Abstract: In many fields like, renewal process, life testing problem, stochastic modeling the assumption of exponentiality is heavily used. In many studies dealing with equipment of failure and repair time ,often these times are assumed to be exponentially distributed. However, considerable efforts have been dedicated to testing for exponentiality. Some of the workers in this fields are Kolmogorov-Smirnov, Von Mises (1931), Bartholomew (1957), Kuiper (1960), Epstein (1954,1960), Watson (1961), Lilliefors (1969), Gail and Gastwirth (1978), Dágostino and Stephen (1976) , Doksum and Yandell (1984) etc which are based on empirical distribution. Among the most recent approaches emphasized are based on entropy estimator ,divergence measures and Kullback-Laibler information’s., In this paper we wish to study performance of some of these tests under different alternative hypotheses, viz. under lognormal distribution, Weibull distribution and gamma distributions etc. Results are obtained using Monte Carlo simulation technique and displayed in different tables and graphs. Discussions are made based on simulated results and conclusion is drawn accordingly.

Keywords: Goodness of fit test, Exponential distribution, Lognormal, Weibull and gamma distribution, Monte Carlo technique.