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

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.

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