Computational Statistics & Data Analysis 43 (2003) 179–196 www.elsevier.com/locate/csda Discriminating between Weibull and generalized exponential distributions Rameshwar D. Gupta a ; 1 , Debasis Kundu b; ∗ a Department of Applied Statistics and Computer Science, The University of New Brunswick, Saint John, Canada E2L 4L5 b Department of Mathematics, Indian Institute of Technology Kanpur, Kanpur 208016, India Received 1 November 2001; received in revised form 1 April 2002 Abstract Recently the two-parameter generalized exponential (GE) distribution was introduced by the authors. It is observed that a GE distribution can be considered for situations where a skewed distribution for a non-negative random variable is needed. The ratio of the maximized likelihoods (RML) is used in discriminating between Weibull and GE distributions. Asymptotic distributions of the logarithm of the RML under null hypotheses are obtained and they are used to deter- mine the minimum sample size required in discriminating between two overlapping families of distributions for a user specied probability of correct selection and tolerance limit. c  2003 Elsevier Science B.V. All rights reserved. Keywords: Asymptotic distributions; Generalized exponential distribution; Kolmogorov–Smirnov distance; Likelihood ratio statistic; Weibull distribution 1. Introduction Recently, the two-parameter generalized exponential (GE) distribution has been intro- duced and studied quite extensively by the authors (Gupta and Kundu, 1999, 2001a,b). The two-parameter GE distribution has the distribution function F GE (x; ;)=(1 - e -x )  ; ;¿ 0; (1.1) * Corresponding author. Tel.: 91-512-597141; fax: 91-512-597500. E-mail address: kundu@iitk.ac.in (D. Kundu). 1 Part of the work was supported by a grant from the Natural Sciences and Engineering Research Council. 0167-9473/03/$-see front matter c  2003 Elsevier Science B.V. All rights reserved. PII:S0167-9473(02)00206-2