A Class of Combined Population Mean Estimators Using Transformed Variables in Double Sampling: A Case Study on Fine Particulate Matter in Chiang Rai, Thailand

Air quality in Thailand has raised countless concerns due to the levels of fine particulate matter being detrimental to not only that of health, quality of life, and the environment, but also to the economy. Data on fine particulate matter are imperative for the protection of all these fundamental sectors. The population mean estimator’s efficiency can be increased using the transformation technique to change the shape of the variables’s distribution. A class of combined estimators using the transformed variables on the study variable and auxiliary variable have been suggested under double sampling. The bias and mean square error of the estimators are investigated. Simulation studies and applications to Thailand air pollution data are established to assess the estimators. The proposed class of combined estimators showed a higher efficiency compared to existing estimators. The results from the application to estimate the average level of fine particulate matter per month showed that the proposed estimator gave the superior efficiency between $$255\%$$ and $$317\%$$ in this scenario and gave closer estimated values for the fine particulate matter. The proposed class of combined transformed estimators using the optimum constant can assist in removing the error of the estimators, resulting in higher efficiency with respect to the single estimators for estimating population mean.