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;
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.