Asymmetric uncertainties in measurements: SOAD a Python package based on Monte Carlo Simulations

Abstract

Handling uncertainties has a great importance in order to avoid biased results. The nature of these uncertainties is mostly convenient for specific assumptions, making calculations easier. However, when the uncertainties are not small, symmetric and Normally distributed, one needs more sophisticated methods. In this case, using Monte Carlo Simulations is one of the most reliable options among others, with least assumptions. In this work, we present our newly developed Python package, SOAD (Statistics Of Asymmetric Distributions) that handles calculations using measurements with asymmetric uncertainties by Monte Carlo Simulations, which is easy to use and capable of performing multiple mathematical operations consecutively. The theoretical background of the algorithm and the selected Probability Distribution Function for representing the asymmetric uncertainties are obtained from the literature. The codes were successfully applied to High Energy Astrophysics data and compared with some other methods to see in which circumstances they differ from each other.