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Some characterizations of the multivariate t distribution

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  • Lin, Pi-Erh

Abstract

A multivariate t vector X is represented in two different forms, one associated with a normal vector and an independent chi-squared variable, and the other with a normal vector and an independent Wishart matrix. We show that X is multivariate t with mean [mu], covariance matrix [nu]([nu] - 2)-1[Sigma], [nu] > 2 and degrees of freedom [nu] if and only if for any a [not equal to] 0, (a'[Sigma]a)-1/2a'(X - [mu]) has the Student's t distribution with [nu] degrees of freedom under both representations. Some other characterizations are also obtained.

Suggested Citation

  • Lin, Pi-Erh, 1972. "Some characterizations of the multivariate t distribution," Journal of Multivariate Analysis, Elsevier, vol. 2(3), pages 339-344, September.
    • Handle: RePEc:eee:jmvana:v:2:y:1972:i:3:p:339-344
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    Citations

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    Cited by:

    1. Katarzyna Budny, 2019. "Power Generalization Of Chebyshev’S Inequality – Multivariate Case," Statistics in Transition New Series, Polish Statistical Association, vol. 20(3), pages 155-170, September.
    2. Chunyan Cai & Jin Piao & Jing Ning & Xuelin Huang, 2018. "Efficient Two-Stage Designs and Proper Inference for Animal Studies," Statistics in Biosciences, Springer;International Chinese Statistical Association, vol. 10(1), pages 217-232, April.
    3. Budny Katarzyna, 2019. "Power Generalization Of Chebyshev’S Inequality – Multivariate Case," Statistics in Transition New Series, Statistics Poland, vol. 20(3), pages 155-170, September.
    4. Emna Ghorbel & Mahdi Louati, 2024. "An expectation maximization algorithm for the hidden markov models with multiparameter student-t observations," Computational Statistics, Springer, vol. 39(6), pages 3287-3301, September.
    5. Budny, Katarzyna, 2022. "Improved probability inequalities for Mardia’s coefficient of kurtosis," Statistics & Probability Letters, Elsevier, vol. 191(C).
    6. Yu-Fang Chien & Haiming Zhou & Timothy Hanson & Theodore Lystig, 2023. "Informative g -Priors for Mixed Models," Stats, MDPI, vol. 6(1), pages 1-23, January.

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