An efficient point estimate method for probabilistic analysis

A new and efficient point estimate method is developed to calculate the statistical moments of a random quantity, Z, that is a function of n random variables, X. The method is an extension of Rosenbluethʹs two-point concentration method. The method uses m × n concentrations matching up to the first m × n non-crossed moments of each random variable and crossed second order moments of the random variables. The kth moment of Z is calculated by weighting the value of Z to the power of k evaluated at n × m locations. Simple to use formulas are provided for two special cases of the method, i.e. 2n-concentration scheme and 2n + 1-concentration scheme. This 2n-concentration scheme considers the skewness of probability density function. The 2n + 1-concentration scheme considers the skewness and kurtosis of probabilility density function. The correlations between the random variables are considered by using a rotational transformation based on the eigenvector of covariance matrix. Illustrative examples are presented.