A Family of Correlation Coefficients Based on Extended Gini

• Activity Number: 176
• Type: Contributed
• Date/Time: Tuesday, August 13, 2002 : 8:30 AM to 10:20 AM
• Sponsor: Business & Economics Statistics Section*
• Author(s): Edna Schechtman*+ and Shlomo Yitzhaki
• Affiliation(s): Ben Gurion University and Hebrew University of Jerusalem
• Keywords: Extended Gini; ; Gini correlation; ; decomposition

Abstract

The extended Gini is a family of measures of variability which is mainly used in the areas of finance and income distribution. Each index in the family is defined by specifying one parameter. The higher the parameter, the more weight is attached to the lower portion of the cumulative distribution. In this talk, we list and investigate the properties of the equivalents of the correlation coefficient that are associated with the extended Gini family. In addition, we show that the extended Gini of a linear combination of random variables can be decomposed in a way that is similar to the decomposition of the variance. The decomposition includes terms which are equivalent to the terms involved in the decomposition of the variance, plus additional terms that reflect the assymetry of the correlation coefficient. The implication of these properties is that under some conditions, any model, based on the decomposition of the variance (i.e. OLS regression), can be replicated by an infinite number of models that are based on the Extended Gini, using Extended Gini as a substitute for the variance as a measure of dispersion.