View source for Gini average difference

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A magnitude characterizing the [[Dispersion|dispersion]] of the values of a random variable  $  X $. 
It was introduced by C. Gini in 1912 and is defined by the formula

$$ 
\Delta  =  \int\limits _ {- \infty } ^  \infty   \int\limits _ {- \infty } ^  \infty  
| x - y |  dF ( x)  dF ( y) ,
$$

where  $  F ( \cdot ) $
is the distribution function of the random variable. Another variable which is also occasionally considered is the Gini dispersion coefficient

$$ 
G  =  
\frac \Delta {2 \mu }
 ,
$$

where  $  \mu $
is the [[Mathematical expectation|mathematical expectation]] of the random variable  $  X $.

====References====
<table><TR><TD valign="top">[1]</TD> <TD valign="top">  M.G. Kendall,   A. Stuart,   "The advanced theory of statistics. Distribution theory" , '''3. Design and analysis''' , Griffin  (1969)</TD></TR></table>