Please use this identifier to cite or link to this item: https://hdl.handle.net/10419/309571 
Year of Publication: 
2023
Citation: 
[Journal:] METRON [ISSN:] 2281-695X [Volume:] 81 [Issue:] 2 [Publisher:] Springer Milan [Place:] Milano [Year:] 2023 [Pages:] 163-180
Publisher: 
Springer Milan, Milano
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.
Subjects: 
Bivariate beta distribution
Correlated beta distribution
Covariance
Moment matching
Persistent Identifier of the first edition: 
Creative Commons License: 
cc-by Logo
Document Type: 
Article
Document Version: 
Published Version

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