Some novel sine-type estimators for finite population mean utilizing known auxiliary information

Abstract

In sampling, the population mean estimate is essential because it offers a clear snapshot of the population’s average, helping with analysis and informed choices in areas such as environmental science, economics, and public health. To improve the efficiency and accuracy of estimators in estimating unknown population parameters, auxiliary information is often utilized, which typically results in reduced mean squared error (MSE) and increased percentage relative efficiency (PRE). In this paper, we modified conventional estimators and introduced some novel sine-type estimators, along with proposing a new exponential-cum-sine-type estimator to enhance finite population mean estimation with auxiliary data under simple random sampling. We compute the bias and MSE of the proposed estimator by applying first-order approximation techniques. The effectiveness and practical utility of the newly proposed estimator are validated using both real-world datasets and simulation studies. The proposed estimator proves to be consistently more efficient than both the sample mean and several competing sine-type estimators (ratio, product, regression, etc.) analyzed in this research. The results are summarized and followed by an analysis of the estimator’s practical applicability in real-world scenarios. The improved efficiency and reliability of the proposed estimator highlight its practical relevance in real-world data analysis. Its applicability across different domains underscores its potential as a robust tool for finite population mean estimation using auxiliary information. © The Author(s), under exclusive licence to Springer Nature B.V. 2025.