A class of consistent tests for exponentiality based on the empirical Laplace transform

Abstract. The Laplace transform ¢(t) = E[exp(-tX)] of a random variable with exponential density A exp(-Ax), x> 0, satisfies the differential equation (A + t)¢'(t) + ¢(t)- 0, t _> 0. We study the behaviour of a class of consistent ("omnibus") tests for exponentiality based on a suitably weighted integral of [(A, ~ + t)¢~(t) + Cn(t)] 2, where ~, ~ is the maximum-likelihood-estimate of A and ¢, ~ is the empirical Laplace transform, each based on an i.i.d, sample X1,. • •, X,~. Key words and phrases: Exponential distribution, goodness-of-fit test, empir