A dependent bivariate t distribution with marginals on different degrees of freedom
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.
Year of publication: |
2002
|
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Authors: | Jones, M. C. |
Published in: |
Statistics & Probability Letters. - Elsevier, ISSN 0167-7152. - Vol. 56.2002, 2, p. 163-170
|
Publisher: |
Elsevier |
Keywords: | Bivariate distribution Spherical symmetry Student's t distribution |
Saved in:
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