×

zbMATH — the first resource for mathematics

\(k\)-sample median test for vague data. (English) Zbl 1160.62039
Summary: Classical statistical tests may be sensitive to violations of the fundamental model assumptions inherent in the derivation and construction of these tests. It is obvious that such violations are much more probable in the presence of vague data. Thus nonparametric tests seem to be promising statistical tools. In the present paper, a distribution-free statistical test for the so-called “many-one problem” with vague data is suggested. This test is a generalization of the \(k\)-sample median test. In our approach, we utilize the necessity index of strict dominance, suggested by D. Dubois and H. Prade [Inf. Sci. 30, 183–224 (1983; Zbl 0569.94031)].

MSC:
62G10 Nonparametric hypothesis testing
62F03 Parametric hypothesis testing
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Grzegorzewski, Testing hypotheses in fuzzy environment, Mathware Soft Comput 4 pp 203– (1997) · Zbl 0893.68139
[2] Grzegorzewski, Soft computing for risk evaluation and management pp 55– (2001) · doi:10.1007/978-3-7908-1814-7_4
[3] Grzegorzewski, Statical inference about the median from vague data, Control Cybern 27 pp 447– (1998) · Zbl 0945.62038
[4] Grzegorzewski, Soft methodology and random information systems pp 495– (2004) · doi:10.1007/978-3-540-44465-7_61
[5] Grzegorzewski P. Two-sample median test for vague data. In: Proc 4th Conf European Society for Fuzzy Logic and Technology-Eusflat 2005, Barcelona, September 7-9, 2005. pp 621-626.
[6] Dubois, Ranking fuzzy numbers in the setting of possibility theory, Inform Sci 30 pp 183– (1983) · Zbl 0569.94031
[7] Jonckheere, A distribution-free k-sample test against ordered alternatives, Biometrika 41 pp 133– (1954) · Zbl 0058.35304 · doi:10.1093/biomet/41.1-2.133
[8] Terpstra, The exact probability distribution of the T Statistic for testing against trend and its normal approximation, Indagationes Math 14 pp 433– (1953) · Zbl 0051.36604 · doi:10.1016/S1385-7258(53)50055-1
[9] Chakraborti, Generalization of Mathisen’median test for comparing several treatments with a control, Commun Stat Simul Comput 17 pp 947– (1988)
[10] Gibbons, Nonparametric statical inference (2003)
[11] Dubois, Operations on fuzzy numbers, Int J Syst Sci 9 pp 613– (1978) · Zbl 0383.94045
[12] Kwakernaak, Fuzzy random variables, Part I: definitions and theorems, Inform Sci 15 pp 1– (1978) · Zbl 0438.60004
[13] Kwakernaak, Fuzzy random variables, Part II: algorithms and examples for the discrete case, Inform Sci 17 pp 253– (1979) · Zbl 0438.60005
[14] Kruse, The strong law of large numbers for fuzzy random variables, Inform Sci 28 pp 233– (1982) · Zbl 0571.60039
[15] Puri, Fuzzy random variables, J Math Anal Appl 114 pp 409– (1986) · Zbl 0592.60004
[16] Kruse, Statistics with vague data (1987) · doi:10.1007/978-94-009-3943-1
[17] Bortolan, A review of some methods for ranking fuzzy subsets, Fuzzy Sets Syst 15 pp 1– (1985) · Zbl 0567.90056
[18] Zhu, Fuzzy regression analysis pp 21– (1992)
[19] Grzegorzewski, Statistical modeling, analysis and management of fuzzy data pp 213– (2002) · doi:10.1007/978-3-7908-1800-0_14
[20] Grzegorzewski, Testing Statistical hypotheses with vague data, Fuzzy Sets Syst 112 pp 501– (2000) · Zbl 0948.62010
[21] Grzegorzewski, Fuzzy tests-defuzzification and randomization, Fuzzy Sets Syst 118 pp 437– (2001) · Zbl 0996.62013
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.