Special cases of second order Wiener germ approximations
type: Item
instance of: scholarly article
title: Special cases of second order Wiener germ approximations
zbMATH Open document ID: 0694.60003
DOI: 10.1007/BF00333142
publication date: 1989-01-01T00:00:00Z
review text: The paper is concerned with the distribution functions of densities of the form \[ f_{\epsilon}(x)\sim const.(2\pi \epsilon)^{-1/2}\exp \{- K(x)/\epsilon \}{\mathcal D}(x)\exp \{\epsilon S(x)\} \] where the functions K(x), S(x), \({\mathcal D}(x)\) satisfy certain conditions. Such family of densities, roughly speeking, is called Wiener germ, a mathematical theory which the author has initiated. Some results of this theory are applied to get approximations for the tail probabilities of various interesting distributions (e.g. Student's t-distribution, beta-distribution, gamma- distribution etc.). Sums of i.i.d. random variables are investigated, too.
Mathematics Subject Classification ID: 60B10
Mathematics Subject Classification ID: 60F99
zbMATH DE Number: 4137076
zbMATH Keywords: densities
zbMATH Keywords: Wiener germ
zbMATH Keywords: tail probabilities
author: Hermann Dinges
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf00333142
OpenAlex ID: W2332041924
published in: Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete
description: scientific article; zbMATH DE number 4137076