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

The characteristic function $\varphi(t)$ of an exponentially distributed random variable is characterized by having its squared modulus identically equal to the real part of $\varphi(t)$. 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. Bibl. – 25 titles.