New Point Estimates for Probability Moments

Abstract

There are many areas of structural safety and structural dynamics in which it is often desirable to compute the first few statistical moments of a function of random variables. The usual approximation is by the Taylor expansion method. This approach requires the computation of derivatives. In order to avoid the computation of derivatives, point estimates for probability moments have been proposed. However, the accuracy is quite low, and sometimes, the estimating points may be outside the region in which the random variable is defined. In the present paper, new point estimates for probability moments are proposed, in which increasing the number of estimating points is easier because the estimating points are independent of the random variable in its original space and the use of high-order moments of the random variables is not required. By using this approximation, the practicability and accuracy of point estimates can be much improved.