Histogram Arithmetic under Uncertainty of Probability Density Function

TL;DR

This paper introduces a method for performing arithmetic operations on variables with unknown distributions by using histogram-based evaluations of empirical density functions, enabling probabilistic interval analysis.

Contribution

It presents a novel approach to arithmetic with uncertain variables using histogram evaluations of empirical density functions, applicable to algebraic and differential equations.

Findings

Enables arithmetic operations on uncertain variables using histograms.

Provides probabilistic intervals for solutions of equations with unknown distributions.

Applicable to systems of algebraic and differential equations.

Abstract

In this article we propose a method of performing arithmetic operations on varia-bles with unknown distribution. The approach to the evaluation results of arithme-tic operations can select probability intervals of the algebraic equations and their systems solutions, of differential equations and their systems in case of histogram evaluation of the empirical density distributions of random parameters.