delta.GMM {LambertW} | R Documentation |
Given μ_x and σ_x, this function minimizes the distance (default: Euclidean) between the theoretical skewness gamma(X), and the sample skewness of the back-transformed data widehat{boldsymbol x}_{theta}. Note that only an interative application of this function will give a good estimate of theta rightarrow see IGMM
.
A robust measure of the asymmetry can also be used(see MedCouple estimator: mc
).
delta.GMM(y, c = median(y), s = sqrt(var(y)), gamma_x = 0, robust = FALSE)
y |
a numeric vector of data values. |
c |
value that centers y ; default: sample median of y |
s |
standardizing constant for y-c ; default: sample standard deviation of y |
gamma_x |
theoretical skewness. default: 0 |
robust |
robust estimation of the sample skewness (see mc )? default FALSE |
A 3-dimensional vector containing: the minimizing delta given c
and s
; the sample mean, and sample standard deviation of widehat{boldsymbol x}_{theta}.
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 Unpublished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 asymmetry; IGMM
for an iterative method to estimate all parameters accurately
set.seed(1) y = rLambertW(n=1000, theta=c(0.4,1,2)) ## very highly skewed delta.GMM(y) # after the first iteration IGMM(y)$theta # after the final iteration; conversion has been reached. ## note the big difference between the first and last iteration; ## only a small change in delta, but a huge one in mu and sigma