Abstract
The Kolmogorov-Smirnov two-sample test (K-S two sample test) is a goodness-of-fit test which is used to determine whether two underlying one-dimensional probability distributions differ. In order to find the statistic pivot of a K-S two-sample test, we calculate the cumulative function by means of empirical distribution function. When we deal with fuzzy data, it is essential to know how to find the empirical distribution function for continuous fuzzy data. In our paper, we define a new function, the weight function that can be used to deal with continuous fuzzy data. Moreover we can divide samples into different classes. The cumulative function can be calculated with those divided data. The paper explains that the K-S two sample test for continuous fuzzy data can make it possible to judge whether two independent samples of continuous fuzzy data come from the same population. The results show that it is realistic and reasonable in social science research to use the K-S two-sample test for continuous fuzzy data.
Access provided by Autonomous University of Puebla. Download to read the full chapter text
Chapter PDF
Similar content being viewed by others
Keywords
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
References
Conover, W.J.: Practical nonparametric statistics, New York (1971)
Cheng, C.H.: A new approach for ranking fuzzy numbers by distance method. Fuzzy sets and systems 95(3), 307–317 (1998)
Dixon, W.J.: Power under normality of several nonparametric tests. The Annals of Mathematical Statistics 25(3), 610–614 (1954)
Epstein, B.: Comparison of Some Non-Parametric Tests against Normal Alternatives with an Application to Life Testing. Journal of the American Statistical Association 50(271), 894–900 (1955)
Gaenssler, P., Stute, W.: Empirical processes: a survey of results for independent and identically distributed random variables. Annals of Applied Probability 7(2), 193–243 (1979)
Gine, E., Zinn, J.: Some limit theorems for empirical measures (with discussion). Annals of Applied Probability 12(4), 929–989 (1984)
Thomas Jr., G.B.: 11th Thomas Calculus. Pearson Education, Inc., Boston (2005)
Kaufmann, A., Gupta, M.M.: Fuzzy mathematical models in engineering and management science. Elsevier Science Publishers BV, New York (1988)
Larson, R., Hostetler, R., Edwards, B.H.: Essential Calculus: Early Transcendental Functions. Houghton Mifflin Company, Boston (2008)
Liou, T.S., Wang, M.J.: Ranking fuzzy numbers with integral value. Fuzzy Sets and Systems 50(3), 247–255 (1992)
Serfling, R.J.: Approximation theorems of mathematical statistics, New York (1980)
Schroer, G., Trenkler, D.: Exact and randomization distributions of Kolmogorov-Smirnov tests two or three samples. Computational Statistics and Data Analysis 20(2), 185–202 (1995)
Siegel, S., Castellan, N.J.: Nonparametric statistics for the behavioral sciences, 2nd edn., New York (1988)
Smirnov, N.V.: Estimate of deviation between empirical distribution functions in two independent samples (Russian) Bulletin Moscow Univ. 2(2), 3–16 (1939)
Yager, R.R.: A procedure for ordering fuzzy subsets of the unit interval. Information Science 24(2), 143–161 (1981)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2010 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Lin, PC., Wu, B., Watada, J. (2010). Kolmogorov-Smirnov Two Sample Test with Continuous Fuzzy Data. In: Huynh, VN., Nakamori, Y., Lawry, J., Inuiguchi, M. (eds) Integrated Uncertainty Management and Applications. Advances in Intelligent and Soft Computing, vol 68. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-11960-6_17
Download citation
DOI: https://doi.org/10.1007/978-3-642-11960-6_17
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-11959-0
Online ISBN: 978-3-642-11960-6
eBook Packages: EngineeringEngineering (R0)