Generalized Exponential Estimator for the Estimation of Clustered Population Variance in Adaptive Cluster Sampling

Abstract

In this paper, we proposed a generalized exponential estimator with two auxiliary variables for the estimation of highly clumped population variance under adaptive cluster sampling design. The expressions of approximate bias and minimum mean square error are derived. A family of exponential ratio and exponential product estimator is obtained by using different values of generalized and optimized constants. A numerical study is carried out on real and artificial populations to examine the performance of the proposed estimator over the competing estimators. Related results show that the proposed generalized exponential estimator is able to provide considerably better results over the competing estimators for the estimation of rare and highly clustered population variance.

Keywords

• Adaptive cluster sampling
• Auxiliary information
• Exponential estimators
• Hansen-Hurwitz estimation
• Simulated population and Poisson clustered process