Comparison of the Power of Lognormality Tests with Different Right-Tail Alternative Distributions
Publication: Journal of Hydrologic Engineering
Volume 18, Issue 1
Abstract
In flood frequency analysis (FFA), the adequate choice of distribution to fit data is a major problem. The three-parameter lognormal (LN3) distribution has an intermediate tail behavior between the distributions of the Class C (regularly varying distributions) and those of the Class D (subexponential distributions). HYFRAN software performs a complete frequency analysis for approximately twenty distributions often used in hydrology including the LN3 and distributions of Classes C and D. A decision support system (DSS) was added to the HYFRAN software to become the HYFRAN-PLUS software. It allows distinguishing between the distributions of Classes C and D. The objective of the present study is to discriminate between the LN3 distribution and that of Class C of regularly varying distributions (heavier tail) and D of subexponential distributions (lighter tail) and then to improve the current version of the DSS. The power of several normality tests is evaluated for log-transformed variates using a Monte Carlo approach for different alternative hypothesis. The Jarque-Bera test has been found the most powerful on transformed data. Results show a strong dependence between the values of the parameters and the power of the test as well as the quantile estimation errors. Results lead to the development of a LN3 goodness-of-fit procedure, based on the coefficient of variation, the coefficient of skewness and the Jarque-Bera normality test. This procedure will be added to the Decision Support System of the HYFRAN-PLUS software.
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Acknowledgments
The financial support provided by the Natural Sciences and Engineering Research Council of Canada (NSERC) is gratefully acknowledged. The authors would like to thank the anonymous reviewers for their comments that helped to improve the quality of the manuscript.
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Published In
Journal of Hydrologic Engineering
Volume 18 • Issue 1 • January 2013
Pages: 1 - 9
Copyright
© 2013 American Society of Civil Engineers.
History
Received: Sep 22, 2010
Accepted: Jan 13, 2012
Published online: Jan 16, 2012
Published in print: Jan 1, 2013
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