Three procedures for selection of annual flood peak distribution

Four 2 parameter probability distributions, Gamma (Ga), Lognormal (LN), Weibull (We) and Convective Diffusion (CD), were considered as alternative models for the distribution of annual peak flow discharges of Polish rivers. They are lower bounded at zero. To find the best fitting distribution, three model discrimination procedures were applied: (1) the maximized logarithm of the likelihood function (called K procedure); (2) the density function of the scale transformation maximal invariant (called QK procedure); and (3) the difference between maximum likelihood method (MLM) and method of moment (MOM) estimates of 1% quantile (called R procedure). The results obtained for thirty-nine historical time series of seventy years long were found contradictory. The CD model was selected by the first and third procedures as the best fitting model with a selection ratio of 0.69 and 0.97, respectively, while the LN model by the second procedure with a selection ratio of 0.97. Even though the two models offered similar fits for each sample size they differed in respect to the upper quantile values. Moreover the model choice of each procedure is highly influenced by the sample size. This means that it is difficult to get the same model from a sample of another duration. To evaluate the performance of each procedure, simulation experiments were considered for the analysed cases of choice among any two and all four models. The variation in the efficiency of the procedures was investigated for various pairs of the considered distributions for different values of the coefficient of variation and sample size. Usually, one of the models was favoured by a given discrimination procedure as shown by the values of the probability of correct selection (PCS). In particular, the CD distribution was the preferred model in the case of the K and R procedures, while the LN distribution was when the QK procedure was applied. It is shown that the mutual use of several model discrimination procedures combined with the knowledge of their efficiency for a given case is a promising way to enhance the efficiency of the model selection techniques in flood frequency analysis.