On F-Independence for Nonnegative, Bounded-Sum Variables When the Bound is Large.

Consider r is greater than or equal to 2 random variables X[sub 1, sup (t)], ..... X[sub r, sup(t)], each taking values in [0, t], but subject to the constraint SIGMA[sup r, sub j = 1] X[sub j, sup(t)] less than or equal to t. The concept of F-independence for such variables is a modification of the concept of independence, which takes the constraint into account, and is applicable when (X[sub 1, sup (t)],.... X[sub r, sup (t)]) is an element of {(X[sub 1, sup (t)],..... X[sub r, sup (t)]); t' is an element of l} for some index set l [2, 3]. We consider F-independence properties as t arrow right Infinity. We show that F independence properties become independence properties or neutrality properties [1, 5], respectively, when the variables converge properly, or are asymptotically proportional to the bound. Examples of important families of distributions which satisfy the convergence criteria a re given. [ABSTRACT FROM AUTHOR]