ADS Advances in Decision Sciences 2090-3367 2090-3359 Hindawi Publishing Corporation 463097 10.1155/2011/463097 463097 Research Article The Refined Positive Definite and Unimodal Regions for the Gram-Charlier and Edgeworth Series Expansion Spiring Fred fspiring@mymts.net 1 Peiris Shelton 1 Department of Statistics The University of Manitoba 941 Kilkenny Drive Winnipeg MB Canada R3T 3Z4 umanitoba.ca 2011 2652011 2011 01 12 2010 07 03 2011 2011 Copyright © 2011 Fred Spiring.

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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.