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A bivariate distribution with gamma and beta marginals with application to drought data

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  • Saralees Nadarajah

Abstract

The first known bivariate distribution with gamma and beta marginals is introduced. Various representations are derived for its joint probability density function (pdf), joint cumulative distribution function (cdf), product moments, conditional pdfs, conditional cdfs, conditional moments, joint moment generating function, joint characteristic function and entropies. The method of maximum likelihood and the method of moments are used to derive the associated estimation procedures as well as the Fisher information matrix, variance-covariance matrix and the profile likelihood confidence intervals. An application to drought data from Nebraska is provided. Some other applications are also discussed. Finally, an extension of the bivariate distribution to the multivariate case is proposed.

Suggested Citation

  • 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.
    • Handle: RePEc:taf:japsta:v:36:y:2009:i:3:p:277-301
    DOI: 10.1080/02664760802443996
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    References listed on IDEAS

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    1. J. Shiau, 2006. "Fitting Drought Duration and Severity with Two-Dimensional Copulas," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 20(5), pages 795-815, October.
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    Cited by:

    1. Arnold, Barry C. & Tony Ng, Hon Keung, 2011. "Flexible bivariate beta distributions," Journal of Multivariate Analysis, Elsevier, vol. 102(8), pages 1194-1202, September.
    2. Ana Silva & Jailson Rodrigues & Lucas Chaves & Devanil Souza, 2013. "Sums, Products and Ratios for Crovelli’s Bivariate Gamma Distribution," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 27(5), pages 1363-1376, March.
    3. Homa Razmkhah, 2017. "Comparing Threshold Level Methods in Development of Stream Flow Drought Severity-Duration-Frequency Curves," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 31(13), pages 4045-4061, October.
    4. Martel-Escobar, M. & Hernández-Bastida, A. & Vázquez-Polo, F.J., 2012. "On the independence between risk profiles in the compound collective risk actuarial model," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 82(8), pages 1419-1431.
    5. Milan Cisty & Anna Becova & Lubomir Celar, 2016. "Analysis of Irrigation Needs Using an Approach Based on a Bivariate Copula Methodology," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 30(1), pages 167-182, January.
    6. Jones, M.C., 2022. "Duals of multiplicative relationships involving beta and gamma random variables," Statistics & Probability Letters, Elsevier, vol. 191(C).
    7. 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.
    8. Ali Genç, 2014. "Distribution of product and quotient of bivariate generalized exponential distribution," Statistical Papers, Springer, vol. 55(3), pages 785-803, August.
    9. 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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