  We provide a method that enables the simple calculation of the maximal
correlation coefficient of a bivariate distribution, under suitable conditions.
In particular, the method readily applies to known results on order statistics
and records. As an application we provide a new characterization of the
exponential distribution: Under a splitting model on independent identically
distributed observations, it is the (unique, up to a location-scale
transformation) parent distribution that maximizes the correlation coefficient
between the records among two different branches of the splitting sequence.
