A characterization and a class of omnibus tests for the exponential distribution based on the empirical characteristic function

The characteristic function φ(t) of an exponentially distributed random variable is characterized by having its squared modulus identically equal to the real part of φ(t). We study the behavior of a class of consistent tests for exponentiality based on a weighted integral involving the empirical counterparts of these quantities, corresponding to suitably rescaled data. Bibliography: 25 titles.