Abstract
The most flexible bivariate distribution to date is proposed with one variable restricted to [0, 1] and the other taking any non-negative value. Various mathematical properties and maximum likelihood estimation are addressed. The mathematical properties derived include shape of the distribution, covariance, correlation coefficient, joint moment generating function, Rényi entropy and Shannon entropy. For interval estimation, explicit expressions are derived for the information matrix. Illustrations using two real data sets show that the proposed distribution performs better than all other known distributions of its kind.
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Acknowledgements
The research work of DKN was supported by the Sistema Universitario de Investigación, Universidad de Antioquia under the project no. IN10231CE. The authors would like to thank the Editor and the three referees for careful reading and comments which greatly improved the paper.
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Nagar, D.K., Nadarajah, S. & Okorie, I.E. A New Bivariate Distribution with One Marginal Defined on the Unit Interval. Ann. Data. Sci. 4, 405–420 (2017). https://doi.org/10.1007/s40745-017-0111-6
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DOI: https://doi.org/10.1007/s40745-017-0111-6