The mean difference of selected continuous and discrete distributions

A paper on Gini mean difference (Yitzhaki, 2003) shows the superiority of mean difference as a measure of variability for non normal distributions and contains a survey of the main past and recent scholarly contributions on the topic. The two previous gaps of the mean difference (difficulty of calculation and lack of inferential results) appear overcome with the mean difference presently having a substantially basic knowledge comparable with that of other variability indexes, thus offering the prospect of more widespread use. This perspective requires a greater attention to the ability of the mean difference and other variability indexes to characterize distributions. Apart from its use in measuring the variability of a series of observations, mean difference can also be used to measure the distribution variability. Knowledge of the formulas of the mean difference of distributions, and particularly their relations with the parameters, is an unavoidable step towards an increase in characterization of distributions provided by other variability indexes. The aim of this paper is to obtain explicit formulas of the mean difference, if possible in compact form, for some continuous and discrete distributions.