A novel generalized class of trigonometric estimators for population mean estimation using auxiliary information: Theory, simulation, and real-data evidence

The effective estimation of the population mean using auxiliary information in survey sampling remains a significant research topic because of its broad practical applications in agriculture, economics, environmental studies, and industrial quality control. A new generalized trigonometric-exponential type estimator is presented in this work in order to estimate the finite population mean under simple random sampling without replacement. The suggested estimator effectively captures both linear and nonlinear correlations between the study and auxiliary variables by combining sine, cosine, and exponential adjustment components with carefully selected constants. Up to the first order of approximation, theoretical formulas for the bias and mean squared error of the suggested estimator are obtained. Additionally, by minimizing the mean squared error expression, the optimal values of the unknown parameters are found, resulting in an effective and adaptable class of estimators. Additionally, a thorough theoretical comparison is provided with several current estimators, such as ratio, product, exponential, regression, and other modified estimators. The suggested estimator is assessed on six actual data sets from various application domains. The empirical analysis confirms the suggested estimator’s wide applicability across various correlation patterns and demographic characteristics. Compared with the competing estimators, the findings consistently show lower mean squared error and higher percent relative efficiency. A comprehensive simulation study based on a non-linear population, normal population, log-normal population, and weibull population with different correlation values further supports the theoretical and empirical results. The findings show that the suggested estimator is effective, reliable, and useful for finite population surveys in practice.