Representation and Problem Solving with the Distribution Envelope Determination (DEnv) Method

Daniel Berleant and Jianzhong Zhang Department of Electrical and Computer Engineering 2215 Coover Hall Iowa State University Ames, Iowa 50011 [email protected] Abstract Distribution Envelope Determination (DEnv) is a technique for computing descriptions of derived random variables. Derived random variables have samples that are a function of samples of other random variable(s), which are termed inputs. DEnv can compute these descriptions despite uncertainty about the precise forms of probability distributions describing the inputs. For example, inputs whose distribution functions have means and variances known only to within intervals can be handled. More generally, inputs can be handled if the set of all plausible cumulative distributions describing them can be enclosed between left and right envelopes. When inputs are these envelopes rather than specific distribution functions, or when inputs are specific distribution functions but their dependency relationship is unspecified, or both, derived distributions will typically be envelopes. For example in the case of specific input distribution functions with unspecified dependency relationships, each of the infinite number of possible dependency relationships would imply some specific output distribution, and the set of all such output distributions can be bounded with envelopes. The DEnv algorithm is one way to obtain the bounding envelopes, and is implemented in a tool used to solve problems from a benchmark set.