# delta_GMM: Estimate delta In LambertW: Probabilistic Models to Analyze and Gaussianize Heavy-Tailed, Skewed Data

 delta_GMM R Documentation

## Estimate delta

### Description

This function minimizes the Euclidean distance between the sample kurtosis of the back-transformed data W_{δ}(\boldsymbol z) and a user-specified target kurtosis as a function of δ (see References). Only an iterative application of this function will give a good estimate of δ (see IGMM).

### Usage

delta_GMM(
z,
type = c("h", "hh"),
kurtosis.x = 3,
skewness.x = 0,
delta.init = delta_Taylor(z),

### Value

A list with two elements:

 delta optimal δ for data z, iterations number of iterations (NA for 'optimize').

gamma_GMM for the skewed version of this function; IGMM to estimate all parameters jointly.

### Examples


# very heavy-tailed (like a Cauchy)
y <- rLambertW(n = 1000, theta = list(beta = c(1, 2), delta = 1),
distname = "normal")
delta_GMM(y) # after the first iteration



LambertW documentation built on Sept. 22, 2022, 5:07 p.m.