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Probabilities of Competing Binomial Random Variables

Published online by Cambridge University Press:  04 February 2016


Wenbo V. Li
Affiliation:
University of Delaware
Vladislav V. Vysotsky
Affiliation:
Arizona State University, Steklov Mathematical Institute and St. Petersburg State University
Corresponding

Abstract

Suppose that both you and your friend toss an unfair coin n times, for which the probability of heads is equal to α. What is the probability that you obtain at least d more heads than your friend if you make r additional tosses? We obtain asymptotic and monotonicity/convexity properties for this competing probability as a function of n, and demonstrate surprising phase transition phenomenon as the parameters d, r, and α vary. Our main tools are integral representations based on Fourier analysis.


Type
Research Article
Copyright
© Applied Probability Trust 

Footnotes

Supported in part by NSF grants DMS-0805929, NSFC-6398100, and CAS-2008DP173182.

The author began this work at the University of Delaware, and was supported in part by the grant NSh. 4472-2010-1.


References

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