Adaptive cluster sampling based on ranked sets

Abstract

In many surveys, characteristic of interest is sparsely distributed but highly aggregated; in such situations the adaptive cluster sampling is very useful. Examples of such populations can be found in fisheries, mineral investigations (unevenly distributed ore concentrations), animal and plant populations (rare and endangered species), pollution concentrations and hot spot investigations, and epidemiology of rare diseases. Ranked Set Sampling (RSS) is another useful technique for improving the estimates of mean and variance when the sampling units in a study can be more easily ranked than measured. Under equal and unequal allocation, RSS is found to be more precise than simple random sampling, as it contains information about each order statistics. This paper deal with the problem in which the value of the characteristic under study on the sampled places is low or negligible but the neighbourhoods of these places may have a few scattered pockets of the same. We proposed an adaptive cluster sampling theory based on ranked sets. Different estimators of the population mean are considered and the proposed design is demonstrated with the help of one simple example of small populations. The proposed procedure appears to perform better than the existing procedures of adaptive cluster sampling.