Maximum likelihood estimation for the Bradley-Terry model based on Lehmann more than two player competitions and related problem

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In two player competitions, the Bradley-Terry model is a well-known probability model. There are several ways of derivation for this model. One of the derivations is given by Lehmann. This idea can be extended to the cases in more than two player competitions. See Funo (2009). In this paper we discuss how to obtain the MLE (maximum likelihood estimator) of the Bradley-Terry model based on Lehmann among three or more player competitions. Obtaining the MLE for another probability model is also discussed.

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