Representation and problem solving with Distribution Envelope Determination (DEnv)

Distribution Envelope Determination (DEnv) is a method for computing the CDFs of random variables whose samples are a function of samples of other random variable(s), termed inputs. DEnv computes envelopes around these CDFs when there is uncertainty about the precise form of the probability distribution describing any input. 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 each input can be enclosed between left and right envelopes. Results will typically be in the form of envelopes when inputs are envelopes, when the dependency relationship of the inputs is unspecified, or both. 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 a way to obtain the bounding envelopes. DEnv is implemented in a tool which is used to solve problems from a benchmark set.