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The multivariate t-distribution with multiple degrees of freedom

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  • Haruhiko Ogasawara

Abstract

A multivariate t-distribution is introduced such that each element of a normal vector is scaled by using a chi-square that is independent of the chi-squares for the remaining elements of the vector with possibly distinct degrees of freedom. The integral and series expressions of the probability density function are given. The absolute values of the covariances/correlations and Mardia’s multivariate measure of kurtosis are shown to be smaller than those for the corresponding usual multivariate t with a common chi-square. An extended multivariate t with common and unique chi-squares is also proposed, which takes a form like factor analysis.

Suggested Citation

  • Haruhiko Ogasawara, 2024. "The multivariate t-distribution with multiple degrees of freedom," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 53(1), pages 144-169, January.
    • Handle: RePEc:taf:lstaxx:v:53:y:2024:i:1:p:144-169
    DOI: 10.1080/03610926.2022.2076122
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