ESTIMATION OF GEOMETRIC MEAN OF SKEWED POPULATIONS WITH AND WITHOUT USING AUXILIARY INFORMATION

Abstract

There are certain situations, for example, positively skewed distributions, where geometric mean is more appropriate measure of location than the arithmetic mean as it gives larger weight to smaller values than larger values of variables. It is specifically useful in averaging ratios, percentages and rates of change in one period over the other. In this paper we propose two different types of estimators for estimating population geometric mean of the characteristic under study variable y, one with and the other without using auxiliary information. To investigate the properties of these estimators we obtain their Bias and Mean Square Errors (MSE) along with the upper bounds for their mean square errors under certain realistic assumptions. Empirical example is also given showing the relative efficiencies of the proposed estimators.