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Closure of multivariate t and related distributions

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  • Jensen, D. R.

Abstract

Let be a Studentizing transformation of the type T(Y) = [nu]A'Y/||B'Y||, and let GM(n) consist of scale mixtures of Gaussian laws on [bumpy equals]k; 1 [less-than-or-equals, slant] k [less-than-or-equals, slant] n[bumpy equals]. It is shown that GM(n) is closed under T(·). Concentration properties of these distributions are studied via peakedness on varying their parameters, showing that peakedness may be diminished, preserved, or increased under T(·). Random ratios having moments of arbitrary order are exhibited when neither the numerator nor denominator has moments of any order.

Suggested Citation

  • Jensen, D. R., 1994. "Closure of multivariate t and related distributions," Statistics & Probability Letters, Elsevier, vol. 20(4), pages 307-312, July.
    • Handle: RePEc:eee:stapro:v:20:y:1994:i:4:p:307-312
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    Cited by:

    1. De la Cruz, Rolando, 2008. "Bayesian non-linear regression models with skew-elliptical errors: Applications to the classification of longitudinal profiles," Computational Statistics & Data Analysis, Elsevier, vol. 53(2), pages 436-449, December.
    2. Iwashita, Toshiya & Kakizawa, Yoshihide & Inoue, Tatsuki & Seo, Takashi, 2009. "An asymptotic expansion of the distribution of Student's t type statistic under spherical distributions," Statistics & Probability Letters, Elsevier, vol. 79(18), pages 1935-1942, September.

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