Cramér-von Mises and Anderson-Darling Goodness-of-Fit Tests for the Two-Parameter Kappa Distribution
Publication: Journal of Hydrologic Engineering
Volume 18, Issue 12
Abstract
In hydrology, one often needs to use goodness-of-fit tests to describe how well a statistical frequency model fits a set of observations. The two-parameter kappa (KAP2) distribution is a frequency model that has already shown useful hydrological applications. The Cramér-von Mises and the Anderson-Darling tests are among the most frequently used goodness-of-fit tests in statistical practice. To apply these tests to the KAP2 distribution, statistical tables of critical values are needed. Such tables already exist for various other statistical distributions, but have not yet been developed for KAP2. This paper fills the gap by developing such tables for the KAP2 distribution. These tables are based on large sample theory, but correction formulas are also provided that make them applicable to small samples. KAP2 and the generalized Pareto distribution (GPD) are two subfamilies of the four-parameter kappa distribution that have been used in extreme value hydrological applications in the past. A detailed example is given that shows the usefulness of the KAP2 model for fitting some types of extreme hydrological data, and another example is provided to show how KAP2 may be used as an alternative to the GPD in certain extreme value applications.
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Published In
Journal of Hydrologic Engineering
Volume 18 • Issue 12 • December 2013
Pages: 1749 - 1757
Copyright
© 2013 American Society of Civil Engineers.
History
Received: May 23, 2012
Accepted: Sep 26, 2012
Published online: Sep 29, 2012
Discussion open until: Feb 28, 2013
Published in print: Dec 1, 2013
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