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

## 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

## 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, ... )

### 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;

### Details

\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.

### Author(s)

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

### References

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

### Examples

x <- rnorm(100)

RobExtremes documentation built on May 29, 2024, 6:05 a.m.