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Fisher's method of combining dependent statistics using generalizations of the gamma distribution with applications to genetic pleiotropic associations A class of distributions is defined and studied which includes as particular cases (cf. Section 13) the ordinary $\beta$-distribution, the (univariate) triangular distribution, the uniform distribution over any nondegenerate simplex, and a continuous range of other distributions over such a simplex, called basic $\beta$-distributions (Section 6) and immediately analogous to the ordinary $\beta$-distribution.

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