On Taylor Series Expansion for Statistical Moments of Functions of Correlated Random Variables dagger
Loading...
Date
2020-08-31
Authors
ORCID
Advisor
Referee
Mark
Journal Title
Journal ISSN
Volume Title
Publisher
MDPI
Altmetrics
Abstract
The paper is focused on Taylor series expansion for statistical analysis of functions of random variables with special attention to correlated input random variables. It is shown that the standard approach leads to significant deviations in estimated variance of non-linear functions. Moreover, input random variables are often correlated in industrial applications; thus, it is crucial to obtain accurate estimations of partial derivatives by a numerical differencing scheme. Therefore, a novel methodology for construction of Taylor series expansion of increasing complexity of differencing schemes is proposed and applied on several analytical examples. The methodology is adapted for engineering applications by proposed asymmetric difference quotients in combination with a specific step-size parameter. It is shown that proposed differencing schemes are suitable for functions of correlated random variables. Finally, the accuracy, efficiency, and limitations of the proposed methodology are discussed.
Description
Citation
Document type
Peer-reviewed
Document version
Published version
Date of access to the full text
Language of document
en