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

journal contribution
posted on 2023-05-19, 04:48 authored by Nataliya NikolovaNataliya Nikolova, Ivanova, S, Christopher ChinChristopher Chin, Kiril TenekedjievKiril Tenekedjiev
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.

History

Publication title

Proceedings of the Jangjeon Mathematical Society

Volume

20

Pagination

269-311

ISSN

1598-7264

Department/School

Australian Maritime College

Publisher

Jangjeon Research Institute for Mathematical Sciences and Physics

Place of publication

South Korea

Rights statement

Copyright 2017 JANGJEON Mathematical Society

Repository Status

  • Restricted

Socio-economic Objectives

Expanding knowledge in the information and computing sciences

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