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Independent k-Sample Equality Distribution Test Based on the Fuzzy Representation

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Soft Methods for Data Science (SMPS 2016)

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 456))

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Abstract

Classical tests for the equality of distributions of real-valued random variables are widely applied in Statistics. When the normality assumption for the variables fails, non-parametric techniques are to be considered; Mann-Whitney, Wilcoxon, Kruskal-Wallis, Friedman tests, among other alternatives. Fuzzy representations of real-valued random variables have been recently shown to describe in an effective way the statistical behaviour of the variables. Indeed, the expected value of certain fuzzy representations fully characterizes the distribution of the variable. The aim of this paper is to use this characterization to test the equality of distribution for two or more real-valued random variables, as an alternative to classical procedures. The inferential problem is solved through a parametric test for the equality of expectations of fuzzy-valued random variables. Theoretical results on inferences for fuzzy random variables support the validity of the test. Besides, simulation studies and practical applications show the empirical goodness of the method.

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Acknowledgments

The research in this paper is partially supported by the Spanish National Grant MTM2013-44212-P, and the Regional Grant FC-15-GRUPIN-14-005. Their financial support is gratefully acknowledged.

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Authors and Affiliations

  1. Departament of Statistics and Operational Research, University of Oviedo, C/Calvo Sotelo, s/n, 33007, Oviedo, Spain

    Angela Blanco-Fernández & Ana B. Ramos-Guajardo

Authors
  1. Angela Blanco-Fernández
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  2. Ana B. Ramos-Guajardo
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Corresponding author

Correspondence to Angela Blanco-Fernández .

Editor information

Editors and Affiliations

  1. Department of Statistical Sciences, Sapienza University of Rome, Rome, Italy

    Maria Brigida Ferraro

  2. Department of Statistical Sciences, Sapienza University of Rome, Roma, Italy

    Paolo Giordani

  3. Dept of Basic & Applied Sciences Engg, Sapienza University of Rome, Rome, Italy

    Barbara Vantaggi

  4. Dept of Stoc Metds,Polish Academy of Sci, Systems Research Institute, Warsaw, Poland

    Marek Gagolewski

  5. Dept of Statis&OR and MD, Univ de Oviedo, Oviedo, Spain

    María Ángeles Gil

  6. Dept of Stoc Metds,Polish Aca of Science, Systems Res Inst, Warsaw, Poland

    Przemysław Grzegorzewski

  7. Sys Res Inti, Dept of Stoch Methods, Polish Acadmy Sci in Warsaw, Warsaw, Poland

    Olgierd Hryniewicz

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Blanco-Fernández, A., Ramos-Guajardo, A.B. (2017). Independent k-Sample Equality Distribution Test Based on the Fuzzy Representation. In: Ferraro, M., et al. Soft Methods for Data Science. SMPS 2016. Advances in Intelligent Systems and Computing, vol 456. Springer, Cham. https://doi.org/10.1007/978-3-319-42972-4_8

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  • DOI: https://doi.org/10.1007/978-3-319-42972-4_8

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-42971-7

  • Online ISBN: 978-3-319-42972-4

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