Some characterizations of the multivariate t distribution

Pi-Erh Lin

Journal of Multivariate Analysis, 1972, vol. 2, issue 3, 339-344

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.

Keywords: Symmetric; square; root; of; a; positive; definite; matrix; conditionally; independent; conditional; marginal; probability; density; almost; surely; with; respect; to; a; [sigma]-finite; measure (search for similar items in EconPapers)
Date: 1972
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Citations: View citations in EconPapers (6)

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