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On some characterizations of the t-distribution

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  • Arellano-Valle, Reinaldo B.
  • Bolfarine, Heleno

Abstract

In this paper we discuss three different characterizations of the generalized t-distribution within the class of the eliptical distributions. We show that this distribution can be characterized in terms of its unconditional and conditional marginals and in terms of quadratic forms. Similar results have been proved for the normal distribution. An additional characterization of the t distribution within the subclass of the compound normal distributions (or scale mixture of normal distributions) is also studied.

Suggested Citation

  • Arellano-Valle, Reinaldo B. & Bolfarine, Heleno, 1995. "On some characterizations of the t-distribution," Statistics & Probability Letters, Elsevier, vol. 25(1), pages 79-85, October.
    • Handle: RePEc:eee:stapro:v:25:y:1995:i:1:p:79-85
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    References listed on IDEAS

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    1. Khatri, C. G. & Mukerjee, Rahul, 1987. "Characterization of normality within the class of elliptical contoured distributions," Statistics & Probability Letters, Elsevier, vol. 5(3), pages 187-190, April.
    2. 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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