Multivariate normal mean–variance mixture distribution based on Birnbaum–Saunders distribution

Abstract

A multivariate normal mean–variance mixture based on a Birnbaum–Saunders (NMVMBS) distribution is introduced and several properties of this new distribution are discussed. A new robust non-Gaussian ARCH-type model is proposed in which there exists a relation between the variance of the observations, and the marginal distributions are NMVMBS. A simple EM-based maximum likelihood estimation procedure to estimate the parameters of this normal mean–variance mixture distribution is given. A simulation study and some real data are used to demonstrate the modelling strength of this new model.

Keywords:

• Birnbaum–Saunders distribution
• generalized hyperbolic distribution
• EM-Algorithm
• non-Gaussian Arch process

AMS Subject Classification:

• 62E15
• 62M10

Acknowledgements

The authors wish to thank professor Mahbano Tata for her valuable comments on an earlier version of this manuscripts. The authors also express their sincere thanks to the associated editor and anonymous reviewer for several helpful and insightful comments on this manuscript which led to this improved version.