In this paper, we study the effect of dependence on the distributional properties of functions
of two random variables. Expressions for the cumulative distribution functions of the
linear combinations, products and ratios of two dependent random variables in terms of their
associated copula are derived. We discuss the effect of dependence on quantities such as the
variances of linear combinations of functions, the value-at-risk measure and the stress-strength
parameter. Several examples, a simulation study and a real data analysis are provided to illustrate
the result.
کلید واژگان :
Copula; Dependent random variables; Distribution of sums; Stress-Strength measure
