This is the program for the 2010 Joint Statistical Meetings in Vancouver, British Columbia.
Abstract Details
Activity Number:
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585
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Type:
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Contributed
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Date/Time:
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Wednesday, August 4, 2010 : 2:00 PM to 3:50 PM
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Sponsor:
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IMS
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Abstract - #307916 |
Title:
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Growth Rates of Moment Sequences
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Author(s):
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William L. Harkness*+
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Companies:
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Penn State
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Address:
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318 Thomas Bldg., University Park, PA, 16802,
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Keywords:
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Ratios of Moments ;
Growth rates ;
regularly varying functions
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Abstract:
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General properties of growth rates of moment sequences of nonnegative random variables are presented. Then asymptotic results on moment sequences are derived for two classes of distribution functions. Explicitly, let g be a monotone increasing twice differentiable regularly varying function at infinity with g(+8)=+8 and index of variation ? = 0. Define the distribution function F by -ln[1-F(x)] = g-inverse(x). Then an explicit expression for the nth moment is given in terms of g and it is shown that the ratio of the (n+1)st and nth moments is asymptotically equal to g(tn), where tn satisfies the equation ng'(tn)/g(tn)=1. A second class of distribution functions is defined by setting -ln[1-F(x)] = g-inverse(ln x), where now ? = 1, and similar results are obtained in this case. Finally, examples are given to illustrate the possible asymptotic growth rates of moments.
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