Kolmogorov-smirnov two-sample test in fuzzy environment

Document Type : Research Paper

Authors

1 Department of Statistics, Behshahr branch, Islamic Azad University, Behshahr, Iran

2 Department of Statistics, Faculty of Mathematical Sciences, Ferdowsi University of Mashhad , Iran

3 Department of Statistics, University of Payamenoor, 19395-3697, Tehran, Iran

Abstract

Kolmogorov-Smirnov two-sample test, is a common test for fitting statistical population model. Statistic of this test is defined based on the empirical distribution function and so, sorting sample observations plays a key role in determination of the empirical distribution function. In this paper, a new approach to generalize the Kolmogorov-Smirnov two-sample test has been provided, where the sample observations is defined as imprecise numbers and hypotheses testing are precisely defined. To do this, first, a new method for ranking fuzzy numbers using Dp,q metric was proposed. We used this metric for separating fuzzy data to separate classes and then placed fuzzy data in certain classes. Then, we have defined an extension of the empirical distribution function and similar to the classic case, calculated Kolmogorov-Smirnov two-sample test statistic and accomplished to make decision about accepting or rejecting the null hypothesis as completely exact. Finally, with a numerical example the proposed approach was evaluated and compared.

Keywords

References

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Journal of Hyperstructures
Volume 6, Issue 2
December 2017
Pages 147-155

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