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Momeni, Fereshteh, sadeghpour Gildeh, Bahram, Hesamian, Gholamreza. (1396). Kolmogorov-smirnov two-sample test in fuzzy environment. سامانه مدیریت نشریات علمی, 6(2), 147-155. doi: 10.22098/jhs.2017.2669
Fereshteh Momeni; Bahram sadeghpour Gildeh; Gholamreza Hesamian. "Kolmogorov-smirnov two-sample test in fuzzy environment". سامانه مدیریت نشریات علمی, 6, 2, 1396, 147-155. doi: 10.22098/jhs.2017.2669
Momeni, Fereshteh, sadeghpour Gildeh, Bahram, Hesamian, Gholamreza. (1396). 'Kolmogorov-smirnov two-sample test in fuzzy environment', سامانه مدیریت نشریات علمی, 6(2), pp. 147-155. doi: 10.22098/jhs.2017.2669
Momeni, Fereshteh, sadeghpour Gildeh, Bahram, Hesamian, Gholamreza. Kolmogorov-smirnov two-sample test in fuzzy environment. سامانه مدیریت نشریات علمی, 1396; 6(2): 147-155. doi: 10.22098/jhs.2017.2669

Kolmogorov-smirnov two-sample test in fuzzy environment

Journal of Hyperstructures
دوره 6، شماره 2، اسفند 2017، صفحه 147-155    اصل مقاله (314.17 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22098/jhs.2017.2669
نویسندگان
Fereshteh Momeni* 1؛ Bahram sadeghpour Gildeh2؛ Gholamreza Hesamian3
1Department of Statistics, Behshahr branch, Islamic Azad University, Behshahr, Iran
2Department of Statistics, Faculty of Mathematical Sciences, Ferdowsi University of Mashhad , Iran
3Department of Statistics, University of Payamenoor, 19395-3697, Tehran, Iran
چکیده
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.
کلیدواژه‌ها
Fuzzy data؛ Kolmogorov-Smirnov test؛ Goodness of fit test؛ Dp؛ q-ranking method؛ empirical distribution function
مراجع
[1] D. Dubois, H.Prade, Ranking of fuzzy numbers in the setting of possibility theory,Information Sciences,30(1983),183-224.
[2] P. Gaenssler and W. Stute, Emperical process: a survey of results for independent and identically distributed random variables, Ann. Probab, 7 (1979), 193-243.
[3] J. D. Gibbons, S. Chakraborti, Non-Parametric Statistical Inference, New York: Marcel Dekker (2003).
[4] E. Gine and J. Zinn, Some limit theorem for emperical measure ( with discussion), Ann. Probab, 12 (1984), 929-989.
[5] G. Hesamian and Chachi, Kolmogorov-Smirnov two sample test for fuzzy random variables, Statistical Papers, 56 (2015), 61-82.
[6] P. Lin, B. Wu and J. Watada Kolmogorov-Smirnov two sample test with contin-uous fuzzy data Advances in intelligent and soft computing, 68 (2010), 175-186.
[7] K. H. Lee, First Course on Fuzzy Theory and Applications, Heidelberg: Springer (2005).

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