IDEAS home Printed from https://ideas.repec.org/a/spr/stpapr/v56y2015i1p61-82.html
   My bibliography  Save this article

Two-sample Kolmogorov–Smirnov fuzzy test for fuzzy random variables

Author

Listed:
  • Gholamreza Hesamian
  • Jalal Chachi

Abstract

In this paper, a new method is proposed for developing two-sample Kolmogorov–Smirnov test for the case when the data are observations of fuzzy random variables, and the hypotheses are imprecise rather than crisp. In this approach, first a new notion of fuzzy random variables is introduced. Then, the $$\alpha $$ α -pessimistic values of the imprecise observations are transacted to extend the usual method of two-sample Kolmogorov–Smirnov test. To do this, the concepts of fuzzy cumulative distribution function and fuzzy empirical cumulative distribution function are defined. We also develop a well-known large sample property of the classical empirical cumulative distribution function for fuzzy empirical cumulative distribution function. In addition, the Kolmogorov–Smirnov two-sample test statistic is extended for fuzzy random variables. After that, the method of computing the so-called fuzzy $$p$$ p value is introduced to evaluate the imprecise hypotheses of interest. In this regard, applying an index called credibility degree, the obtained fuzzy $$p$$ p value and the crisp significance level are compared. The result provides a fuzzy test function which leads to some degrees to accept or to reject the null hypothesis. Some numerical examples are provided throughout the paper clarifying the discussions made in this paper. Copyright Springer-Verlag Berlin Heidelberg 2015

Suggested Citation

  • Gholamreza Hesamian & Jalal Chachi, 2015. "Two-sample Kolmogorov–Smirnov fuzzy test for fuzzy random variables," Statistical Papers, Springer, vol. 56(1), pages 61-82, February.
    • Handle: RePEc:spr:stpapr:v:56:y:2015:i:1:p:61-82
    DOI: 10.1007/s00362-013-0566-2
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s00362-013-0566-2
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s00362-013-0566-2?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Ana Colubi & Renato Coppi & Pierpaolo D’urso & Maria angeles Gil, 2007. "Statistics with fuzzy random variables," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(3), pages 277-303.
    2. Colubi, Ana & Gonzalez-Rodriguez, Gil, 2007. "Triangular fuzzification of random variables and power of distribution tests: Empirical discussion," Computational Statistics & Data Analysis, Elsevier, vol. 51(9), pages 4742-4750, May.
    3. Shapiro, Arnold F., 2009. "Fuzzy random variables," Insurance: Mathematics and Economics, Elsevier, vol. 44(2), pages 307-314, April.
    4. S. Taheri & G. Hesamian, 2013. "A generalization of the Wilcoxon signed-rank test and its applications," Statistical Papers, Springer, vol. 54(2), pages 457-470, May.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Vahid Ranjbar & Gholamreza Hesamian, 2020. "Copula function for fuzzy random variables: applications in measuring association between two fuzzy random variables," Statistical Papers, Springer, vol. 61(1), pages 503-522, February.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. A. Blanco-Fernández & A. Ramos-Guajardo & A. Colubi, 2013. "Fuzzy representations of real-valued random variables: applications to exploratory and inferential studies," METRON, Springer;Sapienza Università di Roma, vol. 71(3), pages 245-259, November.
    2. Shvedov, Alexey, 2016. "Estimating the means and the covariances of fuzzy random variables," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 42, pages 121-138.
    3. Ming Shan & Yu-Shan Li & Bon-Gang Hwang & Jia-En Chua, 2021. "Productivity Metrics and Its Implementations in Construction Projects: A Case Study of Singapore," Sustainability, MDPI, vol. 13(21), pages 1-19, November.
    4. Mbairadjim Moussa, A. & Sadefo Kamdem, J. & Terraza, M., 2014. "Fuzzy value-at-risk and expected shortfall for portfolios with heavy-tailed returns," Economic Modelling, Elsevier, vol. 39(C), pages 247-256.
    5. Alfred Mbairadjim Moussa & Jules Sadefo Kamdem, 2022. "A fuzzy multifactor asset pricing model," Annals of Operations Research, Springer, vol. 313(2), pages 1221-1241, June.
    6. Seongmin Kang & Seong-Dong Kim & Eui-Chan Jeon, 2020. "Ammonia Emission Sources Characteristics and Emission Factor Uncertainty at Liquefied Natural Gas Power Plants," IJERPH, MDPI, vol. 17(11), pages 1-10, May.
    7. Mbairadjim Moussa, A. & Sadefo Kamdem, J. & Shapiro, A.F. & Terraza, M., 2014. "CAPM with fuzzy returns and hypothesis testing," Insurance: Mathematics and Economics, Elsevier, vol. 55(C), pages 40-57.
    8. de Andrés-Sánchez, Jorge & González-Vila Puchades, Laura, 2017. "The valuation of life contingencies: A symmetrical triangular fuzzy approximation," Insurance: Mathematics and Economics, Elsevier, vol. 72(C), pages 83-94.
    9. Emily Tang & Chelsea Jones & Lorraine Smith-MacDonald & Matthew R. G. Brown & Eric H. G. J. M. Vermetten & Suzette Brémault-Phillips, 2021. "Decreased Emotional Dysregulation Following Multi-Modal Motion-Assisted Memory Desensitization and Reconsolidation Therapy (3MDR): Identifying Possible Driving Factors in Remediation of Treatment-Resi," IJERPH, MDPI, vol. 18(22), pages 1-12, November.
    10. Colubi, Ana & Ramos-Guajardo, Ana Belén, 2023. "Fuzzy sets and (fuzzy) random sets in Econometrics and Statistics," Econometrics and Statistics, Elsevier, vol. 26(C), pages 84-98.
    11. Giacomo Benini & Adam Brandt & Valerio Dotti & Hassan El-Houjeiri, 2023. "The Economic and Environmental Consequences of the Petroleum Industry Extensive Margin," Working Papers 2023:14, Department of Economics, University of Venice "Ca' Foscari".
    12. Belles-Sampera, Jaume & Merigó, José M. & Guillén, Montserrat & Santolino, Miguel, 2013. "The connection between distortion risk measures and ordered weighted averaging operators," Insurance: Mathematics and Economics, Elsevier, vol. 52(2), pages 411-420.
    13. Abbas Parchami & S. Mahmoud Taheri & Reinhard Viertl & Mashaallah Mashinchi, 2018. "Minimax test for fuzzy hypotheses," Statistical Papers, Springer, vol. 59(4), pages 1623-1648, December.
    14. Ravi Shankar Kumar & M. K. Tiwari & A. Goswami, 2016. "Two-echelon fuzzy stochastic supply chain for the manufacturer–buyer integrated production–inventory system," Journal of Intelligent Manufacturing, Springer, vol. 27(4), pages 875-888, August.
    15. Sadefo Kamdem, J. & Mbairadjim Moussa, A. & Terraza, M., 2012. "Fuzzy risk adjusted performance measures: Application to hedge funds," Insurance: Mathematics and Economics, Elsevier, vol. 51(3), pages 702-712.
    16. Shima Yosefi & Mohsen Arefi & Mohammad Ghasem Akbari, 2016. "A new approach for testing fuzzy hypotheses based on likelihood ratio statistic," Statistical Papers, Springer, vol. 57(3), pages 665-688, September.
    17. Antonio Faúndez-Ugalde & Patricia Toledo-Zúñiga & Pedro Castro-Rodríguez, 2022. "Tax Sustainability: Tax Transparency in Latin America and the Chilean Case," Sustainability, MDPI, vol. 14(4), pages 1-17, February.
    18. Shapiro, Arnold F., 2013. "Modeling future lifetime as a fuzzy random variable," Insurance: Mathematics and Economics, Elsevier, vol. 53(3), pages 864-870.
    19. A. Shibu & M. Reddy, 2014. "Optimal Design of Water Distribution Networks Considering Fuzzy Randomness of Demands Using Cross Entropy Optimization," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 28(12), pages 4075-4094, September.
    20. Rachida Hennani & Michel Terraza, 2012. "Value-at-Risk stressée chaotique d’un portefeuille bancaire," Working Papers 12-23, LAMETA, Universtiy of Montpellier, revised Sep 2012.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:stpapr:v:56:y:2015:i:1:p:61-82. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.