Estimating the Abundance of Clustered Animal Population by Using Adaptive Cluster Sampling
and Negative Binomial Distribution
Yizhou Bo*, Naima Shifa**
*
Department of Mathematics, DePauw University,
Greencastle, IN, USA 46135, yizhoubo_2014@depauw.edu
**
Department of Mathematics, DePauw University,
Greencastle, IN, USA 46135, naimashifa@depauw.edu
To maintain the balance in nature, to meet the challenges of sustaining life on earth, or to provide
sound and effective public policy, researchers always would like to estimate the density or the
total of natural populations. It is not always easy and straightforward to obtain the abundance of
animal populations when the study area is vast and animals are clustered and mobile. In this
research work, we propose a multistage stage sampling design for estimating the animal
populations that spread over an extensive area, and highly clustered. This model is based on
adaptive cluster sampling (ACS) to identify the location of the population and negative binomial
distribution to estimate the total in each site. To identify the location of the population we
consider both sampling with replacement (WR) and sampling without replacement (WOR).
Some mathematical properties of the model are also developed.
Key words: Adaptive cluster sampling, negative binomial distribution, sampling with or without
replacement, rare or clustered population, population size estimation.