Advances in Decision Sciences
Volume 2011 (2011), Article ID 463097, 18 pages
Research Article

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

Department of Statistics, The University of Manitoba, 941 Kilkenny Drive, Winnipeg MB, Canada R3T 3Z4

Received 1 December 2010; Accepted 7 March 2011

Academic Editor: Shelton Peiris

Copyright © 2011 Fred Spiring. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.