Point‐Estimate Method for Calculating Statistical Moments

Abstract

A number of approximate methods exist in the literature for estimating the statistical moments of a random function. The usual approach is based on Taylor series expansion about the mean values of the random variables. This approach requires the calculation of the derivatives of the random function. For complex functions or functions that cannot be expressed in an explicit form, it is desirable to use the so-called point-estimate methods, which do not require the calculation of the derivatives. Point-estimate methods enable the calculation of the expectation of a random function to be calculated based on the values of the function at a specific set of input parameters. In this paper, an efficient point-estimate method is developed, which requires only (\In\N²+3\In\N+2)/2 evaluations of a random function with \In\N random variables. The method is applicable to correlated random variables, and is more accurate than the commonly used Rosenblueth method, which requires a total of 2\I\un\N evaluations of the random function.