Estimating statistical moments of random systems based on appropriate reference variables

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.