Goodness-of-Fit Tests Based on a New Characterization of the Exponential Distribution

The characteristic function of a random variable X with exponential density , satisfies the equation , where u(t) and v(t) denote the real and the imaginary part of , respectively. We study a new class of consistent tests for exponentiality based on a suitably weighted integral of , where is the maximum-likelihood estimate of θ, and u n and v n denote the empirical counterparts of u(t) and v(t), respectively. As the decay of the weight function tends to infinity, the test statistic approaches the square of a linear combination of the first two nonzero components of Neyman's smooth test for exponentiality. The new tests are compared with other omnibus tests for exponentiality.