Discriminating Between the Generalized Rayleigh and Log-Normal Distribution Debasis Kundu 1 and Mohammad Z. Raqab 2 Abstract Surles and Padgett recently introduced two-parameter Burr Type X distribution, which can also be described as the generalized Rayleigh distribution. It is observed that the generalized Rayleigh and log-normal distributions have many common properties and both the distributions can be used quite effectively to analyze skewed data set. For a given data set the problem of selecting either generalized Rayleigh or log-normal distribution is discussed in this paper. The ratio of maximized likelihood is used in discriminating between the two distributing functions. Asymptotic distributions of the ratio of the maximized likelihoods under null hypotheses are obtained and they are used to determine the minimum sample size required in discriminating between these two families of distributions for a used specified probability of correct selection and the tolerance limit. Key Words and Phrases: Burr Type X distribution; Maximum likelihood estimator; Hazard function; Asymptotic distributions; Likelihood Ratio Test; Probability of Correct Selection; Tolerance limit. Address of correspondence: Debasis Kundu, e-mail: kundu@iitk.ac.in, Phone no. 91- 512-2597141, Fax no. 91-512-2597500. 1 Department of Mathematics and Statistics, Indian Institute of Technology Kanpur, Pin 208016, India. 2 Department of Mathematics, University of Jordon Amman 11942, JORDON. 1