Maximum entropy pdfs and the moment problem under near-Gaussian conditions |
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Authors: | Ernani V Volpe Donald Baganoff |
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Affiliation: | a Department of Mechanical Engineering, University of Sao Paulo, Av. Prof. Mello Moraes 2231, CEP 05508-900, Sao Paulo, SP, Brazil;b Department of Aeronautics and Astronautics, Stanford University, Durand Building 4305, Stanford, CA 94305-2210, USA |
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Abstract: | This paper focuses on a class of continuous probability density functions (pdfs) that are generated by the maximum entropy method (mem), which are of potential interest in fluid dynamics. It discusses their properties and presents a method for obtaining approximate solutions to the moment problem that is associated with this class of pdfs. The method allows one to express pdf parameters in terms of constrained moments, alone. The results thus obtained hold for pdfs that represent small perturbations from a known pdf within this class. On combining these results with exact moment equations, one obtains successful approximations to the closure relations that are associated with these pdfs. The Gaussian pdf belongs in this class, and the method can be used to explore the near-Gaussian region. |
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Keywords: | Probability density functions Maximum entropy method Moment problem Small disturbance expansion |
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