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

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Date
2011-5-26
Authors
Spiring, Fred
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Abstract
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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Fred Spiring, “The Refined Positive Definite and Unimodal Regions for the Gram-Charlier and Edgeworth Series Expansion,” Advances in Decision Sciences, vol. 2011, Article ID 463097, 18 pages, 2011. doi:10.1155/2011/463097