Before revision:  Unlike Gaussian quadrature, the proposed quadrature exactly evaluates both positive and negative moments, thus improving evaluation accuracy. The generalized hyperbolic distribution is efficiently approximated as a finite normal variance-mean mixture with the quadrature .
After revision:  Unlike Gaussian quadrature, the proposed quadrature exactly evaluates both positive and negative orders. Using the quadrature, the generalized hyperbolic distribution is efficiently approximated as a finite normal variance-mean mixture with the quadrature .