Earlier risk analysis studies emphasized the correct description of the univariate characteristics of the random variables in risk models, but more recently it is recognized that realistic risk models should also correctly describe the dependence among the variables. By reviewing some important but often overlooked statistical concepts, this paper points out some serious short-comings of the "conventional" approach of describing two dependent variables by their marginal distributions and their correlation coefficient. A "functional approach" for describing dependent variables is then presented, followed by discussions of its practicality and theoretical robustness. In short, the paper points out the necessary and desirability of the alternative approach in modelling dependent random variables.
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