An inequality unscented transformation for estimating the statistical moments

Point estimate method (PEM) is convenient for estimating statistical moments. This paper focuses on discussing the existing PEMs and presenting a new PEM for the efficient and accurate estimation of statistical moments. Firstly, a classification method of PEMs is proposed based on the strategy of choosing sigma points. Secondly, the minimum number of sigma points and the error of inverse Nataf transformation are derived corresponding to certain order and dimensionality of PEMs. Then the inequality unscented transformation (IUT) is presented to estimate the statistical moments. The proposed IUT permits the existing of limited errors in the matching of the first several order moments to decrease the number of sigma points, it opens new strategy of PEMs. The proposed method has two advantages. The first advantage is overcoming the growth of the number of sigma points with dimensionality since it parameterizes the number of sigma points and accuracy order. The second advantage is the wide applicability, for it has the ability to handle correlated and asymmetric random input variables and to match cross moments. Numerical and engineering results show the good accuracy and efficiency of the proposed IUT.