mc {LambertW} | R Documentation |
A robust measure of asymmetry. Details see references.
mc(x)
x |
data |
a numerical value, indicating the amount of asymmetry
Georg M. Goerg
Brys, G., M. Hubert, and A. Struyf (2004). “A robust measure of skewness”. Journal of Computa- tional and Graphical Statistics 13 (4), 996 - 1017.
## a little simulation/demonstration n.sim = 100 ################# Gaussian (Symmetric) #### A = cbind(0,0) for (i in 1:n.sim) { x = rnorm(100) A = rbind(A, c(mc(x), skewness(x))) } A = A[-1,] ################# Gaussian (Symmetric) #### theta.s = delta.01(0.2) # zero mean, unit variance, but positive skewness round(mLambertW(theta.s),5) B = cbind(0,0) for (i in 1:n.sim) { y = rLambertW(n=100, theta=theta.s) B = rbind(B, c(mc(y), skewness(y))) } B = B[-1,] colnames(A) = colnames(B) = c("MedCouple", "Pearson Skewness") op=par(no.readonly=TRUE) par(mfrow=c(2,2), mar=c(4,4,3,1)) plot(A, main="Gaussian") boxplot(A) abline(h=0) plot(B, main="Lambert W -Gaussian") boxplot(B) abline(h=mLambertW(theta.s)[3]) par(op) apply(A, 2, mean) apply(A, 2, sd) apply(B, 2, mean) apply(B, 2, sd)