Comparison of two fitting methods for the log-logistic distribution

We investigate generalized probability weighted moments (GPWM) and maximum likelihood (ML) fitting methods in the two-parameter log-logistic (LL) model. Parameter and quantiles estimators are computed along with their asymptotic variances and covariances. A comparison of these methods is done by simulation. It is concluded that for estimating beta, GPWM can provide better results than the ML method. However, for estimating quantiles, GPWM provides better results only for very small sample sizes, especially when the distribution is quite asymmetrical. Although presently, LL is not one of the distributions frequently used in hydrology, we agree with some authors that it merits wider use in hydrological practice. For a clearer idea on the merits of LL, we compare it with three other distributions for fitting flood data from 114 hydrometric stations in Canada. The results support our view regarding the good fitting potential of the LL distribution to extreme hydrologic data.