A fuzzy bootstrap test for the mean with D p,q -distance

Bahram Sadeghpour-Gildeh and Sedigheh Rahimpour ()
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Bahram Sadeghpour-Gildeh: University of Mazandaran
Sedigheh Rahimpour: University of Mazandaran

Fuzzy Information and Engineering, 2011, vol. 3, issue 4, 351-358

Abstract: Abstract In this paper, we consider the problem of testing a simple hypothesis about the mean of a fuzzy random variable. For this purpose, we take a distance between the sample mean and the mean in the null hypothesis as a test statistic. An asymptotic test about the fuzzy mean is obtained by using a central limit theorem. The asymptotical distribution is ω 2-distribution. The ω 2-distribution is only known for special cases, thus we have considered random LR-fuzzy numbers. In the fuzzy concept, in addition to the existence of several versions of the central limit theorem, there is another practical disadvantage: The limit law is, in most cases, difficult to handle. Therefore, the central limit theorem for fuzzy random variable does not seem to be a very useful tool to make inferences on the mean of fuzzy random variable. Thus we use the bootstrap technique. Finally, by means of a simulation study, we show that the bootstrap method is a powerful tool in the statistical hypothesis testing about the mean of fuzzy random variables.

Keywords: Bootstrap sampling; Fuzzy random variable; D p; q -distance; LR-fuzzy numbers (search for similar items in EconPapers)
Date: 2011
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DOI: 10.1007/s12543-011-0090-9

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