Jones, M. C.
(2002).
A dependent bivariate t distribution with marginals on different degrees of freedom.
Statistics & Probability Letters, 56(2) pp. 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 {√n1Z1/√W1, √n1Z2/√W1} 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 {√ν1Z1/√W1, √ν2Z2/√W1+W2} where ν1=n1, ν2=n1+n2. This bivariate distribution has marginal distributions which are Student t distributions on different degrees of freedom if ν1≠ν2. The marginals remain uncorrelated, as in the spherically symmetric case, but are also by no means independent.
| Item Type: |
Journal Article
|
| Copyright Holders: |
2002 Elsevier Science B.V. |
| ISSN: |
0167-7152 |
| Extra Information: |
Please note the mathematical notation in the above abstract may not be accurate due to font limitations. |
| Keywords: |
bivariate distribution; spherical symmetry; student's t distribution |
| Academic Unit/Department: |
Mathematics, Computing and Technology > Mathematics and Statistics |
| Item ID: |
22662 |
| Depositing User: |
Sarah Frain
|
| Date Deposited: |
11 Aug 2010 10:51 |
| Last Modified: |
02 Dec 2010 21:02 |
| URI: |
http://oro.open.ac.uk/id/eprint/22662 |
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