Joint Influence of Exponential Ratio and Exponential Product Estimators for the Estimation of Clustered Population Variance in Adaptive Cluster Sampling
Adaptive cluster sampling (ACS) is considered to be the most efficient sampling design for the estimation of statistical parameters of rare and clustered populations. In this paper, we proposed an estimator that jointly incorporate the exponential ratio and exponential product type estimators using single auxiliary variable based on the averages of the networks in adaptive cluster sampling. The expressions of approximate bias and mean square error of the proposed estimator are derived. A numerical study is carried out using real and artificial populations to demonstrate and compare the efficiency of the proposed estimator over the traditional variance estimator under simple random sampling (SRS). The results of relative efficiencies show that the proposed estimator is more efficient than all the adaptive and non-adaptive estimators considered in this paper.