Hydrological Applications of the Burr Distribution: Practical Method for Parameter Estimation
Publication: Journal of Hydrologic Engineering
Volume 20, Issue 11
Abstract
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.
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Acknowledgments
Funding from the Italian Ministry of Education, Universities and Research (FIRB-RBFR12BA3Y project) is acknowledged. The authors are also grateful to the journal editor and three reviewers for their comments and suggestions.
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Published In
Journal of Hydrologic Engineering
Volume 20 • Issue 11 • November 2015
Copyright
© 2015 American Society of Civil Engineers.
History
Received: May 13, 2014
Accepted: Feb 9, 2015
Published online: Mar 19, 2015
Discussion open until: Aug 19, 2015
Published in print: Nov 1, 2015
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