Multivariate t and beta distributions associated with the multivariate F distribution |
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Authors: | M C Jones |
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Institution: | (1) Department of Statistics, The Open University, Walton Hall, Milton Keynes, MK7 6AA, U.K. (Email: m.c.jones@open.ac.uk.), GB |
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Abstract: | Relationships between F, skew t and beta distributions in the univariate case are in this paper extended in a natural way to the multivariate case. The result
is two new distributions: a multivariate t/skew t distribution (on ℜm) and a multivariate beta distribution (on (0,1)m). A special case of the former distribution is a new multivariate symmetric t distribution. The new distributions have a natural relationship to the standard multivariate F distribution (on (ℜ+)m) and many of their properties run in parallel. We look at: joint distributions, mathematically and graphically; marginal
and conditional distributions; moments; correlations; local dependence; and some limiting cases.
Received: March 2001 |
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Keywords: | and phrases: multivariate distributions skew t distribution Student t distribution |
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