IDEAS home Printed from
   My bibliography  Save this article

A bivariate beta distribution


  • Olkin, Ingram
  • Liu, Ruixue


The Dirichlet distribution is often used as a prior distribution for the parameters of a multinomial distribution. Because this distribution has support on the simplex 0[less-than-or-equals, slant]xi[less-than-or-equals, slant]1, [summation operator]xi=1, it does not serve as the prior for a correlated binomial distribution. We here present a bivariate beta distribution that has support on 0[less-than-or-equals, slant]xi[less-than-or-equals, slant]1, i=1,2. When expanded in a power series it is related to the hypergeometric function. This bivariate density is positively likelihood ratio dependent and hence is positive quadrant dependent.

Suggested Citation

  • Olkin, Ingram & Liu, Ruixue, 2003. "A bivariate beta distribution," Statistics & Probability Letters, Elsevier, vol. 62(4), pages 407-412, May.
  • Handle: RePEc:eee:stapro:v:62:y:2003:i:4:p:407-412

    Download full text from publisher

    File URL:
    Download Restriction: Full text for ScienceDirect subscribers only

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

    References listed on IDEAS

    1. Saw, John G., 1984. "Ultraspherical polynomials and statistics on the m-sphere," Journal of Multivariate Analysis, Elsevier, vol. 14(1), pages 105-113, February.
    Full references (including those not matched with items on IDEAS)


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

    Cited by:

    1. Bibby, Bo Martin & Væth, Michael, 2011. "The two-dimensional beta binomial distribution," Statistics & Probability Letters, Elsevier, vol. 81(7), pages 884-891, July.
    2. Laradji, A., 2015. "Sums of totally positive functions of order 2 and applications," Statistics & Probability Letters, Elsevier, vol. 105(C), pages 176-180.
    3. Arjun Gupta & Johanna Orozco-Castañeda & Daya Nagar, 2011. "Non-central bivariate beta distribution," Statistical Papers, Springer, vol. 52(1), pages 139-152, February.
    4. M. Jones, 2004. "Families of distributions arising from distributions of order statistics," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 13(1), pages 1-43, June.
    5. Bassetti, Federico & Casarin, Roberto & Leisen, Fabrizio, 2014. "Beta-product dependent Pitman–Yor processes for Bayesian inference," Journal of Econometrics, Elsevier, vol. 180(1), pages 49-72.
    6. A. El-Bassiouny & M. Jones, 2009. "A bivariate F distribution with marginals on arbitrary numerator and denominator degrees of freedom, and related bivariate beta and t distributions," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 18(4), pages 465-481, November.
    7. Arnold, Barry C. & Tony Ng, Hon Keung, 2011. "Flexible bivariate beta distributions," Journal of Multivariate Analysis, Elsevier, vol. 102(8), pages 1194-1202, September.
    8. 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.
    9. Olkin, Ingram & Trikalinos, Thomas A., 2015. "Constructions for a bivariate beta distribution," Statistics & Probability Letters, Elsevier, vol. 96(C), pages 54-60.
    10. Bassetti, Federico & Casarin, Roberto & Leisen, Fabrizio, 2011. "Beta-product Poisson-Dirichlet Processes," DES - Working Papers. Statistics and Econometrics. WS 12160, Universidad Carlos III de Madrid. Departamento de Estadística.
    11. Wiper, Michael Peter & Ausín Olivera, María Concepción & Zhao, Yanyun, 2013. "Bayesian multivariate Bernstein polynomial density estimation," DES - Working Papers. Statistics and Econometrics. WS ws131211, Universidad Carlos III de Madrid. Departamento de Estadística.
    12. Zikopoulos, Christos & Tagaras, George, 2007. "Impact of uncertainty in the quality of returns on the profitability of a single-period refurbishing operation," European Journal of Operational Research, Elsevier, vol. 182(1), pages 205-225, October.
    13. José Díaz-García & Ramón Gutiérrez-Jáimez, 2011. "Noncentral bimatrix variate generalised beta distributions," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 73(3), pages 317-333, May.
    14. repec:eee:reensy:v:126:y:2014:i:c:p:116-125 is not listed on IDEAS
    15. Saraless Nadarajah, 2006. "Exact and approximate distributions for the product of inverted Dirichlet components," Statistical Papers, Springer, vol. 47(4), pages 551-568, October.
    16. repec:bla:istatr:v:84:y:2016:i:3:p:390-412 is not listed on IDEAS
    17. Peluso, Stefano & Mira, Antonietta & Muliere, Pietro, 2015. "Reinforced urn processes for credit risk models," Journal of Econometrics, Elsevier, vol. 184(1), pages 1-12.


    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:eee:stapro:v:62:y:2003:i:4:p:407-412. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Dana Niculescu). General contact details of provider: .

    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.

    We have no references for this item. You can help adding them by using 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.

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

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.