arameter Estimations of Hyperbolic and Normal Inverse Gaussian Distributions

by Mounir Aout.

Abstract: Generalized Hyperbolic distributions, introduced by Barndorff-Nielsen in 1977, have become quite popular in various areas of theoretical and applied statistics. These distributions possess a number of attractive properties and they allow representation of the skewness and their tails tend to be heavier than those of the normal. In this paper we develop a numerical algorithm for estimating the parameters of both Hyperbolic (HYP) and Normal Inverse Gaussian (NIG) distributions via Maximum Likelihood. This task relies on numerical methods for solving systems of nonlinear equations. We also give two C programs, based on GSL library available under GPL license, for the estimation procedure.

Key Words: Hyperbolic distributions, Normal Inverse Gaussian distributions, maximum likelihood, C programs

Mounir Aout,

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