Generalized estimator for the estimation of clustered population mean in adaptive cluster sampling

In many real-world survey situations, the use of auxiliary information together with the survey variable is very common phenomenon. The ratio and regression estimators are most commonly used estimation methods that incorporate the auxiliary information in various forms to improve the efficiency of the estimators. Adaptive cluster sampling is specifically developed for the estimation of rare and clustered population parameters and applied to a wide range of situations like, plants and animals of rare and endangered species, uneven minerals and drug users. In this paper, we proposed a generalized estimator with a single auxiliary variable for the estimation of highly clumped population mean under adaptive cluster sampling design. The proposed estimator utilizes the different combination of known parameters of the auxiliary variable. The expressions of approximate bias and mean square error are derived up to the first-order approximation. The Proposed estimator is found to be more efficient than the estimators proposed under certain conditions. A numerical study is carried out on real and artificial bivariate populations to support the performance of the proposed estimator over the above-mentioned estimators.