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

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 centra...

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Veröffentlicht in:Fuzzy information and engineering 2011-12, Vol.3 (4), p.351-358
Hauptverfasser: Sadeghpour-Gildeh, Bahram, Rahimpour, Sedigheh
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Sprache:eng
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Zusammenfassung: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.
ISSN:1616-8658
1616-8666
DOI:10.1007/s12543-011-0090-9