The Refined Positive Definite and Unimodal Regions for the Gram-Charlier and Edgeworth Series Expansion | Zendy

Fred Spiring | Zendy

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The Refined Positive Definite and Unimodal Regions for the Gram-Charlier and Edgeworth Series Expansion

Author(s) -

Fred Spiring

Publication year - 2011

Publication title -

advances in decision sciences

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.178

H-Index - 13

eISSN - 2090-3367

pISSN - 2090-3359

DOI - 10.1155/2011/463097

Subject(s) - edgeworth series , series (stratigraphy) , mathematics , boundary (topology) , probability density function , field (mathematics) , representation (politics) , series expansion , moment (physics) , statistics , mathematical analysis , pure mathematics , geology , physics , paleontology , classical mechanics , politics , political science , law

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

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