On the homogeneity measures

Abstract

The usual homogeneity indices take their lowest value according to a minimum homogeneity state which is not always verificable in the examined statistical collective. The A. shows that the reference to a minimum homogeneity situation not actually achievable could lead to contradictions. To resolve these inconsistencies the A. suggests referring to the actual minimum homogeneity state. It is possible to find a homogeneity measure by a quantification of the diversity between the examined situation and the minimum actual state. This procedure elicits generalizations of the usual homogeneity indices. A different way of finding homogeneity indices is based on an indirect comparison between distributions made by the appropriate quantities inferred from them. Using this procedure the A. also constructs a homogeneity curve and a homogeneity ratio that allows him to find a correlation between the homogeneity notion and the concentration notion.