On minimum divergence adaptation of discrete bivariate distributions to given marginals

This correspondence considers the class P of discrete bivariate distributions p with marginals a(p), b(p) and the subclass Pa,b ⊂ P of distributions with given marginals a and b. For an arbitrary q ∈ P we study the distributions p˜ ∈ P_a,b minimizing on P_a,b various φ-divergences D_φ(p, q) for convex φ with finite φ(0).