gini.mean.diff {lmomco}R Documentation

Gini Mean Difference Statistic

Description

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.

Usage

gini.mean.diff(x)

Arguments

x A vector of data values that will be reduced to non-missing values.

Value

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”.

Author(s)

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, 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.

See Also

lmoms

Examples

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]))

[Package lmomco version 0.96.3 Index]