Generalized Rayleigh (GR) and Weibull (WE) distributions are used quite effectively for analysing skewed lifetime data. In this paper, we consider the problem of selecting either GR or WE distribution as a more appropriate fitting model for a given data set. We use the ratio of maximized
likelihoods (RML) for discriminating between the two distributions. The asymptotic and simulated distributions of the logarithm of the RML are applied to determine the probability of correctly selecting between these two families of distributions. It is examined numerically that the asymptotic
results work quite well even for small sample sizes. A real data set involving the annual rainfall recorded at Los Angeles Civic Center during 25 years is analysed to illustrate the procedures developed here.
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