Three-parameter discontinuous distributions for hydrological samples with zero values

A consistent approach to the frequency analysis of hydrologic data in and and semiarid regions, i.e. the data series containing several zero values (e.g. monthly precipitation in dry seasons, annual peak flow discharges, etc.), requires using discontinuous probability distribution functions. Such an approach has received relatively limited attention. Along the lines of physically based models, the extensions of the Muskingum-based models to three parameter forms are considered. Using 44 peak flow series from the USGS data bank, the fitting ability of four three-parameter models was investigated: (1) the Dirac delta combined with Gamma distribution; (2) the Dirac delta combined with two-parameter generalized Pareto distribution; (3) the Dirac delta combined with two-parameter Weibull (DWe) distribution; (4) the kinematic diffusion with one additional parameter that controls the probability of the zero event (KD3). The goodness of fit of the models was assessed and compared both by evaluation of discrepancies between the results of both estimation methods (i.e. the method of moments (MOM) and the maximum likelihood method (MLM)) and using the log of likelihood function as a criterion. In most cases, the DWe distribution with MLM-estimated parameters showed the best fit of all the three-parameter models. Copyright (c) 2005 John Wiley & Sons, Ltd.