Enhanced direct and synthetic estimators for domain mean with simulation and applications

This article considers the issue of domain mean estimation utilizing bivariate auxiliary information based enhanced direct and synthetic logarithmic type estimators under simple random sampling (SRS). The expressions of mean square error (MSE) of the proposed estimators are provided to the $$ order approximation. The efficiency criteria are derived to exhibit the dominance of the proposed estimators. To exemplify the theoretical results, a simulation study is conducted on a hypothetically drawn trivariate normal population from R programming language. Some applications of the suggested methods are also provided by analyzing the actual data from the municipalities of Sweden and acreage of paddy crop in the Mohanlal Ganj tehsil of the Indian state of Uttar Pradesh. The findings of the simulation and real data application exhibit that the proposed direct and synthetic logarithmic estimators dominate the conventional direct and synthetic mean, ratio, and logarithmic estimators in terms of least MSE and highest percent relative efficiency.