RobExtremes (version 1.3.2)

kMAD: Asymmetric Median of Absolute Deviations for Skewed Distributions

Description

Function for the computation of asymmetric median absolute deviation (kMAD) It coincides with ordinary median absolute deviation (MAD) for \(k=1\).

Usage

kMAD(x,k,...)
# S4 method for numeric,numeric
kMAD(x, k = 1, na.rm = TRUE, 
                eps = .Machine$double.eps, ... )
# S4 method for UnivariateDistribution,numeric
kMAD(x, k = 1, up = NULL, ... )

Arguments

x

a numeric vector or a distribution.

k

numeric; tunning parameter for asymmetrical MAD; has to be of length 1 and larger than 1.

na.rm

logical; if TRUE then NA values are stripped from x before computation takes place.

eps

numeric; accuracy up to which to state equality of two numeric values

up

numeric; upper bound for search interval; important in distributions without left/right endpoint.

...

additional arguments for other functions; not used so far;

Author

Peter Ruckdeschel , Nataliya Horbenko

Details

For kMAD (asymmetrial MAD) is a root of the equation: $$\mathop{\rm kMAD}(F,k) = \inf\{t>0\;\mid \;F(m+kt)-F(m-t)\ge 1/2 \}$$, where F is the cumulative distribution function, m is the median of F.

References

Ruckdeschel, P., Horbenko, N. (2010): Robustness Properties for Generalized Pareto Distributions. ITWM Report 182.

See Also

mad

Examples

x <- rnorm(100)
kMAD(x,k=10)
kMAD(Norm(),k=10)