Abstract
Certain bivariate densities constructed from marginals have recently been suggested as models of hydrologic variates such as rainfall intensity and depth. It is pointed out that (i) these densities belong to the families of the Farlie-Gumbel-Morgenstern densities and the Farlie polynomial densities, which have been extensively studied in the statistical literature, and that (ii) these densities have a limited potential applicability in hydrology since they can model only weakly associated variates, whose product-moment correlationR is within the range |R|≤1/3, under the first family of densities, and |R|≤1/2 under the second family.
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Long, D., Krzysztofowicz, R. Farlie-Gumbel-Morgenstern bivariate densities: Are they applicable in hydrology?. Stochastic Hydrol Hydraul 6, 47–54 (1992). https://doi.org/10.1007/BF01581674
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DOI: https://doi.org/10.1007/BF01581674