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Products of Independent Beta Variables with Application to Connor and Mosimann's Generalized Dirichlet Distribution

1972; Volume: 67; Issue: 340 Linguagem: Inglês

10.1080/01621459.1972.10481316

1537-274X

Ian James,

Statistical Distribution Estimation and Applications

Abstract Necessary and sufficient conditions are found for the product of independent beta variables to be a beta variable, and it is shown that if Z is a beta variable of the second kind and X an independent, non-degenerate random variable taking values in (0, 1), then the product XZ is a beta variable of the second kind if and only if X is beta with appropriate parameters. These results are then applied to show that if certain ratios of proportions are assumed to have marginal beta distributions, the generality of Connor and Mosimann's generalized Dirichlet distribution is severely restricted.