Enhancing variance estimation in adaptive cluster sampling using exponential estimators with auxiliary information...

This article focuses on improving the variance estimation for African hartebeest population using adaptive cluster sampling methodology, with particular emphasis on the effective use of exponential estimators and auxiliary information to enhance the accuracy of the estimates. We proposed few modified exponential estimators using different forms of auxiliary variable and derived the expressions of approximate bias and mean squared error using Taylor and exponential expansions. In addition, we develop proposed a generalized exponential estimator by unifies all proposed modified exponential estimators into a single formulation. The properties of this generalized exponential estimator are derived and multiple special cases for the modified exponential estimators are obtained by employing different known parameters of the auxiliary variable. We also provide mathematical comparisons by relating the mean squared error expressions of the existing estimators with the generalized exponential estimator. We do a thorough numerical study using real population of African Hartebeests for the variance estimation to evaluate the efficacy of the suggested exponential estimators. Furthermore, a simulation study is also conducted to verify the estimates obtained from the real data.