The Gini mean difference statistic \(\mathcal{G}\) is a robust estimator of distribution scale and is closely related to the second L-moment \(\lambda_2 = \mathcal{G}/2\).
$$\mathcal{G} = \frac{2}{n(n-1)}\sum_{i=1}^n (2i - n - 1) x_{i:n}\mbox{,}$$
where \(x_{i:n}\) are the sample order statistics.
Usage
gini.mean.diff(x)
Value
An R
list is returned.
gini
The gini mean difference \(\mathcal{G}\).
L2
The L-scale (second L-moment) because \(\lambda_2 = 0.5\times\mathcal{G}\) (see lmom.ub).
source
An attribute identifying the computational source of the Gini's Mean Difference: “gini.mean.diff”.
Arguments
x
A vector of data values that will be reduced to non-missing values.
Author
W.H. Asquith
References
Hosking, J.R.M., 1990, L-moments---Analysis and estimation of
distributions using linear combinations of order statistics: Journal of the Royal Statistical Society, Series B, v. 52, pp. 105--124.
Jurečková, J., and Picek, J., 2006, Robust statistical methods with R: Boca Raton, Fla., Chapman and Hall/CRC, ISBN 1--58488--454--1.