GH_MGF function

GH Moment Generating Function

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

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.