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On the asymptotic normality of the number of replications of a paired comparison

Published online by Cambridge University Press:  14 July 2016

V. V. Menon  and
N. K. Indira
V. V. Menon*
Affiliation:
Banaras Hindu University
N. K. Indira*
Affiliation:
Banaras Hindu University
*
∗ Postal address for both authors: Applied Mathematics Section, Institute of Technology, Banaras Hindu University, Varanasi 221005, India.
∗ Postal address for both authors: Applied Mathematics Section, Institute of Technology, Banaras Hindu University, Varanasi 221005, India.
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Abstract

Consider the number Xm of comparisons made in a sequence of comparisons between two opponents, which terminates as soon as one opponent wins m comparisons. The convergence of Xm to the normal variable is completely characterized. The normal approximations to the probability function and to the distribution function of Xm are obtained for any sufficiently large m, together with estimates of the errors in these approximations. Similar results are obtained for the negative binomial distribution as well. Finally, some simple estimates of the mean, variance and the incomplete beta function with equal arguments are constructed.

Keywords

PAIRED COMPARISONSGENERALIZED BANACH MATCH BOX PROBLEMNEGATIVE BINOMIAL DISTRIBUTIONLOCAL CENTRAL LIMIT THEOREMNORMAL APPROXIMATIONRATE OF CONVERGENCEINCOMPLETE BETA FUNCTION WITH EQUAL ARGUMENTS
Type
Research Papers
Information
Journal of Applied Probability , Volume 20 , Issue 3 , September 1983 , pp. 554 - 562
Copyright
Copyright © Applied Probability Trust 1983 

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References

[1] Cramér, H. (1958) Mathematical Methods of Statistics. Princeton University Press, Princeton, NJ.Google Scholar
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