An EM type algorithm for maximum likelihood estimation of the normal-inverse Gaussian distribution (Q1613039)

The normal-inverse Gaussian distribution arises as a normal variance-mean mixture with an inverse Gaussian mixing distribution. This article deals with maximum likelihood estimation of the parameters of the normal-inverse Gaussian distribution. Due to the complexity of the likelihood, direct maximization is difficult. An EM type algorithm is provided for the maximum likelihood estimation of the normal-inverse Gaussian distribution. This algorithm overcomes numerical difliculties occurring when standard numerical techniques are used. An application to a data set concerning the general index of the Athens Stock Exchange is given. Some operating characteristics of the algorithm are discussed.