POINT ESTIMATE FOR THE FUNCTION WITH DISCRETE RANDOM VARIABLES

The point estimate method is one of the simplest and most efficient methods for calculating statistical moments of stochastic systems or functions which only involve continuous random variables. However, when discrete random variables exist, inherently or artificially, existing point estimate methods are no longer suitable. To solve this problem, this paper presents a point estimate method for calculating statistical moments of stochastic systems or functions involving discrete random variables. The proposed method is deduced in two steps: the theoretical formulas for statistical moments of a stochastic system with discrete variables are derived based on the formal analytical solution of the general stochastic system, then the point estimate for a stochastic system or function with discrete variables are developed by introducing the existing point estimate for conditional statistical moment. At last, the rationality and validity of this method is verified by theoretical analysis and numerical examples involving two elementary mathematical functions and one single degree of freedom system. Results indicate that the proposed method provide an accurate estimates of statistical moments and show the potential of the proposed method for stochastic analysis of general engineering structures.