On estimating the finite population mean using improved estimators in adaptive cluster sampling design

This article introduces a generalized class of estimators tailored for estimating the finite population mean within the framework of Adaptive Cluster Sampling (ACS) design. The proposed class is designed to encompass numerous existing estimators as its particular cases while also introducing several new novel estimators. It should be noted that the existing estimators which are presented in Section 3 are members of the proposed log type generalized class $T_g$. From the proposed log type generalized class $T_g$, four new log type estimators are developed. We derive the expressions for bias and mean square error (MSE) up to the first order of approximation. Through simulation studies and a real data application, we compare the performance of the new estimators derived from this proposed class with existing ones, demonstrating that the newly developed estimators outperform their existing counterparts. For the better understanding of the performances of our suggested class of estimators, we present the numerical results graphically.