Goodness-of-Fit Tests for Generalized Normal Distribution for Use in Hydrological Frequency Analysis
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The use of three-parameter generalized normal (GNO) as a hydrological frequency distribution is well recognized, but its application is limited due to unavailability of popular goodness-of-fit (GOF) test statistics. This study develops popular empirical distribution function (EDF)-based test statistics to investigate the goodness-of-fit of the GNO distribution. The focus is on the case most relevant to the hydrologist, namely, that in which the parameter values are unidentified and estimated from a sample using the method of L-moments. The widely used EDF tests such as Kolmogorov–Smirnov, Cramer von Mises, and Anderson–Darling (AD) are considered in this study. A modified version of AD, namely, the Modified Anderson–Darling (MAD) test, is also considered and its performance is assessed against other EDF tests using a power study that incorporates six specific Wakeby distributions (WA-1, WA-2, WA-3, WA-4, WA-5, and WA-6) as the alternative distributions. The critical values of the proposed test statistics are approximated using Monte Carlo techniques and are summarized in chart and regression equation form to show the dependence of shape parameter and sample size. The performance results obtained from the power study suggest that the AD and a variant of the MAD (MAD-L) are the most powerful tests. Finally, the study performs case studies involving annual maximum flow data of selected gauged sites from Irish and US catchments to show the application of the derived critical values and recommends further assessments to be carried out on flow data sets of rivers with various hydrological regimes.
KeywordsFlood frequency analysis goodness-of-fit tests generalized normal distribution hydrology
The author would like to acknowledge the financial support in the form of faculty start-up fund made available by the Nanjing University of Information Science and Technology (NUIST), Nanjing, China. Selected Irish flood data sets were obtained during the author’s stay at NUI Galway, Ireland. The data series of selected stations are also available freely at the Irish Office of Public Works, Ireland: http://www.opw.ie/hydro-data. The selected US data sets were freely obtained from the USGS website: https://nwis.waterdata.usgs.gov/nwis. Comments and suggestions from two anonymous reviewers are gratefully acknowledged.
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