Abstract
J. N. Darroch and D. Ratcliff ( J. Amer. Statist. Assoc. 66 (1971) , 641–643) have given a characterization of the Dirichlet distributions based on the properties of independence of various functions of the random variables ( X 1, X 2, …, X k ) having a joint continuous distribution over the k-dimensional simplex: 0 ≤ x 1 ≤ Σ x i ≤ 1. In this paper we provide a further characterization of this family of distributions essentially based on the properties of linear regression. Some extra conditions have been imposed and these are indeed indispensable.
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