The Relationship between the Gini and the Mean Absolute Deviation
9 Pages Posted: 18 Oct 2011
Date Written: October 18, 2011
The aim of this note is to argue that the between-group Gini mean difference (BGMD) includes the mean absolute deviation (MAD), the least absolute deviation (LAD), and the absolute deviation from a given quantile (QUAD) as special cases. Those measures can be interpreted as equivalents to BGMD measures, according to the particular partition of the data. As such they possess the properties of the Gini mean difference but they omit the intra-group variability. It is argued that the loss of the intra-group information is too heavy a price to pay.
Keywords: Gini, LAD, MAD, QUAD
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