To estimate a finite population mean when the population mean of the auxiliary variable is known, we propose a new family of finite population mean estimators designed for use in simple random sampling situations. We performed first-order approximations of these new estimates and presented mathematical models for their biases and mean square error (MSE). To evaluate the effectiveness of these predictions, we made theoretical and empirical comparisons under different conditions and compared them with traditional predictions. This article demonstrates the advantages and benefits of these new estimators in the forecasting process by providing information on their performance in various simulation configurations.

mean, simple random sampling, auxiliary information, mean square error, percentage relative efficiency, numerical comparisons, simulation study, visualization, graphs.

Received: September 1, 2024; Revised: December 1, 2024; Accepted: December 28, 2024

How to cite this article: Ali Algarni, Optimum family of estimators in simple random sampling of finite population mean using two auxiliary variables with applications in fisheries and economics sectors, JP Journal of Biostatistics 25(2) (2025), 223-242. https://doi.org/10.17654/0973514325011

This Open Access Article is Licensed under Creative Commons Attribution 4.0 International License

References:
[1] Sohaib Ahmad and Javid Shabbir, Use of extreme values to estimate the finite population mean under PPS sampling scheme, Journal of Reliability and Statistical Studies 11(2) (2018), 99-112.
[2] M. S. Ahmed and W. Abu-Dayyeh, Estimation of finite-population distribution function using multivariate auxiliary information, Statistics in Transition 5(3) (2001), 501-507.
[3] S. Bahl and R. K. Tuteja, Ratio and product type exponential estimators, Journal of Information and Optimization Sciences 12(1) (1991), 159-164.
[4] R. L. Chambers, Alan H. Dorfman and Peter Hall, Properties of estimators of the finite population distribution function, Biometrika 79(3) (1992), 577-582.
[5] R. L. Chambers and R. Dunstan, Estimating distribution functions from survey data, Biometrika 73(3) (1986), 597-604.
[6] W. G. Cochran, 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) (1940), 262-275.
[7] Alan H. Dorfman, A comparison of design-based and model-based estimators of the finite population distribution function, Australian and New Zealand Journal of Statistics 35(1) (1993), 29-41.
[8] Alan H. Dorfman, Inference on distribution functions and quantiles, Handbook of Statistics 29 (2009), 371-395.
[9] L. K. Grover and P. Kaur, Ratio type exponential estimators of population mean under linear transformation of auxiliary variable: theory and methods, South African Statistical Journal 45(2) (2011), 205-230.
[10] L. K. Grover and P. Kaur, A generalized class of ratio type exponential estimators of population mean under linear transformation of auxiliary variable, Comm. Statist. Simulation Comput. 43(7) (2014), 1552-1574.
[11] A. Haq, M. Khan and Z. Hussain, A new estimator of finite population mean based on the dual use of the auxiliary information, Comm. Statist. Theory Methods 46(9) (2017), 4425-4436.
[12] Sardar Hussain, Sohaib Ahmad, Sohail Akhtar, Amara Javed and Uzma Yasmeen, Estimation of finite population distribution function with dual use of auxiliary information under non-response, PloS ONE 15(12) (2020), e0243584.
[13] Sardar Hussain, Sohaib Ahmad, Mariyam Saleem and Sohail Akhtar, Finite population distribution function estimation with dual use of auxiliary information under simple and stratified random sampling, PloS ONE 15(9) (2020), e0239098.
[14] A. Y. C. Kuk, A kernel method for estimating finite population distribution functions using auxiliary information, Biometrika 80(2) (1993), 385-392.
[15] Tak K. Mak and Anthony Kuk, A new method for estimating finite-population quantiles using auxiliary information, Canad. J. Statist. 21(1) (1993), 29-38.
[16] M. N. Murthy, Product method of estimation, Sankhya: The Indian Journal of Statistics, Series A 26(1) (1964), 69-74.
[17] J. Rao, Estimating totals and distribution functions using auxiliary information at the estimation stage, Journal of Official Statistics 10(2) (1994), 153.
[18] T. J. Rao, On certail methods of improving ration and regression estimators, Comm. Statist. Theory Methods 20(10) (1991), 3325-3340.
[19] Housila P. Singh and Sunil Kumar, A general procedure of estimating the population mean in the presence of non-response under double sampling using auxiliary information, Statistics and Operations Research Transactions 33(1) (2009), 71-84.
[20] L. N. Upadhyaya and H. P. Singh, Use of transformed auxiliary variable in estimating the finite population mean, Biom. J. 41(5) (1999), 627-636.
[21] M. Yaqub and J. Shabbir, Estimation of population distribution function in the presence of non-response, Hacet. J. Math. Stat. 47(2) (2018), 471-511.
[22] D. N. Gujarati, Basic Econometrics, Tata McGraw-Hill Education, 2009.
[23] N. Koyuncu and C. Kadilar, Ratio and product estimators in stratified random sampling, Journal of Statistical Planning and Inference 139(8) (2009), 2552-2558.
[24] S. Singh, Advanced Sampling Theory with Applications: How Michael ‘Selected’ Amy, Springer Science & Business Media, Volume 1, 2003.
[25] Ali Algarni, Parameters estimation for constant partially accelerated life tests of half logistic distribution based on progressive type-II censoring, J. Comput. Theor. Nanosci. 13 (2016), 9082-9089.
[26] Ali Algarni, Monitoring process variance using GEWM for exponentially distributed characteristics, Far East Journal of Theoretical Statistics 55(2) (2019), 113-134. http://dx.doi.org/10.17654/TS055020113.
[27] M. Aslam and Ali Algarni, Design and construction of sampling plan for exponential distribution using repetitive sampling, Journal of Computational and Theoretical Nanoscience (CTN) 13(10) (2016), 6568-6575.