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A bivariate beta distribution

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  • Olkin, Ingram
  • Liu, Ruixue
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    Abstract

    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.

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    Bibliographic Info

    Article provided by Elsevier in its journal Statistics & Probability Letters.

    Volume (Year): 62 (2003)
    Issue (Month): 4 (May)
    Pages: 407-412

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    Handle: RePEc:eee:stapro:v:62:y:2003:i:4:p:407-412

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    Related research

    Keywords: Bayesian analysis Dirichlet distribution Multinomial distribution Hypergeometric function;

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    Cited by:
    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. 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.
    3. 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, vol. 13(1), pages 1-43, June.
    4. Saraless Nadarajah, 2006. "Exact and approximate distributions for the product of inverted Dirichlet components," Statistical Papers, Springer, vol. 47(4), pages 551-568, October.
    5. 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 and Applications, Springer, vol. 18(4), pages 465-481, November.
    6. Arnold, Barry C. & Tony Ng, Hon Keung, 2011. "Flexible bivariate beta distributions," Journal of Multivariate Analysis, Elsevier, vol. 102(8), pages 1194-1202, September.
    7. Bibby, Bo Martin & Væth, Michael, 2011. "The two-dimensional beta binomial distribution," Statistics & Probability Letters, Elsevier, vol. 81(7), pages 884-891, July.
    8. José Díaz-García & Ramón Gutiérrez-Jáimez, 2011. "Noncentral bimatrix variate generalised beta distributions," Metrika, Springer, vol. 73(3), pages 317-333, May.
    9. Federico Bassetti & Roberto Casarin & Fabrizio Leisen, 2013. "Beta-Product Dependent Pitman-Yor Processes for Bayesian Inference," Working Papers 2013:13, Department of Economics, University of Venice "Ca' Foscari".
    10. Yanyun Zhao & Concepción Ausín & Michael P. Wiper, 2013. "Bayesian multivariate Bernstein polynomial density estimation," Statistics and Econometrics Working Papers ws131211, Universidad Carlos III, Departamento de Estadística y Econometría.

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