A Flexible Transformation-Based Estimator Using Extreme-Value Auxiliary Information for Finite Population Mean Estimation Under Systematic Random Sampling

Estimation of a finite population mean under systematic random sampling can be affected by skewness and extreme observations in the auxiliary variable. This study develops a new estimator that combines ratio, difference, and exponential transformations with auxiliary characteristics describing the distribution and extreme values of the auxiliary variable. The ratio transformation is considered for the parameter values α=−1,0,1, while the difference transformation is examined for β=−1,0,1. The exponential transformation is considered for b=−1,0.5,1, and the contribution of the interquartile range is assessed using η=0.5,1,1.5. In addition to the interquartile range, the minimum, maximum, and range of the auxiliary variable are used to construct different subclasses of the proposed estimator. The estimator is developed theoretically through bias and mean squared error derivations, and its unknown constants are determined by minimizing the resulting mean squared error. Conditions for comparison with existing estimators under systematic random sampling are also derived. Its performance is assessed through Monte Carlo simulations using linear, nonlinear, skewed, heavy-tailed, periodic, and contaminated populations, together with different levels of association between the study and auxiliary variables. Additional simulation settings are considered to examine the effect of different proportions of extreme observations. The proposed estimator is compared with the usual systematic sample mean and a range of existing ratio, product, difference, regression, exponential ratio, exponential product, and transformed estimators using bias, mean squared error, and percent relative efficiency. Applications to three real finite populations are also considered to examine the empirical performance of the proposed estimator under different population characteristics.