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

Nataliya Chukhrova () and Arne Johannssen ()
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Nataliya Chukhrova: University of Hamburg
Arne Johannssen: University of Hamburg

Statistical Papers, 2020, vol. 61, issue 6, No 15, 2605-2641

Abstract: 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.

Keywords: Fuzzy statistics; Fuzzy hypotheses; Hypergeometric test; Hypothesis testing for a proportion; Randomized test; Test of significance; Alternative test; Creditworthiness (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/s00362-018-1058-1

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