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Multivariate Normal α-Stable Exponential Families

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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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Authors and Affiliations

  1. Sfax National School of Electronics and Telecommunications, B.P. 1163, Sfax, Tunisia

    Mahdi Louati

  2. Laboratory of Probability and Statistics, Sfax Faculty of Sciences, B.P. 1171, Sfax, Tunisia

    Afif Masmoudi

  3. Laboratory of Probability and Statistics, Sfax University, B.P. 1171, Sfax, Tunisia

    Farouk Mselmi

Authors
  1. Mahdi Louati
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  2. Afif Masmoudi
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  3. Farouk Mselmi
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Correspondence to Mahdi Louati.

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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

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