A study on the estimation of population coefficient of variation using auxiliary variable under simple random sampling
摘要
This paper addresses the problem of estimating the coefficient of variation of a study variable when the population coefficient of variation of an auxiliary variable is known, under a simple random sampling without replacement scheme. Five classes of estimators are proposed for estimating the coefficient of variation of the study variable using the known population coefficient of variation of the auxiliary variable. The biases and mean squared errors (MSEs) of the proposed classes of estimators are derived up to the first order of approximation. The efficiency of the proposed estimators is compared with conventional estimators such as the traditional estimator (which does not utilize auxiliary information), ratio-type estimator, product-type estimator, ratio-type exponential estimator, product-type exponential estimator, ratio and product-type logarithmic estimators and difference-type estimator. Conditions are obtained under which the proposed estimators outperform the conventional ones. A comprehensive numerical and simulation study is performed to assess the effectiveness and reliability of the proposed estimators. In addition, graphical illustrations are provided to compare the performance of the proposed estimators with existing ones.