A New Bivariate Distribution with One Marginal Defined on the Unit Interval

Daya K. Nagar, Saralees Nadarajah () and Idika E. Okorie
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Daya K. Nagar: Universidad de Antioquia
Saralees Nadarajah: University of Manchester
Idika E. Okorie: University of Manchester

Annals of Data Science, 2017, vol. 4, issue 3, No 6, 405-420

Abstract: 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.

Keywords: Beta distribution; Extended beta function; Gamma distribution (search for similar items in EconPapers)
Date: 2017
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DOI: 10.1007/s40745-017-0111-6

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