In this study, we utilize the characteristics of one auxiliary variable to obtain the population mean using proposed estimators in stratified random sampling. By examining the MSE and PRE of the proposed estimator and the existing estimator, we compare the effectiveness of the proposed estimator with each of these existing estimators. Additionally, use a linear cost function and a non-linear cost function to find the minimum mean square error (MSE) and highest PRE of the proposed estimator as compared to some existing estimator. We examine the proposed estimator with the highest PRE. With the use of Cramer's Rule, we can also determine the optimum value of the estimators. Numerical examples are used to validate theoretical observations. Then find out if the proposed estimator is more effective as compared to existing estimators. A proposed estimator verifies its practical applicability in real life widely used in various fields such as: Agriculture: To assess crop yields and disease prevalence. Economics: To study income levels and economic indicators and also use real life applications.
JessenRJ. Statistical investigation of a sample survey for obtaining farm facts. USA: Iowa State University, 1943.
2.
SinghMP. On the estimation of ratio and product of the population parameters. Sankhya: Indian J Stat Ser B, 1965; 321–328.
3.
BediPK. Efficient utilization of auxiliary information at estimation stage. Biometrical J1994; 38: 973–976.
4.
MurthyMN. Product method of estimation. Sankhya: Indian J Stat Ser B1964; 26: 69–74.
5.
PandeyGS. Product–cum–power estimators. Calcutta Stat Asso Bull1980; 29: 103–108.
6.
DalabeharaMSahooLN. A class of estimators in stratified sampling with two auxiliary variables. J Soc Agri Stat1997; 50: 144–149.
7.
DalabeheraMSahooLN. A new estimator with two auxiliary variables for stratified sampling. Statistica1999; 59: 101–107.
8.
KadilarCCingiH. Ratio estimators in stratified random sampling. Biometrical J2003; 45: 218–225.
9.
ShabbirJGuptaS. Improved ratio estimators in stratified sampling. Am J Math Manag Sci2005; 25: 293–311.
10.
GuptaSShabbirJ. On the use of transformed auxiliary variables in estimating population mean by using two auxiliary variables. J Stat Plan Infer2007; 137: 1606–1611.
11.
ChaudharyMKSinghRShuklaRK, et al.A family of estimators for estimating population mean in stratified sampling under non-response. Pak J Stat Oper Res2009; 5: 47–54.
12.
VishwakarmaGKSinghHP. Separate ratio-product estimator for estimating population mean using auxiliary information. J Stat Theory Appl2011; 1538: 78–87.
13.
ClementEPEnangEI. Calibration approach alternative ratio estimator for population mean in stratified sampling. Inter J Stat Econo2015; 16: 83–93.
14.
YasmeenUNoor-ul-AminMHanifM. Exponential ratio and product type estimators of finite population mean. J Stat Manag Syst2016; 19: 55–71.
15.
RenR. Design-based small area estimation: an application to the DHS surveys. SAE2021 BIG4small Book of short papers.2021; 99.
16.
IftikharSKhalilAAliA. A novel and improved logarithmic ratio-product type estimator of mean in stratified random sampling. Math Probl Eng2022; 2022: 6179625.
17.
YadavSKKumar VermaMVarshneyR. Optimal strategy for elevated estimation of population mean in stratified random sampling under linear cost function. Ann Data Sci2025; 12: 517–538.
18.
ZaaganAAVermaMKMahnashiAM, et al.An effective and economic estimation of population mean in stratified random sampling using a linear cost function. Heliyon2024; 10:e31291.
19.
AhmadSShabbirJEmamW, et al.An improved class of estimators for estimation of population distribution functions under stratified random sampling. Heliyon2024; 10.
20.
KyrcheiI. Cramer’s rule for quaternionic systems of linear equations. J Math Sci2008; 155: 839–858.
21.
BahlSTutejaRK. Ratio and product type exponential estimators. Inf Optimi Sci1991; 12: 159–163.
22.
SinghHPTailorR. Use of known correlation coefficient in estimating the finite population mean. Stat Transit2003; 6: 553–560.
23.
JerajuddinMKishunJ. Modified ratio estimators for population mean using size of the sample, selected from population. Inter J Sci Res Sci Eng Technol2016; 2: 10–16.
24.
YadavSKMishraSSGuptaS. An efficient estimator for population variance using parameters of an auxiliary variable. J Stat Manag Syst2019; 22: 1005–1013.
25.
AggarwalSSoniSSChaubeyRS. Estimation of the population mean by developing a new estimator. Bull Pure Appl Sci Math Stat2022; 41: 11–15.
26.
YadavSKVishwakarmaGKVarshneyR,et al.Improved memory type product estimator for population mean in stratified random sampling under linear cost function. SN Comput Sci2023; 4: 235.
27.
ClementEPEkpenyongEJIsehMJ. Modified classes of stratified exponential ratio estimators of population mean with equal optimal efficiency. J Mod Appl Stat Methods2024; 23: 1–21.
28.
MurthyMN. Sampling theory and methods. Calcutta.: Statistical Publishing Society, 1967.
29.
KhanMGMaitiTAhsanMJ. An optimal multivariate stratified sampling design using auxiliary information: an integer solution using goal programming approach. J Official Stat2010; 26: 695–708.
30.
ItoKKunischK. Lagrange multiplier approach to variational problems and applications. Soc Ind Appl Math2008.
31.
SampathS. Sampling theory and methods. Alpha Science Int’l Ltd., 2005.
32.
MradulaYadavSKVarshneyR,et al.Efficient estimation of population mean under stratified random sampling with linear cost function. Commun Stat Simul Comput2021; 50: 4364–4387.
