The relation between the mean difference and the mean deviation in 11 continuous distribution models

Abstract

The aim of this paper is to examine the relations between the mean difference and the mean deviation with reference to the main continuous distribution models. At present, the analytical expressions of the mean difference, in a more or less compact form, have been developed for almost all the continuous distribution models. The numerical calculation of the mean difference is, instead, always possible for any distribution model. The distribution models without the shape parameters, those with only one shape parameter and those with two shape parameters have been considered. The perfect rank correlation between the values of the two indexes for the models without shape parameters have been ensured. In the case of models with only one shape parameter, it has been observed that, when the shape parameter changes, the two indexes are both increasing or both decreasing, so that the relation between the same is growing. The relation between the two indexes has allowed detection of the intervals in which one index is greater than the other and that in which it is less. Similar findings emerged when dealing with models with two shape parameters determining the region in which one index is greater than the other and as well as the complementary one

Mean Difference and Mean Deviation of Tukey Lambda Distribution

“…The purpose of this work is to increase the methodological contributions on the mean difference and on the relationships of the mean difference with other variability indexes [1] [2]. The studies on the mean difference, introduced by Corrado Gini in 1912 as a measure of the variability of the characters according to the aspect of inequality, have aroused the interest of many scholars over years and also recently [3] [4].…”