An adaptive omnibus test for exponentiality

Abstract

Let be independent and identically distributed observations on a non-negative random variable X. If X has the exponential density , its Laplace transform satisfies the differential equation . We show that a strong omnibus test for expo-nentiality may be based on , where is the Maximum-Likelihood- estimate of λ and Ψ_n is the empirical Laplace transform, each based on .

Keywords:

• Exponential distribution
• goodness-of-fit test
• empirical Laplace transform
• consistency
• adaptive test