The objective of the present work is to study the relations between the mean difference and the standard deviation with reference to the most common continuous theoretical distribution models. The continuous distribution models without shape parameters, those with only one shape parameter, and those with two shape parameters have been considered. The shape parameters encountered are inequality indexes, skewness indexes or kurtosis indexes.\ud For the models without shape parameters the perfect equal ranking of the values of the two indexes have been verified. \ud For the models with only one shape parameter it was seen that with variations in the shape parameter both indexes increase or decrease, so that the relation between them is growing. The ratio between the two indexes made it possible to determine the interval in which one index is greater than the other and the one in which it is less. \ud Analogous results emerged for the models with two shape parameters, in particular the region in which one index is greater than the other and the complementary one.\ud It was confirmed that for some models the mean difference has a wider field of definition in terms of the parameters than the standard deviation

In this paper the authors study the sample behavior of the Gini's index of dissimilarity in the case of two samples of equal size drawn from the same uniform population. The paper present the analytical results obtained for the exact distribution of the index of dissimilarity for sample sizes n ≤ 8. This result was obtained by expressing the index of dissimilarity as a linear combination of spacings of the pooled sample. The obtained results allow to achieve the exact expressions of the moments for any sample size and, therefore, to highlight the main features of the sampling distributions of the index of dissimilarity. The present study can enhance inferential statistical aspects about one of the main contributions of Gini.

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

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In the present paper we derived, with direct method, the exact expressions for the sampling probability density function of the Gini concentration ratio for samples from a uniform population of size n = 6, 7, 8, 9 and 10. Moreover, we found some regularities of such distributions valid for any sample size.