Hydrological Applications of the Burr Distribution: Practical Method for Parameter Estimation

The three-parameter Burr XII distribution has been seldom used in hydrological applications, although it is particularly appealing because its range covers positive values only, which is convenient when modeling streamflows or rainfall data. Moreover, it has two shape parameters, allowing it to be quite adaptable to different samples because it covers a wide range of skewness and kurtosis values. Parameter estimation methods currently available in the literature require the numerical solution of two joint nonlinear equations to estimate the shape parameters of the distribution. This work proposes a simplified, although accurate, method to analytically compute the two shape parameters starting from the dimensionless L-moments ratios representing the distribution’s variability (L-CV) and skewness (L-skewness). The obtained parameters can be directly used in practical applications or otherwise may be useful to properly initialize the algorithms to obtain a numerical solution for the shape parameters. A detailed analysis of the accuracy of the approximated solution is performed, showing that the errors in the estimation of the distribution quantiles are negligible compared with the sample variability typically affecting hydrological samples. An extensive data set of empirical flow duration curves from stations located in northwestern Italy is considered to demonstrate the suitability of the extended Burr XII distribution to represent flow duration curves in a wide range of situations.