Distribution arithmetic for stochastical analysis

Abstract

This paper presents a novel arithmetic which allows calculations with fluctuating values. The arithmetic consists of a special representation of random variables and procedures for performing numerical operations between them. Given the distributions of initial random variables, the moments (such as expected value, variance and higher moments) of any calculated variable can be determined. Our approach is not limited to normal distributions and works with linear and nonlinear functions. Correlations between variables are taken into account automatically by the arithmetic. Examples show the accuracy and runtimes compared to Monte Carlo simulation.