Investigation of equivalent correlation coefficient based on the Mehler’s formula

Abstract

Purpose

Conversion of the correlated random variables into independent variables, especially into independent standard normal variables, is the common technology for estimating the statistical moments of response and evaluating reliability of random system, in which calculating the equivalent correlation coefficient is an important component. The purpose of this paper is to investigate an accurate, efficient and easy to implement estimation method for the equivalent correlation coefficient of various incomplete probability systems.

Design/methodology/approach

First, an approach based on the Mehler’s formula for evaluating the equivalent correlation coefficient is introduced, then, by combining with polynomial normal transformations, this approach is improved to be valid for various incomplete probability systems, which is named as the direct method. Next, with the convenient linear reference variables for eight frequently used random variables and the approximation of the Rosenblatt transformation introduced, a further improved implementation without iteration process is developed, which is named as the simplified method. Finally, several examples are investigated to verify the characteristics of the proposed methods.

Findings

The results of the examples in this paper show that both the proposed two methods are of high accuracy, by comparison, the proposed simplified method is more effective and convenient.

Originality/value

Based on the Mehler’s formula, two practical implementations for evaluating the equivalent correlation coefficient are proposed, which are accurate, efficient, easy to implement and valid for various incomplete probability systems.

Citation

Zu, Y., Fan, W., Zhang, J., Li, Z. and Ohsaki, M. (2019), "Investigation of equivalent correlation coefficient based on the Mehler’s formula", Engineering Computations, Vol. 36 No. 4, pp. 1169-1200. https://doi.org/10.1108/EC-07-2018-0316