GH_MGF {BayesLN}

GH Moment Generating Function

Description

Function that implements the moment generating function of the Generalized Hyperbolyc (GH) distribution.

Usage

GH_MGF(r, mu = 0, delta, alpha, lambda, beta = 0)

Arguments

r

Coefficient of the MGF. Can be viewd also as the order of the log-GH moments.

mu

Location parameter, default set to 0.

delta

Concentration parameter, must be positive.

alpha

Tail parameter, must be positive and greater than the modulus of beta.

lambda

Shape parameter.

beta

Skewness parameter, default set to 0 (symmetric case).

Details

This function allows to evaluate the moment generating function of the GH distribution in the point r. It is defined only for points that are lower than the value of \gamma, that is defined as: \gamma^2=\alpha^2-\beta^2. For integer values of r, it could also be considered as the r-th raw moment of the log-GH distribution.