delta.GMM {LambertW}R Documentation

Estimate optimal delta

Description

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).

Usage

delta.GMM(y, c = median(y), s = sqrt(var(y)), gamma_x = 0, robust = FALSE)

Arguments

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

Value

A 3-dimensional vector containing: the minimizing delta given c and s; the sample mean, and sample standard deviation of widehat{boldsymbol x}_{theta}.

Author(s)

Georg M. Goerg

References

Goerg, G.M. (2009). “Lambert W Random Variables - A new class of skewed distribution functions”. Unpublished

See Also

mc for a robust measure of asymmetry; IGMM for an iterative method to estimate all parameters accurately

Examples

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

[Package LambertW version 0.1.9 Index]