Sains Malaysiana 52(7)(2023): 2149-2162

http://doi.org/10.17576/jsm-2023-5207-20

 

On Some New Exponential Ratio Estimator of Population Mean in Two Phase Sampling

(Beberapa Penganggar Nisbah Eksponen Baharu bagi Min Populasi dalam Persampelan Dua Fasa)

 

YASIR HASSAN1,*, MUHAMMAD FAROOQ2, SALEHA YASIR3 & WILL MURRAY4

 

1Lahore Business School, The University of Lahore, Pakistan

2Department of Statistics, COMSATS University Islamabad, Lahore Campus, Lahore, Pakistan

3The University of Lahore, Pakistan

4Department of Mathematics and Statistics, California State University, Long Beach, USA

 

Received: 14 November 2022/Accepted: 12 July 2023

 

Abstract

In this paper, we suggest employing the exponential ratio estimator to estimate the mean of the study variable using a two-phase sample strategy with two modified auxiliary variables. Several researchers discussed the properties of the estimators they proposed and discovered that the estimators in their studies were relatively efficient. The estimators previously studied are listed chronologically in the appendix to this paper. In two phase sampling, the estimator's mean square errors and relative efficiencies are calculated using auxiliary variable information. To assess the properties of our proposed estimator, we noticed that it has a lower mean square error (MSE) than the classical ratio estimator and some other exponential ratio estimators. The estimator is more useful than other estimators in solving real-world issues, notably in engineering, environmental science, management, and biological sciences. The proposed estimator has been applied to real-world data sets such as BRICS, Son's Head Measurement, Number of Hospital Beds, Sale Price of Residence, Ambient Pressure (AP), and Heating Load. In survey research, our suggested estimator has also been demonstrated to be more effective.

 

Keywords: Auxiliary variable; exponential; mean square error; two phase

 

ABSTRAK

Dalam makalah ini, kami mencadangkan penggunaan penganggar nisbah eksponen untuk menganggar min pemboleh ubah kajian menggunakan strategi sampel dua fasa dengan dua pemboleh ubah tambahan yang diubah suai. Beberapa penyelidik membincangkan sifat penganggar yang mereka cadangkan dan mendapati bahawa penganggar dalam kajian mereka adalah agak cekap. Penganggar yang dikaji sebelum ini disenaraikan secara kronologi dalam lampiran kertas ini. Dalam persampelan dua fasa, ralat purata kuasa dua penganggar dan kecekapan relatif dihitung menggunakan maklumat pemboleh ubah tambahan. Untuk menilai sifat penganggar yang dicadangkan ini, kami mendapati ia mempunyai ralat min kuasa dua (MSE) yang lebih rendah daripada penganggar nisbah klasik dan beberapa penganggar nisbah eksponen lain. Penganggar ini lebih baik daripada penganggar lain dalam menyelesaikan isu dunia sebenar, terutamanya dalam kejuruteraan, sains alam sekitar, pengurusan dan sains biologi. Penganggar yang dicadangkan telah digunakan pada set data dunia sebenar seperti BRICS, Ukuran Kepala Anak, Bilangan Katil Hospital, Harga Jualan Kediaman, Tekanan Ambien (AP) dan Beban Pemanasan. Dalam kajian tinjauan, penganggar cadangan kami juga telah ditunjukkan sebagai lebih berkesan.

 

Kata kunci: Eksponen; pemboleh ubah bantu; purata kuasa dua; ralat dua fasa

 

REFERENCES

Akhlaq, T., Ismail, M. & Shahbaz, M.Q. 2019. On efficient estimation of process variability. Symmetry 11(4): 554.

Al-Marshadi, A.H., Alharby, A.H. & Shahbaz, M.Q. 2018. On some new estimators of population variance in single and two-phase sampling. Maejo International Journal of Science and Technology 12(3): 272-281.

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.

Bahl, S. & Tuteja, R.K. 1991. Ratio and product type exponential estimators. Journal of Information and Optimization Sciences 12(1): 159-164.

Bandyopadhyay, S. 1980. Improved ratio and product estimators. Sankhya 42(1-2): 45-49.

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.

Clement, E.P. & Inyang, E.J. 2020. A class of modified calibration ratio estimators of population mean with known coefficient of kurtosis in stratified double sampling. Journal of Modern Mathematics and Statistics 14(4): 55-60.

Cochran, W.G. 1940. The estimation of the yields of cereal experiments by sampling for the ratio of grain to total produce. The Journal of Agricultural Science 30(2): 262-275.

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): 7605-7623.

Hidiroglou, M.A. 2001. Double sampling. Survey Methodology 27(2): 143-154.

Jabeen, R., Sanaullah, A. & Hanif, M. 2015. Efficient class of exponential estimators for population mean in two-stage cluster sampling. Pak. J. Statist. 31(6): 683-696.

Kalita, D., Singh, B.K. & Choudhury, S. 2013. Improved exponential chain ratio and product-type estimators for finite population mean in double sampling. International Journal of Statistical Sciences 13: 21-37.

Khan, H., Gupta, S. & Farhat, H. 2020. A ratio-cum-regression estimator of population mean in unequal probability sampling design. Communications in Statistics-Simulation and Computation 49(2): 484-490.

Khan, M., Shabbir, J., Hussain, Z. & Al-Zahrani, B. 2014. A class of estimators for finite population mean in double sampling under nonresponse using fractional raw moments. Journal of Applied Mathematics 2014: Article ID. 282065.

Lu, J., Yan, Z. & Peng, X. 2014. A new exponential ratio-type estimator with linear combination of two auxiliary variables. PLoS ONE 9(12): e116124.

Neyman, J. 1938. Contribution to the theory of sampling human populations. Journal of the American Statistical Association 33(201): 101-116.

Noor-ul-Amin, M. & Hanif, M. 2012. Some exponential estimators in survey sampling. Pakistan Journal of Statistics 28(3): 367-374.

Rashid, R., ul Amin, M.N. & Hanif, M. 2015. Exponential estimators for population mean using the transformed auxiliary variables. Applied Mathematics & Information Sciences 9(4): 2107-2112.

Robson, D.S. 1957. Applications of multivariate polykays to the theory of unbiased ratio-type estimation. Journal of the American Statistical Association 52(280): 511-522.

Sanaullah, A. 2012. Improved exponential ratio-type estimators in survey sampling. Journal of Reliability and Statistical Studies 5(2): 119-132.

Sanaullah, A., Hanif, M. & Asghar, A. 2016. Generalized exponential estimators for population variance under two-phase sampling. International Journal of Applied and Computational Mathematics 2(1): 75-84.

Sanaullah, A., Khan, H., Ali, H.A. & Singh, R. 2012. Improved exponential ratio-type estimators in survey sampling. Journal of Reliability and Statistical Studies 5(2): 119-132.

Shabbir, J. & Gupta, S. 2017. Estimation of finite population mean using two auxiliary variables in stratified two-phase sampling. Communications in Statistics-Simulation and Computation 46(2): 1238-1256.

Singh, B.K., Choudhury, S. & Kalita, D. 2013. A class of exponential chain ratio-product type estimators with two auxiliary variables under double sampling scheme. Electronic Journal of Applied Statistical Analysis 6(2): 166-174.

Singh, G. & Majhi, D. 2014. Some chain-type exponential estimators of population mean in two-phase sampling. Statistics in Transition New Series 15(2): 221-230.

Singh, H., Tailor, R. & Tailor, R. 2010. On ratio and product methods with certain known population parameters of auxiliary variable in sample surveys. Sort 34(2): 157-180.

Singh, H.P. & Espejo, M.R. 2007. Double sampling ratio-product estimator of a finite population mean in sample surveys. Journal of Applied Statistics 34(1): 71-85.

Singh, H.P. & Vishwakarma, G.K. 2007. Modified exponential ratio and product estimators for finite population mean in double sampling. Austrian Journal of Statistics 36(3): 217-225.

Singh, R., Kumar, M. & Smarandache, F. 2008. Almost unbiased estimator for estimating population mean using known value of some population parameter(s). Pakistan Journal of Statistics and Operation Research 4(2): 63-76.

Singh, R.V.K. & Ahmed, A. 2015. Improved exponential ratio and product type estimators for finite population mean under double sampling scheme. International Journal of Scientific and Engineering Research 6(4): 509-514.

Srivastava, S.K. 1971. A generalized estimator for the mean of a finite population using multi-auxiliary information. Journal of the American Statistical Association 66(334): 404-407.

Srivenkataramana, T. 1980. A dual to ratio estimator in sample surveys. Biometrika 67(1): 199-204.

Sukhatme, B.V. 1962. Some ratio-type estimators in two-phase sampling. Journal of the American Statistical Association 57(299): 628-632.

Tailor, R., Tailor, R., Parmar, R. & Kumar, M. 2012. Dual to ratio-cum-product estimator using known parameters of auxiliary variables. Journal of Reliability and Statistical Studies 5(1): 65-71.

Vishwakarma, G.K. & Kumar, M. 2014. An improved class of chain ratio-product type estimators in two-phase sampling using two auxiliary variables. Journal of Probability and Statistics 2014: 939701.

Vishwakarma, G.K., Kumar, M. & Gangele, R.K. 2014. A general class of chain ratio-product type exponential estimators in double sampling using two auxiliary variates. The Philippine Statistician 63(2): 9-20.

Watson, D.J. 1937. The estimation of leaf areas. Journal Agr. Sci. 27: 474.

Yadav, R., Upadhyaya, L.N., Singh, H.P. & Chatterjee, S. 2013. A chain ratio exponential type estimator in two-phase sampling using auxiliary information. Statistica 73(2): 221-234.

 

*Corresponding author; email:yasirhassan7924@gmail.com

 

 

 

 

 

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