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Sequences of elliptical distributions and mixtures of normal distributions

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  • Gómez-Sánchez-Manzano, E.
  • Gómez-Villegas, M.A.
  • Marín, J.M.

Abstract

Two conditions are shown under which elliptical distributions are scale mixtures of normal distributions with respect to probability distributions. The issue of finding the mixing distribution function is also considered. As a unified theoretical framework, it is also shown that any scale mixture of normal distributions is always a term of a sequence of elliptical distributions, increasing in dimension, and that all the terms of this sequence are also scale mixtures of normal distributions sharing the same mixing distribution function. Some examples are shown as applications of these concepts, showing the way of finding the mixing distribution function.

Suggested Citation

  • Gómez-Sánchez-Manzano, E. & Gómez-Villegas, M.A. & Marín, J.M., 2006. "Sequences of elliptical distributions and mixtures of normal distributions," Journal of Multivariate Analysis, Elsevier, vol. 97(2), pages 295-310, February.
    • Handle: RePEc:eee:jmvana:v:97:y:2006:i:2:p:295-310
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    References listed on IDEAS

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    1. Cambanis, Stamatis & Huang, Steel & Simons, Gordon, 1981. "On the theory of elliptically contoured distributions," Journal of Multivariate Analysis, Elsevier, vol. 11(3), pages 368-385, September.
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    Cited by:

    1. Chen, Xiao & Feng, Zhenghui & Peng, Heng, 2023. "Estimation and order selection for multivariate exponential power mixture models," Journal of Multivariate Analysis, Elsevier, vol. 195(C).

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