Histogram Arithmetic under Uncertainty of Probability Density Function
It addresses the problem of uncertainty quantification in systems with unknown probability density functions, offering a practical approach for engineering and scientific applications.
The paper proposes a method for performing arithmetic operations on variables with unknown distributions using histogram representations, enabling evaluation of probability intervals for solutions of algebraic and differential equations under uncertainty.
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.