FARLIE-GUMBEL-MORGENSTERN BIVARIATE DENSITIES - ARE THEY APPLICABLE IN HYDROLOGY

Certain bivariate densities constructed from marginals have recently b een suggested as models of hydrologic variates such as rainfall intens ity and depth. It is pointed out that (i) these densities belong to th e families of the Farlie-Gumbel-Morgenstern densities and the Farlie p olynomial densities, which have been extensively studied in the statis tical literature, and that (ii) these densities have a limited potenti al applicability in hydrology since they can model only weakly associa ted variates, whose product-moment correlation R is within the range \ R\ less-than-or-equal-to 1/3, under the first family of densities, and \R\ less-than-or-equal-to 1/2 under the second family.