Discriminating between the Lognormal and the Log-Logistic Distributions for Hydrological Frequency Analysis
Publication: Journal of Hydrologic Engineering
Volume 17, Issue 1
Abstract
Discriminating between competitive statistical models is an important problem in hydrological frequency analysis. The present study deals with discrimination between the two-parameter lognormal ( ) and the two-parameter log-logistic ( ) distributions, or, equivalently, between the normal ( ) and the logistic ( ) distributions. Previous work using the likelihood ratio (LR) statistic suggested that discrimination between these distributions is difficult, and that criteria other than LR need to be studied in hope of finding criteria with better discriminating power. In the present study, several criteria other than LR are considered, and their ability to discriminate between the and distributions is assessed using Monte Carlo simulation. The results confirm previous findings that discrimination between the two distributions is difficult with small samples, but a criterion based on the Shapiro-Wilk statistic appears to be the most appropriate for sample sizes typically encountered in hydrology. Two hydrological examples are presented to illustrate how obtained results can be implemented in practice.
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Acknowledgments
We appreciate the helpful comments provided by three referees, which helped in improving this paper. The financial support of the Natural Sciences and Engineering Research Council of Canada is gratefully acknowledged.
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Published In
Journal of Hydrologic Engineering
Volume 17 • Issue 1 • January 2012
Pages: 160 - 167
Copyright
© 2012 American Society of Civil Engineers.
History
Received: Sep 21, 2010
Accepted: Apr 26, 2011
Published online: Apr 29, 2011
Published in print: Jan 1, 2012
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