OnF-Independence for Nonnegative, Bounded-Sum Variables When the Bound is Large
Ian James · Journal of the American Statistical Association · 1977
Consider r ≥ 2 random variables X 1 (t), …, Xτ(t), each taking values in [0, t], but subject to the constraint Ω r j=1 Xj (t) ≤ 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 1 (t), … Xr (t) ∈ {(X 1 (t'), …, X τ (t')); t' ∈ I} for some index set I [2, 3]. We consider F-independence properties as t → ∞. 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 are given.