As a generalization of Gini's mean difference measure of variation for quantitative data, this paper proposes families of summary measures based on the generalized sum and mean of the absolute differences for all data pairs. Some important properties of those generalized measures are discussed. The case of categorical data is also specifically considered.
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References
1.
GiniC. (1912) Variabilitàe Mutabilita, Anno 3, Part 2, p. 80. Studi Econonico-Giuridici della R. Università de Cagliari.
2.
HallM.TidemanN. (1967) Measures of concentration. Journal of the American Statistical Association, 62, 162–168.
HillM. O. (1973) Diversity and evenness: A unifying notation and its consequences. Ecology, 54, 427–431.
5.
KvålsethT. O. (1989) Range measure of qualitative variation. Perceptual and Motor Skills, 68, 1282.
6.
KvålsethT. O. (1993) A measure of homogeneity for nominal categorical data. Perceptual and Motor Skills, 76, 1129–1130.
7.
KvålsethT. O. (1995) Coefficients of variation for nominal and ordinal categorical data. Perceptual and Motor Skills, 80, 843–847.
8.
MagurranA. E. (1988) Ecological diversity and its measurement. Princeton, NJ: Princeton Univer. Press.
9.
MarshallA. W.OlkinI. (1979) Inequalities: Theory of majorization and its applications. New York: Academic Press.
10.
SolomonD. L. (1979) A comparative approach to species diversity. In GrassleJ. F.PatilG. P.SmithW.TaillieC. (Eds.), Ecological diversity in theory and practice. Fairland, MD: International Co-operative Publishing House. Pp. 29–35.
11.
WeisbergH. F. (1992) Central tendency and variability. Newbury Park, CA: Sage.
12.
YuleG. U.KendallM. G. (1950) An introduction to the theory of statistics. (14th ed.) London: Charles Griffin.