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

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  • Daya K. Nagar

    (Universidad de Antioquia)

  • Saralees Nadarajah

    (University of Manchester)

  • Idika E. Okorie

    (University of Manchester)

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.

Suggested Citation

  • Daya K. Nagar & Saralees Nadarajah & Idika E. Okorie, 2017. "A New Bivariate Distribution with One Marginal Defined on the Unit Interval," Annals of Data Science, Springer, vol. 4(3), pages 405-420, September.
    • Handle: RePEc:spr:aodasc:v:4:y:2017:i:3:d:10.1007_s40745-017-0111-6
    DOI: 10.1007/s40745-017-0111-6
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    References listed on IDEAS

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    1. Nagar, Daya K. & Roldán-Correa, Alejandro & Gupta, Arjun K., 2013. "Extended matrix variate gamma and beta functions," Journal of Multivariate Analysis, Elsevier, vol. 122(C), pages 53-69.
    2. Saralees Nadarajah, 2009. "A bivariate distribution with gamma and beta marginals with application to drought data," Journal of Applied Statistics, Taylor & Francis Journals, vol. 36(3), pages 277-301.
    3. Zografos, K. & Nadarajah, S., 2005. "Expressions for Rényi and Shannon entropies for multivariate distributions," Statistics & Probability Letters, Elsevier, vol. 71(1), pages 71-84, January.
    4. Zografos, K., 1999. "On Maximum Entropy Characterization of Pearson's Type II and VII Multivariate Distributions," Journal of Multivariate Analysis, Elsevier, vol. 71(1), pages 67-75, October.
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