kMAD: Asymmetric Median of Absolute Deviations for Skewed...
In RobExtremes: Optimally Robust Estimation for Extreme Value Distributions

Description Usage Arguments Details Author(s) References See Also Examples

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

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

`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;

For kMAD (asymmetrial MAD) is a root of the equation:

kMAD(F,k) = inf{t>0|F(m+kt)-F(m-t)>=1/2}

, where F is the cumulative distribution function, m is the median of F.

Peter Ruckdeschel peter.ruckdeschel@uni-oldenburg.de, Nataliya Horbenko nhorbenko@gmail.com

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

mad

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

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