Partial Product-Exponential Method of Estimation

This research introduces the Partial Product-Exponential Method of Estimation, focusing on utilizing partial auxiliary information for estimating population mean in simple random sampling without replacement.The method proposes novel estimators tailored for situations where only partial auxiliary information is available, particularly when it demonstrates a negative correlation with the study variable within sub-populations.The paper evaluates the performance of the suggested method under two cases: when sub-population weights are known and when they are unknown.Approximate expressions for bias and variance, up to the first order, are derived for the suggested estimators.A comprehensive comparative analysis concludes that the proposed estimators are more efficient than existing estimators, such as mean per unit estimator, partial product estimator, and weighted post-stratified estimator, under specific conditions.Particularly, the proposed estimators outperform the corresponding existing methods when certain conditions are true, demonstrating superiority in both known and unknown weight cases.Furthermore, a simulation study using R software validates the theoretical findings for normal and non-normal populations.The study showcases the practical utility of the proposed estimators, emphasizing their superiority over existing counterparts in real-world applications.Particularly, the proposed estimators are increased accuracy and efficiency in estimating the population mean, enhancing the reliability of sample survey results.In summary, the Partial Product-Exponential Method of Estimation presents a valuable addition to the domain of sample survey methodology, addressing the challenge of partial auxiliary information.The suggested methods demonstrated advantages in efficiency and accuracy, and highlights its potential for practical applications, promising enhanced estimation accuracy in various cases of sample survey.