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 |
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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. |
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ISSN: | 1616-8658 1616-8666 |
DOI: | 10.1007/s12543-011-0090-9 |