CUMULANT CALCULATION ON PERFORMANCE FUNCTION

Abstract

This derives a simple moment-cumulant relationship to calculate the statistics of a safety margin that represents the performance of an engineering system. The r-th order joint moment is expressed by a sum of the product of cumulant and moment up to r-th and (r-1)-th order, respectively. Correlated random variables are transformed into sums of independent ones and the relationships among them are described in detail. Operation with the cumulant-generating function after this transformation simplifies the related calculation. Several ideal examples follow to descrive the calculation procedure. Considerable errors are observed in the cumulant evaluation of non-linear functions via the linear approximation. This is a generalization of the joint cumulant calculation on independent random variables to correlated ones.