Numerical probabilistic arithmetic for generalized piecewise polynomial functions

This paper examines the important case of arithmetic operations on random variables defined by their probability density functions. The capabilities of existing approaches are analyzed and their limitations are highlighted. A new approach is proposed based on representing the distribution laws of arguments as generalized piecewise polynomial functions. For these purposes, probabilistic arithmetic is developed, based on models and methods of computational probabilistic analysis. It is noted that the proposed computational technique allows for the consideration of the properties of probability density functions and the analysis of distributions with "heavy tails." Contribution of the authors: the authors contributed equally to this article. The authors declare no conflicts of interests.

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