Open Journal of Statistics, 2014, 4, 412-418 Published Online August 2014 in SciRes. http://www.scirp.org/journal/ojs http://dx.doi.org/10.4236/ojs.2014.45040 How to cite this paper: Mwangi, C., Islam, A. and Orawo, L. (2014) Efficiency of the Adaptive Cluster Sampling Designs in Estimation of Rare Populations. Open Journal of Statistics, 4, 412-418. http://dx.doi.org/10.4236/ojs.2014.45040 Efficiency of the Adaptive Cluster Sampling Designs in Estimation of Rare Populations Charles Mwangi * , Ali Islam, Luke Orawo Department of Mathematics, Egerton University, Nakuru, Kenya Email: * charlesmwangi59@gmail.com Received 2 July 2014; revised 3 August 2014; accepted 11 August 2014 Copyright © 2014 by authors and Scientific Research Publishing Inc. This work is licensed under the Creative Commons Attribution International License (CC BY). http://creativecommons.org/licenses/by/4.0/ Abstract Adaptive cluster sampling (ACS) has been a very important tool in estimation of population para- meters of rare and clustered population. The fundamental idea behind this sampling plan is to de- cide on an initial sample from a defined population and to keep on sampling within the vicinity of the units that satisfy the condition that at least one characteristic of interest exists in a unit se- lected in the initial sample. Despite being an important tool for sampling rare and clustered pop- ulation, adaptive cluster sampling design is unable to control the final sample size when no prior knowledge of the population is available. Thus adaptive cluster sampling with data-driven stop- ping rule (ACS’) was proposed to control the final sample size when prior knowledge of population structure is not available. This study examined the behavior of the HT, and HH estimator under the ACS design and ACS’ design using artificial population that is designed to have all the characte- ristics of a rare and clustered population. The efficiencies of the HT and HH estimator were used to determine the most efficient design in estimation of population mean in rare and clustered popu- lation. Results of both the simulated data and the real data show that the adaptive cluster sam- pling with stopping rule is more efficient for estimation of rare and clustered population than or- dinary adaptive cluster sampling. Keywords Adaptive Cluster Sampling with Stopping Rule (ACS’), Ordinary Adaptive Cluster Sampling (ACS), Horvitz Thompson Estimator (HT), Hansen-Hurwitz Estimator (HH), Relative Efficiency 1. Introduction In ecology, most of the species are sparse and they tend to be found in clusters. In geology, most of the minerals * Corresponding author.