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Generalized bivariate Kummer-beta distribution with marginals defined on the unit interval

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  • Sina Shabgard
  • Anis Iranmanesh
  • Najmeh Nakhaei Rad
  • Daya K Nagar
  • Saralees Nadarajah

Abstract

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.

Suggested Citation

  • Sina Shabgard & Anis Iranmanesh & Najmeh Nakhaei Rad & Daya K Nagar & Saralees Nadarajah, 2024. "Generalized bivariate Kummer-beta distribution with marginals defined on the unit interval," PLOS ONE, Public Library of Science, vol. 19(10), pages 1-16, October.
    • Handle: RePEc:plo:pone00:0311888
    DOI: 10.1371/journal.pone.0311888
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    References listed on IDEAS

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    1. Arjun Gupta & Johanna Orozco-Castañeda & Daya Nagar, 2011. "Non-central bivariate beta distribution," Statistical Papers, Springer, vol. 52(1), pages 139-152, February.
    2. Arnold, Barry C. & Tony Ng, Hon Keung, 2011. "Flexible bivariate beta distributions," Journal of Multivariate Analysis, Elsevier, vol. 102(8), pages 1194-1202, September.
    3. Olkin, Ingram & Liu, Ruixue, 2003. "A bivariate beta distribution," Statistics & Probability Letters, Elsevier, vol. 62(4), pages 407-412, May.
    4. Saralees Nadarajah, 2007. "A new bivariate beta distribution with application to drought data," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(2), pages 153-174.
    5. Olkin, Ingram & Trikalinos, Thomas A., 2015. "Constructions for a bivariate beta distribution," Statistics & Probability Letters, Elsevier, vol. 96(C), pages 54-60.
    6. Saralees Nadarajah, 2005. "Reliability for some bivariate beta distributions," Mathematical Problems in Engineering, Hindawi, vol. 2005, pages 1-11, January.
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