Improved Point Estimates of Probabilistic Moments for Non-Gaussian Multivariate Environmental Modeling and Uncertainty Analysis

Most parameters of natural phenomena are uncertain because of measurement errors or inherent stochasticity. This paper proposes two improved point estimate methods. The first is based on an adaptive quadrative method and Hong’s method. By dividing the objective function into several regions, Hong’s original method can be applied to more complicated nonlinear functions, and the adaptive quadrative method can then be used to estimate expected errors for various regions. In the second method, the Gauss–Hermite quadrature and Gram–Charlier series are proposed for non-Gaussian variables. For some point estimate methods such as Hong’s method, the distribution of each random variables needs to known a priori, which are often treated as Gaussian variables. In the second proposed method, the assumption of Gaussian distributions for the involved random variables can be relaxed. The approximate probability distribution, generated by the Gram–Charlier expansion, is the normal distribution multiplied by a polynomial function. The expected values of the objective function obtained through these two methods are compared with those from Monte Carlo simulations and the simple adaptive method. If both computation time and precision must be considered, the improved Gauss–Hermite quadrature method is preferred. If accuracy is paramount, the improved Hong’s method is preferred.