Concepts of independence for nonnegative continuous random variables,X1, …,Xk, subject to the constraint ΣXi= 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.