Fourier–Legendre approximation of a probability density from discrete data

We produce a positive approximation of a probability density in [0,1] when only a finite number of values (possibly affected by noise) is available. This approximation is obtained by computing a number of Legendre–Fourier coefficients and applying the Maximum Entropy method. An example of applicatio...

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Bibliographic Details
Published in:	Journal of computational and applied mathematics Vol. 154; no. 1; pp. 161 - 173
Main Author:	Inglese, Gabriele
Format:	Journal Article
Language:	English
Published:	Amsterdam Elsevier B.V 01-05-2003 Elsevier
Subjects:	Approximations and expansions Exact sciences and technology Mathematical analysis Mathematics Probability and statistics Probability theory and stochastic processes Probability theory on algebraic and topological structures Sciences and techniques of general use Uniform convergence Transport equation Smoothing methods Approximation Fourier analysis Minimization Entropy Probability distribution Fourier series Legendre polynomial Numerical approximation Non linear equation Quadrature Probability density Fourier Legendre approximation Smoothing Numerical solution Fokker Planck equation Integrodifferential equation Legendre number Vandermonde matrix
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Summary:	We produce a positive approximation of a probability density in [0,1] when only a finite number of values (possibly affected by noise) is available. This approximation is obtained by computing a number of Legendre–Fourier coefficients and applying the Maximum Entropy method. An example of application of this procedure is data-smoothing in the numerical solution of an identification problem for Fokker–Planck equation.
Bibliography:	ObjectType-Article-2 SourceType-Scholarly Journals-1 ObjectType-Feature-1 content type line 23
ISSN:	0377-0427 1879-1778
DOI:	10.1016/S0377-0427(02)00819-1