A novel statistical estimator for simple random sampling with applications in radiation and library sciences

This paper introduces a novel statistical estimator for the finite population means in the context of simple random sampling (SRS), and extends it to probability proportional to size sampling with auxiliary information. In practice, the units are unequal and of varying significance, and thus, the traditional equal-probability sampling is inefficient in many real-world populations related to risk assessment and decision-making. The proposed estimator addresses this shortcoming by incorporating auxiliary variables that are strongly correlated with the study variable, thereby improving estimation precision and supporting more accurate risk evaluation. First-order approximation techniques are used to derive the mathematical properties of the estimator, such as bias and mean squared error (MSE). Theoretical comparisons show that the proposed estimator is superior to the traditional estimators like ratio, regression, and other estimators in a PPS scheme, especially when population size varies. The effectiveness of the estimator is also demonstrated through empirical applications in radiation science and library science. PPS sampling is more representative of high-risk areas in radiation studies, where exposure levels are many times higher than those in low-risk areas, thus improving the quality of risk assessment and management decisions. In a similar way, in library science auxiliary variables such as collection size or user frequency are useful in estimating resource utilization. In real data, the proposed estimator always has a smaller MSE and greater relative efficiency than existing methods. In general, this study offers an understanding of the importance of using auxiliary information in the sampling to enhance the estimation of population means and improve risk assessment and risk management practices. The results indicate that the proposed estimator is robust, efficient, and applicable in the real world across various areas of science where population heterogeneity is prevalent.