New Point Estimates for Probability Moments
Publication: Journal of Engineering Mechanics
Volume 126, Issue 4
Abstract
There are many areas of structural safety and structural dynamics in which it is often desirable to compute the first few statistical moments of a function of random variables. The usual approximation is by the Taylor expansion method. This approach requires the computation of derivatives. In order to avoid the computation of derivatives, point estimates for probability moments have been proposed. However, the accuracy is quite low, and sometimes, the estimating points may be outside the region in which the random variable is defined. In the present paper, new point estimates for probability moments are proposed, in which increasing the number of estimating points is easier because the estimating points are independent of the random variable in its original space and the use of high-order moments of the random variables is not required. By using this approximation, the practicability and accuracy of point estimates can be much improved.
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References
1.
Abramowitz, M., and Stegum, I. E. (1972). Handbook of mathematical functions, 10th Printing, Dover, New York, 924.
2.
Gorman, M. R. ( 1980). “Reliability of structural systems,” PhD thesis, Case Western Reserve University, Cleveland, Ohio, 320–332.
3.
Hohenbichler, M., and Rackwitz, R. (1981). “Non-normal dependent vectors in structural safety.”J. Engrg. Mech., ASCE, 107(6), 1227–1238.
4.
Ibrahim, R. A. (1987). “Structural dynamics with parameter uncertainties.” Appl. Mech. Rev., 40(3), 309–328.
5.
Ono, T., Idota, H., and Kawahara, H. (1986). “A statistical study on the resistance of steel column and beam using higher order moments.” J. Struct. and Constr. Engrg., 370, 19–27 (in Japanese).
6.
Rosenblueth, E. (1975). “Point estimates for probability moments.” Proc., Nat. Acad. of Sci., 72(10), 3812–3814.
7.
Singh, R., and Lee, P. (1993). “Frequency response of linear systems with parameter uncertainties.” J. Sound and Vibrations, 168, 71–92.
8.
Zhao, Y. G., Ono, T., and Idota, H. (1999). “Response uncertainty evaluation and time variant reliability analysis for hysteretic MDF structures.” Earthquake Engrg. and Struct. Dyn., 28(10), 1187–1213.
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Received: Sep 1, 1998
Published online: Apr 1, 2000
Published in print: Apr 2000
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