Saddlepoint approximation for the generalized inverse Gaussian Lévy process

The generalized inverse Gaussian (GIG) Lévy process is a limit of compound Poisson processes, including the stationary gamma and as special cases. However, fitting GIG to data computationally intractable due fact that marginal distribution not convolution-closed. current work reveals admits simple yet extremely accurate saddlepoint approximation. Particularly, we prove if order parameter greater than or equal −1, can be approximated accurately — no need normalize density. Accordingly, maximum likelihood estimation quick, random number generation from straightforward by using Monte Carlo methods, goodness-of-fit testing undemanding perform. Therefore, major numerical impediments application are removed. We demonstrate accuracy approximation via various experimental setups.