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New Goodness-of-Fit Tests for the Kumaraswamy Distribution: A Simulation Study
Version 1
: Received: 10 March 2024 / Approved: 11 March 2024 / Online: 11 March 2024 (18:09:38 CET)
A peer-reviewed article of this Preprint also exists.
Giles, D.E. New Goodness-of-Fit Tests for the Kumaraswamy Distribution. Stats 2024, 7, 373-389. Giles, D.E. New Goodness-of-Fit Tests for the Kumaraswamy Distribution. Stats 2024, 7, 373-389.
Abstract
The two-parameter distribution introduced by Kumaraswamy (1980) is a very flexible alternative to the Beta distribution with the same (0,1) support. Originally proposed in the field of hydrology, it has subsequently received a good deal of positive attention in both the theoretical and applied statistics literatures. Interestingly, the problem of testing formally for the appropriateness of the Kumaraswamy distribution appears to have received little or no attention to date. To fill this gap, in this paper we apply the “biased transformation” methodology proposed by Raschke (2009) to several standard goodness-of-fit tests based on the empirical distribution function. A simulation study reveals that these (modified) tests perform well in the context of the Kumaraswamy distribution, in terms of both low size distortion, and respectable power. In particular, the “biased transformation” Anderson-Darling test dominates the other tests that are considered.
Keywords
goodness-of-fit testing; empirical distribution function; Kumaraswamy distribution
Subject
Computer Science and Mathematics, Probability and Statistics
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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