Fourier-Legendre approximation of a probability density from discrete data
type: Item
instance of: scholarly article
title: Fourier-Legendre approximation of a probability density from discrete data
zbMATH Open document ID: 1019.65013
DOI: 10.1016/S0377-0427(02)00819-1
published in: Journal of Computational and Applied Mathematics
publication date: 2003-05-22T00:00:00Z
review text: The author describes a positive approximation to a probability density \(u\) on \([0,1]\) if only a finite number of its values affected by noise is available. The procedure starts with estimating a number of Legendre-Fourier coefficients \(\lambda_k=\int_0^1 u(x)L_j(x)dx\). Then the estimate of \(u\) is found by the maximum entropy method that consists in minimising \(\int_0^1 u(x)\log u(x)dx\) over the family of probability densities with the given Legendre-Fourier coefficients. The author provides a theoretical result describing the quality of estimation and an example of application of this procedure in data-smoothing in the numerical solution of an identification problem for Fokker-Planck equation.
Mathematics Subject Classification ID: 65C50
Mathematics Subject Classification ID: 62G07
Mathematics Subject Classification ID: 60E05
zbMATH DE Number: 1915271
zbMATH Keywords: Legendre-Fourier coefficients
zbMATH Keywords: maximum entropy method
zbMATH Keywords: approximation to a probability density
zbMATH Keywords: data-smoothing
zbMATH Keywords: Fokker-Planck equation
author: Gabriele Inglese
reviewed by: Ilya S. Molchanov
MaRDI profile type: Publication
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full work available at URL: s0377-0427(02)00819-1
OpenAlex ID: W2073105925
description: scientific article; zbMATH DE number 1915271