Probability of correct selection from lognormal and convective diffusion models based on the likelihood ratio

The objective of the paper is to show that the use of a discrimination procedure for selecting a flood frequency model without the knowledge of its performance for the considered underlying distributions may lead to erroneous conclusions. The problem considered is one of choosing between lognormal (LN) and convective diffusion (CD) distributions for a given random sample of flood observations. The probability density functions of these distributions are similarly shaped in the range of the main probability mass and the discrepancies grow with the increase in the value of the coefficient of variation (CV). This problem was addressed using the likelihood ratio (LR) procedure. Simulation experiments were performed to determine the probability of correct selection (PCS) for the LR method. Pseudo-random samples were generated for several combinations of sample sizes and the coefficient of variation values from each of the two distributions. Surprisingly, the PCS of the LN model was twice smaller than that of the CD model, rarely exceeding 50%. The results obtained from simulation were analyzed and compared both with those obtained using real data and with the results obtained from another selection procedure known as the QK method. The results from the QK are just the opposite to that of the LR procedure.