Abstract. A wide selection of classical and recent tests for exponentiality are discussed and compared. The classical procedures include the statistics of Kolmogorov-Smirnov and Crame´ r-von Mises, a statistic based on spacings, and a method involving the score function. Among the most recent approaches emphasized are methods based on the empirical Laplace trans- form and the empirical characteristic function, a method based on entropy as well as tests of the Kolmogorov-Smirnov and Crame´r-von Mises type that utilize a characterization of exponentiality via the mean residual life function. We also propose a new goodness-of-fit test utilizing a novel characterization of the exponential distribution through its characteristic function. The finite- sample performance of the tests is investigated in an extensive simulation study. AMS 1991 Classification Numbers: 62G10, 62G20 Key words: Goodness-of-fit test, exponential distribution, empirical charac- teristic function, empirical distribution function, integrated empirical distri- bution function, empirical Laplace transform, entropy, mean residual life function. 1. Introduction and summary The assumption of exponentiality is heavily used in many modelling situa- tions, particularly in life testing and reliability. Standard procedures for checking the validity of the exponential model are the tests of Kolmogorov- Smirnov and Crame´r-von Mises, which utilize the empirical distribution function (EDF), procedures based on properties of normalized spacings and the score test. Recent years, however, have witnessed an increasing interest in using alternative methods, besides those directly involving the density and Metrika (2005) 61: 29–45 DOI 10.1007/s001840400322 Recent and classical tests for exponentiality: a partial review with comparisons Norbert Henze and Simos G. Meintanis Institut fu¨r Mathematische Stochastik, Universita¨t Karlsruhe, Englerstr. 2, 76128 Karlsruhe, Germany and Department of Economics, National and Kapodistrian University of Athens, 8 Pesmazoglou Street, 105 59 Athens, Greece Received: January 2002/Revised: January 2004