An Interval-Based Tool for Verified Arithmetic on Random Variables of Unknown Dependency

When random variables possessing arbitrary distribution functions must be added, subtracted, multiplied, etc., Monte Carlo simulation is commonly employed. However, Monte Carlo simulation typically assumes that the distribution functions to be combined are independent, and must assume either independence or some other specific dependency relationship. Discretization of the distribution function followed by a numerical method is another alternative approach. Numerical methods can relax the requirement of Monte Carlo that the distributions must have a known dependency relationship by producing boundary curves within which the cumulative distribution resulting from any dependency relationship must lie. Furthermore, numerical methods can account for discretization error by producing boundary curves that are more inclusive than they would be if the same problem was run with a finer discretization, thereby accounting for discretization error in the results. This paper describes Statool, a software tool available in source and binary, that runs an interval-based numerical method for performing arithmetic operations on distribution functions that are either independent or have an unknown dependency relationship, and provides inclusion guarantees deriving from its interval based calculations.