Gini Mean Difference Statistic

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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)}∑_{i=1}^n (2i - n - 1) x_{i:n}\mbox{,}

where x_{i:n} are the sample order statistics.

Usage

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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) because λ_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”.

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, 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.

See Also

lmoms

Examples

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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]))

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