A bivariate F distribution with marginals on arbitrary numerator and denominator degrees of freedom, and related bivariate beta and t distributions |
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| Authors: | A H El-Bassiouny M C Jones |
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| Institution: | (1) Department of Applied-Mathematics, National Chung Hsing University, Taichung, Taiwan;(2) Graduate Institute of Finance, National Chiao Tung University, Hsinchu, Taiwan;(3) Institute of Statistics, National Chiao Tung University, Hsinchu, Taiwan |
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| 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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