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An efficient point estimate method for probabilistic analysis
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DOI：10.1016/S0951-8320(97)00071-9.png)
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Abstract
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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 Rosenblueth's two-paint concentration method. The method uses m X n concentrations matching up to the first m X 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 X m locations. Simple to use formulas are provided for two special cases of the method, i.e. 2n-concentration scheme and 2n + I-concentration scheme. This 2n-concentration scheme considers the skewness of probability density function. The 2n + I-concentration scheme considers the skewness and kurtosis of probability 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. (C) 1998 Published by Elsevier Science Limited.
Keywords:
UNCERTAINTY PROPAGATION
DISTRIBUTIONS
MOMENTS
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