Arithmetic on Random Variables: Squeezing the Envelopes with New Joint Distribution Constraints

Uncertainty is a key issue in decision analysis and other kinds of applications. Researchers have developed a number of approaches to address computations on uncertain quantities. When doing arithmetic operations on random variables, an important question has to be considered: the dependency relationships among the variables. In practice, we often have partial information about the dependency relationship between two random variables. This information may result from experience or system requirements. We can use this information to improve bounds on the cumulative distributions of random variables derived from the marginals whose dependency is partially known.