Abstract
We present Statool, a software tool for obtaining bounds on the distributions of sums, products, and various other functions of random variables where the dependency relationship of the random variables need not be specified. Statool implements the DEnv algorithm, which we have described previously [4] but not implemented. Our earlier tool addressed only the much more elementary case of independent random variables [3]. An existing tool, RiskCalc [13], also addresses the case of unknown dependency using a different algorithm [33] based on copulas [23], while descriptions and implementations of still other algorithms for similar problems will be reported soon [17] as the area proceeds through a phase of rapid development.
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Berleant, D., Xie, L. & Zhang, J. Statool: A Tool for Distribution Envelope Determination (DEnv), an Interval-Based Algorithm for Arithmetic on Random Variables. Reliable Computing 9, 91–108 (2003). https://doi.org/10.1023/A:1023082100128
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DOI: https://doi.org/10.1023/A:1023082100128