gini.mean.diff {lmomco} | R Documentation |
The Gini mean difference statistic mathcal{G} is a robust estimator of distribution scale and is closely related to the second L-moment λ_2 = mathcal{G}/2.
mathcal{G} = frac{2}{n(n-1)}sum_{i=1}^n (2i - n - 1) X_{i:n}
where X_{i:n} are the order statistics.
gini.mean.diff(x)
x |
A vector of data values that will be reduced to non-missing values. |
An R list
is returned.
gini |
The gini mean difference mathcal{G} |
L2 |
The L-scale (second L-moment) via 0.5*mathcal{G} |
source |
An attribute identifying the computational source of the Gini's Mean Difference: “gini.mean.diff”. |
W.H. Asquith
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, vol. 52, p. 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, 197~p.
fake.dat <- c(123,34,4,654,37,78) gini <- gini.mean.diff(fake.dat) lmr <- lmoms(fake.dat) str(gini) print(abs(gini$L2 - lmr$lambdas[2]))