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Calculation of the Kolmogorov-Smirnov and Kuiper statistics over fuzzy samples


Nikolova, N and Ivanova, S and Chin, C and Tenekedjiev, K, Calculation of the Kolmogorov-Smirnov and Kuiper statistics over fuzzy samples, Proceedings of the Jangjeon Mathematical Society, 20, (2) pp. 269-311. ISSN 1598-7264 (2017) [Refereed Article]

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Copyright 2017 JANGJEON Mathematical Society

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DOI: doi:10.23001/pjms2017.20.2.269


Fuzzy samples contain measurements that are only partially associated with their underlying population. This paper offers numerical indices for the difference of population distributions approximated over fuzzy samples. Formulae for the Kolmogorov-Smimov (KS) and Kuiper (Ku) statistics in the case of fuzzy empirical cumulative distribution functions are given. It proves that the supreme in these criteria' standard formulae convert to maxima in the analyzed case, which substantially facilitates calculations. As a by-product, the paper also proves formulae for KS and Ku in the case of rigid samples (that are often used but never properly formalized). If Bootstrap and Monte Carlo simulations are employed to construct the distribution of KS and Ku and find the p-value of the tests, then the quick and reliable calculation of the test statistics in each pseudo reality are of great importance. The derived formula for KS and Ku improve the quality of the simulation itself.

Item Details

Item Type:Refereed Article
Keywords:fuzzy samples, hypothesis testing, Kuiper, Kolmogorov-Smirnov, theorem
Research Division:Mathematical Sciences
Research Group:Statistics
Research Field:Applied statistics
Objective Division:Expanding Knowledge
Objective Group:Expanding knowledge
Objective Field:Expanding knowledge in the information and computing sciences
UTAS Author:Nikolova, N (Professor Nataliya Nikolova)
UTAS Author:Chin, C (Dr Chris Chin)
UTAS Author:Tenekedjiev, K (Professor Kiril Tenekedjiev)
ID Code:116590
Year Published:2017
Deposited By:NC Maritime Engineering and Hydrodynamics
Deposited On:2017-05-15
Last Modified:2018-04-19

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