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Concepts of Independence for Proportions with a Generalization of the Dirichlet Distribution

Robert J. Connor and James E. Mosimann
Journal of the American Statistical Association
Vol. 64, No. 325 (Mar., 1969), pp. 194-206
DOI: 10.2307/2283728
Stable URL: http://www.jstor.org/stable/2283728
Page Count: 13
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Concepts of Independence for Proportions with a Generalization of the Dirichlet Distribution
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Abstract

Concepts of independence for nonnegative continuous random variables, X1,⋯, Xk, subject to the constraint Σ Xi = 1 are developed. These concepts provide a means of modeling random vectors of proportions which is useful in analyzing certain kinds of data; and which may be of interest in quantifying prior opinions about multinomial parameters. A generalization of the Dirichlet distribution is given, and its relation to the Dirichlet is simply indicated by means of the concepts. The concepts are used to obtain conclusions of biological interest for data on bone composition in rats and scute growth in turtles.

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