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We provide a method that enables the simple calculation of the maximalcorrelation coefficient of a bivariate distribution, under suitable conditions.In particular, the method readily applies to known results on order statisticsand records. As an application we provide a new characterization of theexponential distribution: Under a splitting model on independent identicallydistributed observations, it is the (unique, up to a location-scaletransformation) parent distribution that maximizes the correlation coefficientbetween the records among two different branches of the splitting sequence.

A Simple Method for Obtaining the Maximal Correlation Coefficient and Related Characterizations