cluster sampling

Sometimes in order to estimate population parameters such as mean and total values, we extract a random sample by cluster sampling method, and after completing sampling, we are interested in using the same sample to estimate the desired parameters in a subset of the population, which is said subpopulation. In this paper, we try to estimate subpopulation parameters in different cases when one-stage cluster sampling design is used.

Gupta and Shabbir (2008) have suggested an alternative form of ratio-type estimator for estimating the population mean. In this paper, we introduced new estimators by mixing two, stratified and cluster sampling method. Then we improved these estimators by using auxiliary variables and introducing new estimators. For sampling in infinite populations with a high geographic dispersion, the population will be divided into some smaller sub-population which leads to dispersion reduction to some extent. This will affect the variance of the estimator. Additionally dividing the population will result in saving cost, time and eases calculations.