delta.GMM {LambertW}R Documentation

GMM estimation of delta only

Description

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.

Usage

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

Arguments

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

Value

Parameter vector theta, where μ_x and σ_x equal simply the sample moments of the back transformed data.

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 Unpublished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 skewness


[Package LambertW version 0.1.6 Index]