IDEAS home Printed from https://ideas.repec.org/a/taf/japsta/v36y2009i3p277-301.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.tandfonline.com/doi/abs/10.1080/02664760802443996
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1080/02664760802443996?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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.
    2. Yo Sheena & A. Gupta & Y. Fujikoshi, 2004. "Estimation of the eigenvalues of noncentrality parameter in matrix variate noncentral beta distribution," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 56(1), pages 101-125, March.
    3. 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.
    4. Arjun K. Gupta & Daya K. Nagar, 2000. "Matrix-variate beta distribution," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 24, pages 1-11, January.
    5. Biondi, Franco & Kozubowski, Tomasz J. & Panorska, Anna K. & Saito, Laurel, 2008. "A new stochastic model of episode peak and duration for eco-hydro-climatic applications," Ecological Modelling, Elsevier, vol. 211(3), pages 383-395.
    6. Jun, Chi-Hyuck & Y. Chang, Soo & Hong, Yushin & Yang, Heejoong, 1999. "A Bayesian approach to prediction of system failure rates by criticalities under event trees," International Journal of Production Economics, Elsevier, vol. 60(1), pages 623-628, April.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Ming Li & Guiwen Wang & Shengwei Zong & Xurong Chai, 2023. "Copula-Based Assessment and Regionalization of Drought Risk in China," IJERPH, MDPI, vol. 20(5), pages 1-16, February.
    2. Ziqiang Xing & Denghua Yan & Cheng Zhang & Gang Wang & Dongdong Zhang, 2015. "Spatial Characterization and Bivariate Frequency Analysis of Precipitation and Runoff in the Upper Huai River Basin, China," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 29(9), pages 3291-3304, July.
    3. Muhinyuza, Stanislas & Bodnar, Taras & Lindholm, Mathias, 2020. "A test on the location of the tangency portfolio on the set of feasible portfolios," Applied Mathematics and Computation, Elsevier, vol. 386(C).
    4. F. Todisco & F. Mannocchi & L. Vergni, 2013. "Severity–duration–frequency curves in the mitigation of drought impact: an agricultural case study," Natural Hazards: Journal of the International Society for the Prevention and Mitigation of Natural Hazards, Springer;International Society for the Prevention and Mitigation of Natural Hazards, vol. 65(3), pages 1863-1881, February.
    5. Hassairi, Abdelhamid & Roula, Amel, 2022. "Exponential and related probability distributions on symmetric matrices," Statistics & Probability Letters, Elsevier, vol. 187(C).
    6. Katarzyna Baran-Gurgul, 2022. "The Risk of Extreme Streamflow Drought in the Polish Carpathians—A Two-Dimensional Approach," IJERPH, MDPI, vol. 19(21), pages 1-27, October.
    7. Nardo, Elvira Di, 2020. "Polynomial traces and elementary symmetric functions in the latent roots of a non-central Wishart matrix," Journal of Multivariate Analysis, Elsevier, vol. 179(C).
    8. Joshua Chan & Arnaud Doucet & Roberto León-González & Rodney W. Strachan, 2018. "Multivariate Stochastic Volatility with Co-Heteroscedasticity," Working Paper series 18-38, Rimini Centre for Economic Analysis.
    9. Fatih Tosunoglu & Ibrahim Can, 2016. "Application of copulas for regional bivariate frequency analysis of meteorological droughts in Turkey," Natural Hazards: Journal of the International Society for the Prevention and Mitigation of Natural Hazards, Springer;International Society for the Prevention and Mitigation of Natural Hazards, vol. 82(3), pages 1457-1477, July.
    10. Zahra Sadat Hosseini & Mahnoosh Moghaddasi & Shahla Paimozd, 2023. "Simultaneous Monitoring of Different Drought Types Using Linear and Nonlinear Combination Approaches," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 37(3), pages 1125-1151, February.
    11. Jie Yang & Yimin Wang & Jun Yao & Jianxia Chang & Guoxin Xu & Xin Wang & Hui Hu, 2020. "Coincidence probability analysis of hydrologic low-flow under the changing environment in the Wei River Basin," Natural Hazards: Journal of the International Society for the Prevention and Mitigation of Natural Hazards, Springer;International Society for the Prevention and Mitigation of Natural Hazards, vol. 103(2), pages 1711-1726, September.
    12. T Matsuda & W E Strawderman, 2022. "Estimation under matrix quadratic loss and matrix superharmonicity [Shrinkage estimation with a matrix loss function]," Biometrika, Biometrika Trust, vol. 109(2), pages 503-519.
    13. Gary King & Ori Rosen & Martin A. Tanner, 1999. "Binomial-Beta Hierarchical Models for Ecological Inference," Sociological Methods & Research, , vol. 28(1), pages 61-90, August.
    14. Mark Bognanni, 2018. "A Class of Time-Varying Parameter Structural VARs for Inference under Exact or Set Identification," Working Papers (Old Series) 1811, Federal Reserve Bank of Cleveland.
    15. Lamneithem Hangshing & Parmendra P. Dabral, 2018. "Multivariate Frequency Analysis of Meteorological Drought Using Copula," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 32(5), pages 1741-1758, March.
    16. Rina Wu & Jiquan Zhang & Yuhai Bao & Enliang Guo, 2019. "Run Theory and Copula-Based Drought Risk Analysis for Songnen Grassland in Northeastern China," Sustainability, MDPI, vol. 11(21), pages 1-17, October.
    17. Xiong-Fei Liu & Shi-Xin Wang & Yi Zhou & Fu-Tao Wang & Guang Yang & Wen-Liang Liu, 2016. "Spatial analysis of meteorological drought return periods in China using Copulas," Natural Hazards: Journal of the International Society for the Prevention and Mitigation of Natural Hazards, Springer;International Society for the Prevention and Mitigation of Natural Hazards, vol. 80(1), pages 367-388, January.
    18. Zahra Fahimirad & Nazanin Shahkarami, 2021. "The Impact of Climate Change on Hydro-Meteorological Droughts Using Copula Functions," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 35(12), pages 3969-3993, September.
    19. Ying Li & Wei Gu & Weijia Cui & Zhiyun Chang & Yingjun Xu, 2015. "Exploration of copula function use in crop meteorological drought risk analysis: a case study of winter wheat in Beijing, China," Natural Hazards: Journal of the International Society for the Prevention and Mitigation of Natural Hazards, Springer;International Society for the Prevention and Mitigation of Natural Hazards, vol. 77(2), pages 1289-1303, June.
    20. Arjun Gupta & Johanna Orozco-Castañeda & Daya Nagar, 2011. "Non-central bivariate beta distribution," Statistical Papers, Springer, vol. 52(1), pages 139-152, February.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:taf:japsta:v:36:y:2009:i:3:p:277-301. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Chris Longhurst (email available below). General contact details of provider: http://www.tandfonline.com/CJAS20 .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.