Inverse two-sided Laplace transform for probability density functions
type: Item
instance of: scholarly article
title: Inverse two-sided Laplace transform for probability density functions
zbMATH Open document ID: 0932.65134
DOI: 10.1016/S0377-0427(98)00013-2
author: Aldo Tagliani
published in: Journal of Computational and Applied Mathematics
publication date: 1999-10-05T00:00:00Z
review text: The author studies numerical inversion of the two-sided Laplace transform corresponding to a positive function, typically a probability density function. He consideres the problem where the data are the values of the first \(M\) derivatives of \(F(s)\) at the origin, related to the moments \(\mu_j\), \(j= 0,1,\dots, M\) of the function \(f(t)\) through the relation: \[ (-1)^j{d^jF(s)\over ds^j}\Biggl|_{s=0}= \mu_j,\quad j\geq 0,\quad \mu_0= 1. \] Then the problem of recovering \(f(t)\) is equivalent to the Hamburger moment problem. As the \(M\) moments do not give a unique probability density, so a widely used criterion is to choose the one which maximizes the entropy.
Mathematics Subject Classification ID: 65R10
Mathematics Subject Classification ID: 44A10
Mathematics Subject Classification ID: 44A60
zbMATH DE Number: 1326312
zbMATH Keywords: inverse two-sided Laplace transform
zbMATH Keywords: Hamburger moment problem
zbMATH Keywords: Hankel determinants
zbMATH Keywords: entropy convergence
zbMATH Keywords: numerical inversion
zbMATH Keywords: probability density function
reviewed by: C. L. Parihar
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1326312