  This paper presents in detail the originally developed Quadratic Point
Estimate Method (QPEM), aimed at efficiently and accurately computing the first
four output moments of probabilistic distributions, using 2n^2+1 sample (or
sigma) points, with n, the number of input random variables. The proposed QPEM
particularly offers an effective, superior, and practical alternative to
existing sampling and quadrature methods for low- and
moderately-high-dimensional problems. Detailed theoretical derivations are
provided proving that the proposed method can achieve a fifth or higher-order
accuracy for symmetric input distributions. Various numerical examples, from
simple polynomial functions to nonlinear finite element analyses with random
field representations, support the theoretical findings and further showcase
the validity, efficiency, and applicability of the QPEM, from low- to
high-dimensional problems.
