Discriminating Between Normal and Gumbel Distributions

Abstract

The normal and Gumbel distributions are much alike in practical engineering, in flood frequency and they are similar in appearance, especially for small samples. So the aim of this paper is to discriminate between these two distributions. Considering the logarithm of the ratio of the maximized likelihood (RML) as test statistic, its asymptotic distribution is found under both normal and Gumbel distributions, which can be used to compute the probability of correct selection (PCS). Finally, Monte Carlo (MC) simulations are performed to examine how the asymptotic results work for finite sample sizes.