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Flexible bivariate beta distributions

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  • Arnold, Barry C.
  • Tony Ng, Hon Keung

Abstract

Bivariate beta distributions which can be used to model data sets exhibiting positive or negative correlation are introduced. Properties of these bivariate beta distributions and their applications in Bayesian analysis are discussed. Three methods for parameter estimation are presented. The performance of these estimators is evaluated based on Monte Carlo simulations. Examples are provided to illustrate how additional parameters can be introduced to gain even more modeling flexibility. A possible extension of the proposed bivariate beta model and a multivariate generalization are also discussed.

Suggested Citation

  • Arnold, Barry C. & Tony Ng, Hon Keung, 2011. "Flexible bivariate beta distributions," Journal of Multivariate Analysis, Elsevier, vol. 102(8), pages 1194-1202, September.
    • Handle: RePEc:eee:jmvana:v:102:y:2011:i:8:p:1194-1202
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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. Olkin, Ingram & Liu, Ruixue, 2003. "A bivariate beta distribution," Statistics & Probability Letters, Elsevier, vol. 62(4), pages 407-412, May.
    3. 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.
    4. A. Gupta & C. Wong, 1985. "On three and five parameter bivariate beta distributions," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 32(1), pages 85-91, December.
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    Cited by:

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    2. Olkin, Ingram & Trikalinos, Thomas A., 2015. "Constructions for a bivariate beta distribution," Statistics & Probability Letters, Elsevier, vol. 96(C), pages 54-60.
    3. Catalina Bolancé & Montserrat Guillen & Albert Pitarque, 2020. "A Sarmanov Distribution with Beta Marginals: An Application to Motor Insurance Pricing," Mathematics, MDPI, vol. 8(11), pages 1-11, November.
    4. Indranil Ghosh, 2023. "A New Class of Alternative Bivariate Kumaraswamy-Type Models: Properties and Applications," Stats, MDPI, vol. 6(1), pages 1-21, January.
    5. Célestin C. Kokonendji & Aboubacar Y. Touré & Amadou Sawadogo, 2020. "Relative variation indexes for multivariate continuous distributions on $$[0,\infty )^k$$[0,∞)k and extensions," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 104(2), pages 285-307, June.
    6. Arnold Barry C. & Arvanitis Matthew, 2021. "On a general class of gamma based copulas," Dependence Modeling, De Gruyter, vol. 9(1), pages 374-384, January.
    7. Nozer D. Singpurwalla & Barry C. Arnold & Joseph L. Gastwirth & Anna S. Gordon & Hon Keung Tony Ng, 2016. "Adversarial and Amiable Inference in Medical Diagnosis, Reliability and Survival Analysis," International Statistical Review, International Statistical Institute, vol. 84(3), pages 390-412, December.

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