Shabgard, SinaIranmaneshID, AnisRad, Najmeh NakhaeiNagar, Daya K.Nadarajah, Saralees2025-05-222025-05-222024-10-28Shabgard, S., Iranmanesh, A., Nakhaei Rad, N., Nagar, D.K., Nadarajah, S. (2024) Generalized bivariate Kummer-beta distribution with marginals defined on the unit interval. PLoS ONE 19(10): e0311888. https://doi.org/10.1371/journal. pone.0311888.1932-6203 (online)10.1371/journal. pone.0311888http://hdl.handle.net/2263/102462SUPPORTING INFORMATION : S1 APPENDIX. Special functions and figures. S2 APPENDIX. R codes.ACKNOWLEDGEMENTS : The authors would like to thank the editor and the two referees for careful reading and comments which greatly improved the paper.In this paper, a generalized bivariate Kummer-beta distribution is proposed. The name derives from the fact that its particular cases include univariate Kummer-beta distributions. This distribution generalizes a number of existing bivariate beta distributions, including Nadarajah’s bivariate distributions, Libby and Novick’s bivariate beta distribution and a central bivariate Kummer-beta distribution. Various properties associated with this newly introduced distribution are derived. The derived properties include product moments, marginal densities, marginal moments, conditional densities, conditional moments, Rényi entropy and Shannon entropy. Motivated by possible applications in economics, genetics, hydrology, meteorology, nuclear physics, and reliability, we also derive distributions of the product and the ratio of the components following the proposed distribution. Parameter estimation by maximum likelihood method is discussed by deriving expressions for score functions. Inference based on maximum likelihood estimation supposes that the maximum likelihood estimators have zero bias and zero mean squared errors. A simulation study is performed to check this for finite samples.en© 2024 Shabgard et al. This is an open access article distributed under the terms of the Creative Commons Attribution License.Finite samplesSquared errorsDistributionsParameter estimationArticle