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Asymptotic properties of the number of replications of a paired comparison

Published online by Cambridge University Press:  14 July 2016

V. R. R. Uppuluri  and
W. J. Blot
V. R. R. Uppuluri
Affiliation:
Oak Ridge National Laboratory, Tennessee
W. J. Blot
Affiliation:
Johns Hopkins University
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Abstract

A discrete random variable describing the number of comparisons made in a sequence of comparisons between two opponents which terminates as soon as one opponent wins m comparisons is studied. By equating two different expressions for the mean of the variable, a closed form for the incomplete beta function with equal arguments is obtained. This expression is used in deriving asymptotic (m-large) expressions for the mean and variance. The standardized variate is shown to converge to the Gaussian distribution as m→ ∞. A result corresponding to the DeMoivre-Laplace limit theorem is proved. Finally applications are made to the genetic code problem, to Banach's Match Box Problem, and to the World Series of baseball.

Keywords

PAIRED COMPARISONSINCOMPLETE BETA FUNCTION WITH EQUAL ARGUMENTSLOCAL LIMIT THEOREMGENERALIZED BANACH MATCH BOX PROBLEMAPPLICATION TO WORLD SERIES AND DNA CODE
Type
Research Papers
Information
Journal of Applied Probability , Volume 11 , Issue 1 , March 1974 , pp. 43 - 52
Copyright
Copyright © Applied Probability Trust 1974 

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References

[1] Feller, W. (1957) An Introduction to Probability Theory and its Applications. Vol. I, 2nd ed. Wiley, New York.Google Scholar
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