The refined positive definite and unimodal regions for the Gram-Charlier and Edgeworth series expansion

DOI10.1155/2011/463097zbMath1221.62029DBLPjournals/jamds/Spiring11OpenAlexW2086632566WikidataQ58653858 ScholiaQ58653858MaRDI QIDQ638152

Fred A. Spiring

Publication date: 9 September 2011

Published in: Advances in Decision Sciences (Search for Journal in Brave)

Full work available at URL: http://hdl.handle.net/1993/30524

Mathematics Subject Classification ID

Asymptotic distribution theory in statistics (62E20) Approximations to statistical distributions (nonasymptotic) (62E17)

Cites Work

• On the generalization of the Edgeworth/Gram-Charlier series
• Computation of one-sided probability density functions from their cumulants
• Expressing a probability density function in terms of another PDF: a generalized Gram-Charlier expansion
• On the representation of a density by an Edgeworth series
• Edgeworth expansion and the bootstrap for stratified sampling without replacement from a finite population
• The Early History of the Cumulants and the Gram‐Charlier Series
• Regions of positive and unimodal series expansion of the Edgeworth and Gram-Charlier approximations
• Exact formulas for additional terms in some 1mportant series expansions
• EFFICIENCY OF THE METHOD OF MOMENTS AND THE GRAM-CHARLIER TYPE A DISTRIBUTION
• The conditions under which Gram-Charlier and Edgeworth curves are positive definite and unimodal
• The bootstrap and Edgeworth expansion
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