Abstract
In this work, approximations for the distribution of the product of independent Beta random variables, based on mixtures of generalized Gamma distributions, are proposed. These mixtures are finite, and the parameters involved are determined using a two-step moment matching technique. A numerical study is conducted in order to assess the precision of the approximation proposed when compared with other approximations based on mixtures of Gamma distributions or mixtures of Beta distributions. Some observations related with the computational implementation of each type of approximations are discussed, particularly that these approximations may be simple yet efficient alternatives to several other approaches which are more complex in nature.
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Acknowledgements
This work was partially supported by the Fundação para a Ciência e a Tecnologia (Portuguese Foundation for Science and Technology) through the project UIDB/00297/2020 (Centro de Matemática e Aplicações) and also based upon research supported by the National Research Foundation, South Africa (SRUG190308422768 nr. 120839) and the Research Development Programme at University of Pretoria 296/2019.
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Marques, F.J., Ghosh, I., Ferreira, J., Bekker, A. (2021). A Note on the Product of Independent Beta Random Variables. In: Ghosh, I., Balakrishnan, N., Ng, H.K.T. (eds) Advances in Statistics - Theory and Applications. Emerging Topics in Statistics and Biostatistics . Springer, Cham. https://doi.org/10.1007/978-3-030-62900-7_4
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