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Parameter estimation for a bivariate beta distribution with arbitrary beta marginals and positive correlation

Author

Listed:
  • Susanne Trick

    (Technical University of Darmstadt
    Technical University of Darmstadt)

  • Constantin A. Rothkopf

    (Technical University of Darmstadt
    Technical University of Darmstadt
    Goethe University)

  • Frank Jäkel

    (Technical University of Darmstadt
    Technical University of Darmstadt)

Abstract

We discuss a bivariate beta distribution that can model arbitrary beta-distributed marginals with a positive correlation. The distribution is constructed from six independent gamma-distributed random variates. While previous work used an approximate and sometimes inaccurate method to compute the distribution’s covariance and estimate its parameters, here, we derive all product moments and the exact covariance, which can be computed numerically. Based on this analysis we present an algorithm for estimating the parameters of the distribution using moment matching. We evaluate this inference method in a simulation study and demonstrate its practical use on a data set consisting of predictions from two correlated forecasters. Furthermore, we generalize the bivariate beta distribution to a correlated Dirichlet distribution, for which the proposed parameter estimation method can be used analogously.

Suggested Citation

  • Susanne Trick & Constantin A. Rothkopf & Frank Jäkel, 2023. "Parameter estimation for a bivariate beta distribution with arbitrary beta marginals and positive correlation," METRON, Springer;Sapienza Università di Roma, vol. 81(2), pages 163-180, August.
    • Handle: RePEc:spr:metron:v:81:y:2023:i:2:d:10.1007_s40300-023-00247-2
    DOI: 10.1007/s40300-023-00247-2
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    References listed on IDEAS

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