# Estimating statistical moments of random systems based on appropriate reference variables

Wenliang Fan (School of Civil Engineering, Chongqing University, Chongqing, China and Key Laboratory of New Technology for Construction of Cities in Mountain Area, Chongqing University, Chongqing, China)
Pengchao Yang (School of Civil Engineering, Chongqing University, Chongqing, China)
Yule Wang (School of Civil Engineering, Chongqing University, Chongqing, China)
Alfredo H.-S. Ang (Department of Civil and Environmental Engineering, University of California-Irvine, Irvine, California, USA)
Zhengliang Li (School of Civil Engineering, Chongqing University, Chongqing, China and Key Laboratory of New Technology for Construction of Cities in Mountain Area, Chongqing University, Chongqing, China)

ISSN: 0264-4401

Article publication date: 7 August 2017

## Abstract

### Purpose

The purpose of this paper is to find an accurate, efficient and easy-to-implement point estimate method (PEM) for the statistical moments of random systems.

### Design/methodology/approach

First, by the theoretical and numerical analysis, the approximate reference variables for the frequently used nine types of random variables are obtained; then by combining with the dimension-reduction method (DRM), a new method which consists of four sub-methods is proposed; and finally, several examples are investigated to verify the characteristics of the proposed method.

### Findings

Two types of reference variables for the frequently used nine types of variables are proposed, and four sub-methods for estimating the moments of responses are presented by combining with the univariate and bivariate DRM.

### Research limitations/implications

In this paper, the number of nodes of one-dimensional integrals is determined subjectively and empirically; therefore, determining the number of nodes rationally is still a challenge.

### Originality/value

Through the linear transformation, the optimal reference variables of random variables are presented, and a PEM based on the linear transformation is proposed which is efficient and easy to implement. By the numerical method, the quasi-optimal reference variables are given, which is the basis of the proposed PEM based on the quasi-optimal reference variables, together with high efficiency and ease of implementation.

## Acknowledgements

The research reported in this paper was conducted with the support of the National Natural Science Foundation of China (Grant No. 51678092 and No. 51478064). This work was continued and prepared while Dr Wenliang Fan was at the University of California, Irvine in 2014-2015 as a Visiting Scholar supported by the China Scholarship Council.

## Citation

Fan, W., Yang, P., Wang, Y., H.-S. Ang, A. and Li, Z. (2017), "Estimating statistical moments of random systems based on appropriate reference variables", Engineering Computations, Vol. 34 No. 6, pp. 2001-2030. https://doi.org/10.1108/EC-08-2016-0288

## Publisher

:

Emerald Publishing Limited