kMAD {RobExtremes} | R Documentation |
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 |
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.
x <- rnorm(100) kMAD(x,k=10) kMAD(Norm(),k=10)