Research Article
Dec 1980
Optimal Estimation of Convolution Integrals
Publication: Journal of the Engineering Mechanics Division
Volume 106, Issue 6
Abstract
Estimators, obtained as linear combinations of distributions from a prescribed reference set, are used to approximate convolution integrals. These linear combinations have non-negative coefficients which sum to unity, and the elements of the reference set have the same first two moments as the convolution integral. Thus, the estimators are distributions that are equal in the second moment sense to the convolution integral. Evaluation of the optimal estimator is based on minimization of objective functions related to moments of the convolution integral and of the distributions in the reference set. It involves only elementary algebraic operations. The optimal estimator is a convenient and generally satisfactory approximation for the convolution integral.
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Published In
Journal of the Engineering Mechanics Division
Volume 106 • Issue 6 • December 1980
Pages: 1349 - 1364
Copyright
© 1980 American Society of Civil Engineers.
History
Published in print: Dec 1980
Published online: Feb 3, 2021
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Mircea Grigoriu, M.ASCE
Assoc. Prof. of Civ. Engrg., Cornell Univ., Ithaca, N.Y.
Niels C. Lind, M.ASCE
Prof. of Civ. Engrg., Univ. of Waterloo, Waterloo, Ontario, Canada
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Terms of Use: ASCE Library Cards are for individual, personal use only. Reselling, republishing, or forwarding the materials to libraries or reading rooms is prohibited.
Terms of Use: ASCE Library Cards are for individual, personal use only. Reselling, republishing, or forwarding the materials to libraries or reading rooms is prohibited.