Copy the page URI to the clipboard
Jones, M. C.
(2002).
DOI: https://doi.org/10.1016/S0167-7152(01)00180-8
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.
Viewing alternatives
Metrics
Public Attention
Altmetrics from AltmetricNumber of Citations
Citations from DimensionsItem Actions
Export
About
- Item ORO ID
- 22662
- Item Type
- Journal Item
- 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 or School
-
Faculty of Science, Technology, Engineering and Mathematics (STEM) > Mathematics and Statistics
Faculty of Science, Technology, Engineering and Mathematics (STEM) - Copyright Holders
- © 2002 Elsevier Science B.V.
- Depositing User
- Sarah Frain