Efficient and Accurate Point Estimate Method for Moments and Probability Distribution Estimation

The point estimate method (PEM) is an alternative to Monte Carlo Simulation (MCS) and First Order Second Moments (FOSM) for evaluating the moments and probability distribution of the system or component performance. Although PEM is a powerful and simple method, it i s often limited by the need to make 2 n or even 3 n evaluations when there are n random variables, which is unaffordable for many engineering applications. In addition, robustly finding 4 -parameter of Beta or Lambda distribution is a difficult task and has n ot been well discussed in the past. This paper proposes two unique methods that enable faster and more accurate estimation for moments and probability distribution s. . These methods include, 1) affordable and more accura te moments estimation by applying different numbers of points for different variables, 2) robust procedure for finding the four parameters of Beta and Lambda distributions. The efficiency and accuracy of the proposed methods are validated with three ben chmark problems.