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Randomized versus non-randomized hypergeometric hypothesis testing with crisp and fuzzy hypotheses

Author

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  • Nataliya Chukhrova

    (University of Hamburg)

  • Arne Johannssen

    (University of Hamburg)

Abstract

This paper is concerned with fuzzy hypothesis testing in the framework of the randomized and non-randomized hypergeometric test for a proportion. Moreover, we differentiate between a test of significance and an alternative test to control the type I error or both error types simultaneously. In contrast to classical (non-)randomized hypothesis testing, fuzzy hypothesis testing provides an additional gradual consideration of the indifference zone in compliance with expert opinion or user priorities. In particular, various types of hypotheses with user-specified membership functions can be formulated. Additionally, the proposed test methods are compared via a comprehensive case study, which demonstrates the high flexibility of fuzzy hypothesis testing in practical applications.

Suggested Citation

  • Nataliya Chukhrova & Arne Johannssen, 2020. "Randomized versus non-randomized hypergeometric hypothesis testing with crisp and fuzzy hypotheses," Statistical Papers, Springer, vol. 61(6), pages 2605-2641, December.
    • Handle: RePEc:spr:stpapr:v:61:y:2020:i:6:d:10.1007_s00362-018-1058-1
    DOI: 10.1007/s00362-018-1058-1
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    References listed on IDEAS

    as
    1. Bernhard Arnold, 1996. "An approach to fuzzy hypothesis testing," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 44(1), pages 119-126, December.
    2. P. Filzmoser & R. Viertl, 2004. "Testing hypotheses with fuzzy data: The fuzzy p-value," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 59(1), pages 21-29, February.
    3. Hamzeh Torabi & Javad Behboodian, 2007. "Likelihood ratio tests for fuzzy hypotheses testing," Statistical Papers, Springer, vol. 48(3), pages 509-522, September.
    4. Abbas Parchami & S. Taheri & Mashaallah Mashinchi, 2012. "Testing fuzzy hypotheses based on vague observations: a p-value approach," Statistical Papers, Springer, vol. 53(2), pages 469-484, May.
    5. Abbas Parchami & S. Taheri & Mashaallah Mashinchi, 2010. "Fuzzy p-value in testing fuzzy hypotheses with crisp data," Statistical Papers, Springer, vol. 51(1), pages 209-226, January.
    6. Hamzeh Torabi & Javad Behboodian & S. Taheri, 2006. "Neyman–Pearson Lemma for Fuzzy Hypotheses Testing with Vague Data," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 64(3), pages 289-304, December.
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