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 [cf. {\itD. Berleant} and {\itC. Goodman-Strauss}, ibid. 4, 147--165 (1998; Zbl 0908.65139)] but not implemented. Our earlier tool addressed only the much more elementary case of independent random variables [cf. {\itD. Berleant} and {\itH. Cheng}, ibid. 4, 71--82 (1998; Zbl 0895.65018)]. An existing tool, RiskCalc [cf. {\itS. Ferson}, RAMAS Risk Calc 4.0: Risk Assessment with Uncertain Numbers, Lewis Press, boca Raton, Florida (2002)], also addresses the case of unknown dependency using a different algorithm [cf. {\itR. C. Williamson} and {\itT. Downs}, Int. J. Approx. Reasoning 4, 89--158 (1990; Zbl 0703.65100)] based on copulas [cf. {\itR. B. Nelsen}, An introduction to copulas. Properties and applications. Lecture Notes in Statistics (Springer). 139 (1999; Zbl 0909.62052)], while descriptions and implementations of still other algorithms for similar problems will be reported soon [cf. {\itJ. Helton} (ed.): Reliability Engineering and System Safety, Synopsis, Special Issue, forthcoming, {\tt}] as the area proceeds through a phase of rapid development.

References in zbMATH (referenced in 9 articles , 1 standard article )

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  1. Xiao, Z.; Han, X.; Jiang, C.; Yang, G.: An efficient uncertainty propagation method for parameterized probability boxes (2016)
  2. Enszer, Joshua A.; Andrei Măceş, D.; Stadtherr, Mark A.: Probability bounds analysis for nonlinear population ecology models (2015)
  3. Han, Ai; Hong, Yongmiao; Lai, K.K.; Wang, Shouyang: Interval time series analysis with an application to the sterling-dollar exchange rate (2008)
  4. Berleant, Daniel J.; Kosheleva, Olga; Kreinovich, Vladik; Nguyen, Hung T.: Unimodality, independence lead to NP-hardness of interval probability problems (2007)
  5. Kreinovich, Vladik; Nguyen, Hung T.; Wu, Berlin: On-line algorithms for computing mean and variance of interval data, and their use in intelligent systems (2007)
  6. Tonon, Fulvio: A search algorithm for calculating validated reliability bounds (2007)
  7. Kreinovich, Vladik; Xiang, Gang; Starks, Scott A.; Longpré, Luc; Ceberio, Martine; Araiza, Roberto; Beck, Jan; Kandathi, Raj; Nayak, Asis; Torres, Roberto; Hajagos, Janos G.: Towards combining probabilistic and interval uncertainty in engineering calculations: algorithms for computing statistics under interval uncertainty, and their computational complexity (2006)
  8. Regan, Helen M.; Ferson, Scott; Berleant, Daniel: Equivalence of methods for uncertainty propagation of real-valued random variables (2004)
  9. Berleant, Daniel; Xie, Lizhi; Zhang, Jianzhong: Statool: A tool for distribution envelope determination (DEnv), an interval-based algorithm for arithmetic on random variables (2003)