Enhanced estimation of finite population mean via power and log-transformed ratio estimators using an auxiliary variable in solar radiation data

Solar radiation data frequently exhibits nonlinear relationships with auxiliary variables such as temperature, altitude, humidity, atmospheric pressure, and other meteorological conditions, which have a significant impact on variability due to factors such as cloud cover, seasonal changes, and geographic location. Standard ratio estimators are poor for estimating the mean of a finite population due to their complex relationships. This research provides an improved family of ratio estimators that combine power and logarithmic transformations within a simple random sampling (SRS) framework, leveraging auxiliary data to increase estimation accuracy. The proposed changes contribute to the linearization of complex relationships, the stabilization of variance, and the reduction of estimator bias, all of which improve predictive performance. The usefulness of these estimators is proven using solar radiation datasets, which exhibit nonlinearity due to temporal variations, spatial heterogeneity, and atmospheric impacts. Mathematical derivations and practical assessments show that the proposed estimators have lower mean squared error (MSE) and higher percentage relative efficiency (PRE) than classic ratio estimators. The findings emphasize the necessity of using auxiliary information in transformation-based estimators to improve solar radiation data processing, hence enabling more accurate solar energy forecasting, climate modeling, and sustainable energy planning in environmental and renewable energy research.