Some Studies on Non-Overlapping Clusters of Two Units

Abstract

Cluster sampling is frequently used in sample surveys on account of cost, convenience and efficiency consideration. Usually we come across situations in which cluster sampling is applied to the populations of natural clusters because list of elements is not available easily. However, sometime natural clusters do not exist and the list of elements is available but because using element as a sampling unit is inconvenient or costly. In such situations, clusters have to be formed artificially considering the important points like cluster size, criterion for forming clusters etc. Further, a criterion may lead to clusters which are overlapping or non-overlapping. Several workers have suggested the method of forming clusters but generally they lead to over-lapping clusters. In this investigation, a criterion for forming non-overlapping clusters (clusters may be unequal) has been suggested where we need not form all the clusters before selecting the sample, we form only as many clusters as are to be actually included in the sample. The method of enumeration is used to enumeration is used for computations of probabilities of inclusion of different units selected in the sample in which all possible samples are enumerated and the relative frequencies of occurrence of different units in the sample. Further, it has been shown in this dissertation, knowing 2’s, the population parameter can be estimated unbiased using Horvits Thompson estimate. In this case, the estimate of variance is high. Further, if 2’s are replace by some function of sample size n1/N, which simplifies the estimation procedure and the estimate of variance is also lower in this case compared to and Horvits estimate, although the estimate obtained in this way is a biased estimate. The magnitude of bias is also not significant, which proves the estimate obtained in this way is more efficient and the sampling scheme is fruitful.