  Following our previous work on copula-based nonsymmetric dependence measures,
we introduce similar measures for discrete random variables. The measures cover
the range between two extremes: independence and complete dependence, which
take minimum value exactly on independence and take maximum value exactly on
complete dependence. We find that the * product on copulas in the continuous
case reduces to matrix product of transition matrices in the discrete case and
we use it to prove the DPI condition. The measures can also be extended to
detect dependence between groups of discrete random variables or conditional
dependence. Unlike the continuous case, one drawback is that the value of the
measures depends on marginal distributions.
