A dependent bivariate t distribution with marginals on different degrees of freedom

M. C. Jones

Statistics & Probability Letters, 2002, vol. 56, issue 2, 163-170

Abstract: Let Z1,Z2 and W1,W2 be mutually independent random variables, each Zi following the standard normal distribution and Wi following the chi-squared distribution on ni degrees of freedom. Then, the pair of random variables , has the bivariate spherically symmetric t distribution; this has both marginals the same, namely Student's t distributions on n1 degrees of freedom. In this paper, we study the joint distribution of {, ,} where [nu]1=n1, [nu]2=n1+n2. This bivariate distribution has marginal distributions which are Student t distributions on different degrees of freedom if [nu]1[not equal to][nu]2. The marginals remain uncorrelated, as in the spherically symmetric case, but are also by no means independent.

Keywords: Bivariate; distribution; Spherical; symmetry; Student's; t; distribution (search for similar items in EconPapers)
Date: 2002
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Citations: View citations in EconPapers (7)

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