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Last data update: 2014.03.03

R: Medcouple, a Robust Measure of Skewness

mc	R Documentation

Medcouple, a Robust Measure of Skewness

Description

Compute the ‘medcouple’, a robust concept and estimator of skewness. The medcouple is defined as a scaled median difference of the left and right half of distribution, and hence not based on the third moment as the classical skewness.

Usage

mc(x, na.rm = FALSE, doReflect = (length(x) <= 100),
   eps1 = .Machine$double.eps, eps2 = .Machine$double.xmin,
   maxit = 100, trace.lev = 0, full.result = FALSE)

Arguments

`x`	a numeric vector
`na.rm`	logical indicating how missing values (`NA`s) should be dealt with.
`doReflect`	logical indicating if the internal MC should also be computed on the reflected sample `-x`, with final result `(mc.(x) - mc.(-x))/2`. This makes sense since the internal MC, `mc.()` computes the himedian() which can differ slightly from the median.

`eps1,eps2`	tolerance in the algorithm; only change with care!
`maxit`	maximul number of iterations; typically a few should be sufficient.
`trace.lev`	integer specifying how much diagnostic output the algorithm (in C) should produce. No output by default, most output for `trace.lev = 5`.
`full.result`	logical indicating if the full return values (from C) should be returned as a list via `attr(*, "mcComp")`.

Value

a number between -1 and 1, which is the medcouple, MC(x). For r <- mc(x, full.result = TRUE, ....), then attr(r, "mcComp") is a list with components

`medc`	the medcouple mc.(x).
`medc2`	the medcouple mc.(-x) if `doReflect=TRUE`.
`eps`	tolerances used.
`iter,iter2`	number of iterations used.
`converged,converged2`	logical specifying “convergence”.

Author(s)

Guy Brys; modifications by Tobias Verbeke and bug fixes and extensions by Manuel Koller and Martin Maechler.

References

Guy Brys, Mia Hubert and Anja Struyf (2004) A Robust Measure of Skewness; JCGS 13 (4), 996–1017.

Hubert, M. and Vandervieren, E. (2008). An adjusted boxplot for skewed distributions, Computational Statistics and Data Analysis 52, 5186–5201.

Examples

mc(1:5) # 0 for a symmetric sample

x1 <- c(1, 2, 7, 9, 10)
mc(x1) # = -1/3

data(cushny)
mc(cushny) # 0.125

stopifnot(mc(c(-20, -5, -2:2, 5, 20)) == 0,
          mc(x1, doReflect=FALSE) ==  -mc(-x1, doReflect=FALSE),
          all.equal(mc(x1, doReflect=FALSE), -1/3, tolerance = 1e-12))