In this paper, the problem of loss of information due to the discretiz
ation of continuous data and its estimate is studied. It is shown that
the rate of convergence of the discretized versions of (h, phi)-diver
gences to their continuous expressions is quadratic. The results of Gh
urye and Johnson (1981) and Zografos, Ferentinos, and Papaioannou (198
6) are generalized and supplemented for the (h, phi)-divergence measur
es.