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Activity Number:
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86
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Type:
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Contributed
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Date/Time:
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Monday, August 9, 2004 : 8:30 AM to 10:20 AM
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Sponsor:
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General Methodology
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| Abstract - #300324 |
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Title:
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The Refined Positive Definite and Unimodal Regions for the Gram-Charlier and Edgeworth Series Expansions
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Author(s):
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Fred Spiring*+ and Bartholomew P.K. Leung and Anthony Yeung
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Companies:
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University of Manitoba and Hong Kong Polytechnic University and University of Manitoba
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Address:
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Department of Statistics, Winnipeg, MB, R3T 3Z4, Canada
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Keywords:
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series expansion ; positive definite ; Sturm's Theorem ; Gram-Charlier ; Edgeworth
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Abstract:
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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 (pdf). 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. This alternative approach is used to develop the boundary of the positive and unimodal regions for both series expansions. Maple and Mathematica codes that allow verification of the moment ratio combinations that result in a proper pdf are provided. This method accurately determines the positive and unimodal regions of the expansions. Tabulated values are provided and plots included that illustrate the proposed method. The results can then be compared with the regions developed by others, including Barton & Dennis (1952).
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