Efficient Estimators of Finite Population Mean Based on Extreme Values in Simple Random Sampling

The use of extreme values of the auxiliary variable is sometimes more beneficial to get the high efficiency of the estimators, and the study variable can have a correlation with the rank of the decently correlated auxiliary variable. As a result, it can be regarded as additional data for the study variable that can be used to improve the estimators’ efficiency. When the knowledge of the minimum and maximum values, as well as the rankings of the auxiliary variable, is known, various better estimators for calculating the finite population mean of the research variable based on extreme values under simple random sampling are proposed in this paper. The suggested estimators’ bias and mean squared error expressions are derived using first-order approximation. The recommended estimators have been compared mathematically to the current estimators. The suggested estimators are more exact in terms of relative efficiency than the other estimators addressed here, as shown by simulation and real datasets used to demonstrate the estimation of a limited population mean based on extreme values.