Gini average difference

A magnitude characterizing the 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 of the random variable $ X $.

References

[1]	M.G. Kendall, A. Stuart, "The advanced theory of statistics. Distribution theory" , 3. Design and analysis , Griffin (1969)