POINT ESIMATE FOR STATISTICAL MOMENTS OF SYSTEMS WITH INCOMPLETE PROBABILITY INFORMATION

According to the known probability information, random system with incomplete probability information can be classified into three classes, namely sub-class I, sub-class II and sub-class III. The existing point estimate methods (PEM) for statistical moments are only suitable for systems with complete information and sub-class I, but not for sub-class II and sub-class III. In this paper, equivalent correlation coefficients (ECC) of variables in the sub-class III are studied, together with the simplified approach for the ECCs of variables in sub-class II. By combining with the univariate dimension reduction model of a multivariable function, the point estimate for moments of system with incomplete information is proposed. The influence of both the reference point and the order of variables on the efficiency of this PEM are discussed in details. Finally, several examples are illustrated to verify the proposed PEM. The results show that 1) the approaches for the ECCs are of high precision, 2) the technology for reordering the variables is effective for improving the efficiency of the PEM, and 3) the proposed PEM are suitable for all systems with incomplete information and accurate for the first lower moments of system.