AsymIntervals: A Python library for uncertainty modeling with asymmetric interval numbers

Abstract

Moore interval arithmetic represents uncertainty using symmetric bounds, yet many real-world quantities and operations exhibit asymmetric behavior. Asymmetric Interval Numbers (AINs) generalize Moore intervals by introducing an expected value within the bounds and allowing the probability density to differ on either side of it. This concept is relatively new, and no widely available software has supported use of AINs. This paper addresses this gap by presenting an open-source Python library that provides complete arithmetic for AINs, functions for probability density and cumulative distribution, quantile evaluation, and straightforward tools for visualization and summary. Built on NumPy and Matplotlib, it allows engineers and researchers to incorporate asymmetric uncertainty into models and calculations with minimal effort.