Experimental Results and Generalizations for the Stopping Problem of Shepp's Urn
By Richard Voepel
A pdf of this paper may be downloaded here.
First Uploaded: Oct. 12, 2017; This version: Oct. 12, 2017
Abstract: In this paper we revisit the stopping problem of Shepp’s Urn,
extending the body of knowledge concerning moments of urn random variables
by adapting a methodology encountered in a paper by Medina and Zeilberger. We then offer generalizations of these random variables by altering the
strategy used to decide when to stop, and provide an experimental analysis of
the results.
Maple Packages, Scripts, and Data
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GeneralizedShepp.txt, a small Maple package that contains procedures for computing PGFs of urn random variables.
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MakeOriginalData.txt, a small script for generating PGFs for Shepp's strategy. Contains comments on parameter choices.
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MakeGeneralData.txt, a small script for generating PGFs for shortsighted risk-averse strategies, as detailed in the associated paper. Contains comments on parameter choices.
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OriginalData.m, a Maple data file containing PGFs for Shepp's strategy for urns U(m,p) with m+p<=1400. When read into Maple, type "OriginalShepp[m,p];" to get specific PGFs.
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GeneralData11.m, a Maple data file containing PGFs for the strategy F(g;1,1/2)>0 for urns U(m,p) with m+p<=1400. When read into Maple, type "GeneralShepp11[m,p];" to get specific PGFs.
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GeneralData12.m, a Maple data file containing PGFs for the strategy F(g;1,1/4)>0 for urns U(m,p) with m+p<=1400. When read into Maple, type "GeneralShepp12[m,p];" to get specific PGFs.
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GeneralData13.m, a Maple data file containing PGFs for the strategy F(g;1,1/8)>0 for urns U(m,p) with m+p<=1400. When read into Maple, type "GeneralShepp13[m,p];" to get specific PGFs.
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GeneralData14.m, a Maple data file containing PGFs for the strategy F(g;1,1/16)>0 for urns U(m,p) with m+p<=1400. When read into Maple, type "GeneralShepp14[m,p];" to get specific PGFs.
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GeneralData22.m, a Maple data file containing PGFs for the strategy F(g;2,1/4)>0 for urns U(m,p) with m+p<=1400. When read into Maple, type "GeneralShepp22[m,p];" to get specific PGFs.
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GeneralData23.m, a Maple data file containing PGFs for the strategy F(g;2,1/8)>0 for urns U(m,p) with m+p<=1400. When read into Maple, type "GeneralShepp23[m,p];" to get specific PGFs.
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GeneralData24.m, a Maple data file containing PGFs for the strategy F(g;2,1/16)>0 for urns U(m,p) with m+p<=1400. When read into Maple, type "GeneralShepp24[m,p];" to get specific PGFs.
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