(Received November 6, 1989; revised May 14, 1990)
Abstract. The Laplace transform psi(t) = E[exp(-tX)] of a random variable with exponential density lambda exp(-lambda x), x > 0, satisfies the differential equation (lambda + t)psi'(t) + psi(t) = 0, t > 0. We study the behaviour of a class of consistent (``omnibus'') tests for exponentiality based on a suitably weighted integral of [(^lambdan + t)psi'n(t) + psin(t)]2, where ^lambdan is the maximum-likelihood-estimate of lambda and psin is the empirical Laplace transform, each based on an i.i.d. sample X1,...., Xn.
Key words and phrases: Exponential distribution, goodness-of-fit test, empirical Laplace transform, consistency.