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In this article, we first discuss a few properties along with limitations of traditional measure of coefficient of dispersion in comparison to the well-known standard measure of variation called the coefficient of variation. To overcome the limitations in the traditional coefficient of dispersion, a new measure of coefficient of dispersion is introduced which is more informative than the conventional one. A new naïve estimator of the newly developed measure of coefficient of dispersion is proposed. The bias and variance expressions for the naïve estimator are derived to the first order of approximation. In the presence of an auxiliary variable, ratio and regression type estimators for estimating the new measure of coefficient of dispersion are also proposed. The bias and the variance expressions to the first order of approximation are derived. A simulation study, using R language, to judge the performance of the proposed ratio and regression type estimators with respect to the naïve estimator is considered. At the end, applications of the proposed ratio and regression type estimators based on real data sets are discussed.

Ratio and regression type estimators of a new measure of coefficient of dispersion