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.

DOI: https://doi.org/10.1007/s10260-008-0103-y

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.

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About

• Item ORO ID
• 22505
• Item Type
• Journal Item
• ISSN
• 1618-2510
• Extra Information
• The original publication is available at www.springerlink.com.
• Keywords
• chi-squared distribution; positive dependence; transformation
• 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
• © 2008 Springer-Verlag
• Depositing User
• Sarah Frain