Abstract
The normal inverse Gaussian distributions are used to introduce the class of multivariate normal α-stable distributions. Some fundamental properties of these new distributions are established. We give the expression of the variance function of the generated natural exponential family and we use the Lévy–Khintchine representation to determine the associated Lévy measure. We also study the relationship between these distributions and the multivariate inverse Gaussian ones.
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Louati, M., Masmoudi, A. & Mselmi, F. Multivariate Normal α-Stable Exponential Families. Mediterr. J. Math. 13, 1307–1323 (2016). https://doi.org/10.1007/s00009-015-0562-y
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DOI: https://doi.org/10.1007/s00009-015-0562-y