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

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, ... )

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

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.

Author(s)

Peter Ruckdeschel [e-mail], Nataliya Horbenko [e-mail]

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)

RobExtremes documentation built on Feb. 12, 2024, 3:01 a.m.