A Unified Hybrid Estimation Strategy Using Multiple Auxiliary Transformations in Systematic Sampling with Simulation and Real-Life Applications

Estimating the finite population mean under systematic sampling becomes challenging when auxiliary information is nonlinear, skewed, or structurally complex, as conventional linear estimators often lose efficiency. This study proposes a new class of weighted hybrid estimators that combine harmonic and geometric transformations of the auxiliary variable. The proposed approach is designed to capture nonlinear relationships while handling skewed data and reducing sensitivity to extreme observations. Expressions for bias and mean squared error are derived, and optimal weights are obtained by minimizing the mean squared error. The theoretical results indicate that the proposed estimators are more efficient than traditional ratio, product, regression, and exponential-type estimators. A simulation study further confirms their improved performance across various population structures, correlation levels, and sampling fractions, with notable improvements in skewed and nonlinear settings. The proposed class provides a flexible and reliable alternative for practical applications in systematic sampling.