Equivalence of methods for uncertainty propagation of real-valued random variables

In this paper we compare four methods for the reliable propagation of uncertainty through calculations involving the binary operations of addition, multiplication, subtraction and division. The methods we investigate are: (i) dependency bounds convolution; (ii) Distribution Envelope Determination; (iii) interval probabilities; and (iv) Dempster–Shafer belief functions. We show that although each of these methods were constructed for different types of applications, they converge to equivalent methods when they are restricted to cumulative distribution functions on the positive reals. We also show that while some of the methods have been formally constructed to deal only with operations on random variables under an assumption of independence, all of the methods can be extended to deal with unknown dependencies and perfect positive and negative dependence among variables. 2003 Elsevier Inc. All rights reserved.