Jones, M. C.
(2002).
| DOI (Digital Object Identifier) Link: | https://doi.org/10.1016/S0167-7152(01)00180-8 |
|---|---|
| Google Scholar: | Look up in Google Scholar |
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 Item |
|---|---|
| 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/School: | Faculty of Science, Technology, Engineering and Mathematics (STEM) > Mathematics and Statistics Faculty of Science, Technology, Engineering and Mathematics (STEM) |
| Item ID: | 22662 |
| Depositing User: | Sarah Frain |
| Date Deposited: | 11 Aug 2010 10:51 |
| Last Modified: | 07 Dec 2018 09:38 |
| URI: | http://oro.open.ac.uk/id/eprint/22662 |
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