delta.GMM {LambertW} | R Documentation |
Given μ_x and σ_x, this function computes such a delta that the sample skewness of the back transformed data equals the theoretical one gamma(X). In particular, for Gaussian and student-t input gamma(X) = 0 (default value), so delta.GMM
finds this delta that "symmetrizes" some given data y
.
A robust measure of the skewness is possible via the MedCouple estimator.
delta.GMM(y, robust = FALSE, c = mean(y), s = sqrt(var(y)), gamma_x = 0)
y |
data |
robust |
Should the skewness be measured in a robust way? robust=TRUE/FALSE ; default is FALSE |
c |
the value that centers y ; default value is the sample mean of y |
s |
standardizing constant for y-c ; default value is the sample standard deviation of y |
gamma_x |
theoretical skewness. default value gamma_x = 0 |
Parameter vector theta, where μ_x and σ_x equal simply the sample moments of the back transformed data.
Georg M. Goerg
Goerg, G.M. (2009). “Lambert W Random Variables - A new class of skewed distribution functions”. Unpublished
mc
for a robust measure of skewness