The Open UniversitySkip to content
 

A bivariate F distribution with marginals on arbitrary numerator and denominator degrees of freedom, and related bivariate beta and t distributions

El-Bassiouny, A. H. and Jones, M. C. (2009). A bivariate F distribution with marginals on arbitrary numerator and denominator degrees of freedom, and related bivariate beta and t distributions. Statistical Methods and Applications, 18(4) pp. 465–481.

Full text available as:
[img]
Preview
PDF (Accepted Manuscript) - Requires a PDF viewer such as GSview, Xpdf or Adobe Acrobat Reader
Download (265Kb)
DOI (Digital Object Identifier) Link: http://doi.org/10.1007/s10260-008-0103-y
Google Scholar: Look up in Google Scholar

Abstract

The classical bivariate F distribution arises from ratios of chi-squared random variables with common denominators. A consequent disadvantage is that its univariate F marginal distributions have one degree of freedom parameter in common. In this paper, we add a further independent chi-squared random variable to the denominator of one of the ratios and explore the extended bivariate F distribution, with marginals on arbitrary degrees of freedom, that results. Transformations linking F, beta and skew t distributions are then applied componentwise to produce bivariate beta and skew t distributions which also afford marginal (beta and skew t) distributions with arbitrary parameter values. We explore a variety of properties of these distributions and give an example of a potential application of the bivariate beta distribution in Bayesian analysis.

Item Type: Journal Article
Copyright Holders: 2008 Springer-Verlag
ISSN: 1618-2510
Extra Information: The original publication is available at www.springerlink.com.
Keywords: chi-squared distribution; positive dependence; transformation
Academic Unit/Department: Mathematics, Computing and Technology > Mathematics and Statistics
Mathematics, Computing and Technology
Item ID: 22505
Depositing User: Sarah Frain
Date Deposited: 10 Aug 2010 11:12
Last Modified: 24 Feb 2016 06:30
URI: http://oro.open.ac.uk/id/eprint/22505
Share this page:

Altmetrics

Scopus Citations

► Automated document suggestions from open access sources

Download history for this item

These details should be considered as only a guide to the number of downloads performed manually. Algorithmic methods have been applied in an attempt to remove automated downloads from the displayed statistics but no guarantee can be made as to the accuracy of the figures.

Actions (login may be required)

Policies | Disclaimer

© The Open University   + 44 (0)870 333 4340   general-enquiries@open.ac.uk