A characterization of Dirichlet distributions

[1], 641-643) have given a characterization of the Dirichlet distributions based on the properties of independence of various functions of the random variables (X1, X2, ..., Xk) having a joint continuous distribution over the k-dimensional simplex: 0 <= x1 <= [Sigma] xi <= 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.