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

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

### Usage

 1 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) 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”.

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

 1 2 3 4 5 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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