The refined positive definite and unimodal regions for the Gram-Charlier and Edgeworth series expansion
type: Item
instance of: scholarly article
title: The refined positive definite and unimodal regions for the Gram-Charlier and Edgeworth series expansion
zbMATH Open document ID: 1221.62029
DOI: 10.1155/2011/463097
published in: Advances in Decision Sciences
publication date: 2011-09-09T00:00:00Z
full work available at URL: http://hdl.handle.net/1993/30524
review text: Summary: Gram-Charlier and Edgeworth series expansions are used in the field of statistics to approximate probability density functions. The expansions have proven useful but have experienced limitations due to the values of the moments that admit a proper probability density function. An alternative approach in developing the boundary conditions for the boundary of the positive region for both series expansions is investigated using Sturm's theorem. The result provides a more accurate representation of the positive region developed by others.
Mathematics Subject Classification ID: 62E17
Mathematics Subject Classification ID: 62E20
zbMATH DE Number: 5946532
Wikidata QID: Q58653858
author: Fred A. Spiring
MaRDI profile type: Publication
OpenAlex ID: W2086632566
cites work: EFFICIENCY OF THE METHOD OF MOMENTS AND THE GRAM-CHARLIER TYPE A DISTRIBUTION
cites work: Regions of positive and unimodal series expansion of the Edgeworth and Gram-Charlier approximations
cites work: The Early History of the Cumulants and the Gram‐Charlier Series
cites work: The bootstrap and Edgeworth expansion
cites work: Edgeworth expansion and the bootstrap for stratified sampling without replacement from a finite population
cites work: Computation of one-sided probability density functions from their cumulants
cites work: Expressing a probability density function in terms of another PDF: a generalized Gram-Charlier expansion
cites work: On the generalization of the Edgeworth/Gram-Charlier series
cites work: The conditions under which Gram-Charlier and Edgeworth curves are positive definite and unimodal
cites work: Exact formulas for additional terms in some 1mportant series expansions
cites work: On the representation of a density by an Edgeworth series
cites work: Q4244407
cites work: Q3757131
cites work: Q5615180
DBLP publication ID: journals/jamds/Spiring11
description: scientific article; zbMATH DE number 5946532