462
• Singh, H. P., & Nigam, P. (2020). Ratio-Ratio-Type exponential estimator of finite population mean in double sampling for stratification. International Journal of Agricultural and Statistical Science, 16(1), 251-257.
• Singh, G. N., & Usman, M. (2019a). Ratio-to-product exponential-type estimators under non-response. Jordan Journal of Mathematics and Statistics, 12(4), 593-616.
• Singh, G. N., & Usman, M. (2019b). Efficient combination of various estimators in the presence of non-response. Communications in Statistics Simulation and Computation, 50(8), 2432-2466. https://www.doi.org/10.1080/03610918.2019.1614618
• Tailor, R., & Lone, H. A. (2014). Separate ratio-type estimators of population mean in stratified random sampling. Journal of Modern Applied Statistical Methods, 13(1), 223-233. https://www.doi.org/10.22237/jmasm/1398917580
• Unal, C., & Kadilar, C. (2019). Exponential type estimator for the population mean in the presence of non-response. Journal of Statistics and Management Systems, 23(3), 603-615. https://www.doi.org/10.1080/09720510.2019.1668158
• Unal, C., & Kadilar, C. (2021). Improved family of estimators using exponential function for the population mean in the presence of nonresponse. Communications in Statistics - Theory and Methods, 50(1), 237-248. https://www.doi.org/10.1080/03610926.2019.1634818
• Unal, C., & Kadilar, C. (2022a). A new population mean estimator under non-response cases. Journal of Taibah University for Science, 16(1), 111-119. https://www.doi.org/10.1080/16583655.2022.2034343
• Unal, C., & Kadilar, C. (2022b). Exponential type estimators using sub-sampling method with applications in agriculture. Journal of Agricultural Sciences (Tarim Bilimleri Dergisi), 28(3), 457-472. https://www.doi.org/10.15832/ankutbd.915999
• Yadav, S. K., Sharma, D. K., & Mishra, S. S. (2021). New modified ratio type estimator of the population mean using the known median of the study variable. International Journal of Operational Research, 41(2), 151-167. https://www.doi.org/10.1504/IJOR.2021.115625
• Yadav, S. K., & Zaman, T. (2021). Use of some conventional and non-conventional parameters for improving the efficiency of ratio-type estimators. Journal of Statistics and Management Systems, 24(5), 1077-1100. https://www.doi.org/10.1080/09720510.2020.1864939
• Yunusa, O., & Kumar, S. (2014). Ratio-cum-product estimator using exponential estimator in the presence of non-response. Journal of Advanced Computing, 3(1), 1-11. https://www.doi.org/10.7726/jac.2014.1001
• Zahid, S., Kamal, A., & Makhdum, M. (2022). Generalized Dual to Exponential Ratio Type Estimator for the Finite Population Mean in the Presence of Nonresponse. In: O. O. Awe, K. Love, & E. A. Vance (Eds.), Promoting Statistical Practice and Collaboration in Developing Countries (2nd ed., pp. 249-263). Chapman and Hall/CRC. https://www.doi.org/10.1201/9781003261148
• Zaman, T., & Kadilar, C. (2019). Novel family of exponential estimators using information of auxiliary attribute. Journal of Statistics and Management Systems, 22(8), 1499-1509. https://www.doi.org/10.1080/09720510.2019.1621488
• Zaman, T., & Kadilar, C. (2021a). Exponential ratio and product type estimators of the mean in stratified two-phase sampling. AIMS Mathematics, 6(5), 4265-4279. https://www.doi.org/10.3934/math.2021252
• Zaman, T., & Kadilar, C. (2021b). New class of exponential estimators for finite population mean in two-phase sampling. Communications in Statistics-Theory and Methods, 50(4), 874-889. https://www.doi.org/10.1080/03610926.2019.1643480