Bivariate Beta Distributions and Beyond
Rianne Jacobs, Andriette Bekker, Schalk W. Human
Department of Statistics, University of Pretoria, Pretoria, South Africa

Kummer distributions have become an integral part of statistical distribution theory (see amongst others Armero and Bayarri, 1997; Ng and Kotz, 1995). In this presentation the bivariate Kummer-beta type IV distribution is introduced and derived via the Laplace transform of the popular Jones' bivariate beta kernel (see Jones, 2001; Olkin and Liu, 2003). Some statistical properties of the bivariate Kummer-beta type IV distribution are studied. We illustrate the significant effect of the new parameter, ψ, (introduced in the bivariate Kummer-beta type IV distribution) on the shape of the bivariate Kummer-beta type IV density, the marginal density and on the correlation between the two dependent components. Lastly, examples of possible applications will be presented.


Armero, C. and Bayarri, M.J. (1997). A Bayesian analysis of a queueing system with unlimited service, Journal of Statistical Planning and Inference, 58, 241-261.

Jones, M.C. (2001). Multivariate t and the beta distributions associated with the multivariate F distribution, Metrika, 54, 215-231.

Ng, K.W. and Kotz, S. (1995). Kummer-gamma and Kummer-beta univariate and multivariate distributions, Research report, 84, The University of Hong Kong.

Olkin, I. and Liu, R. (2003). A Bivariate beta distribution, Statistics and Probability Letters, 62, 407-412.

Keywords: Bivariate Kummer-beta distributions; Bivariate Jones model; Confluent hypergeometric function; Stress-strength model

Biography: Miss Jacobs is currently a Junior Lecturer and MSc student in Mathematical Statistics at the Department of Statistics, University of Pretoria. Her research focus area is statistical distribution theory, but she has also worked in the field of statistical process control. Her Master's dissertation is on the topic of bivariate beta distributions.