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Statistical Methods for Fuzzy Data by Reinhard Viertl

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Part IV

CLASSICAL STATISTICAL INFERENCE FOR FUZZY DATA

Classical statistical inference is based on the assumption that stochastic quantities X have an underlying true probability model P0. In order to estimate P0 usually a family of possible probability distributions is considered, i.e. ={P : P possible distribution of X}.

In the case of parametric families {Pθ : θ ∈ Θ} the generalization of estimators to the situation of fuzzy data is necessary, i.e. to construct estimations for the true parameter θ0 of the underlying probability distribution Pθ0 of X.

Next a generalization of confidence regions in the case of fuzzy data is given, and the resulting fuzzy confidence regions are typical examples of fuzzy sets.

Based on fuzzy samples also test statistics have to be adapted. The values of a test statistic in the case of fuzzy data become fuzzy numbers. Therefore test decisions are not as simple as in the standard situation of data in the form of numbers or vectors. The resulting fuzzy values of test statistics contain more information than in the classical situation because fuzzy values of a test statistic can make it clear that more data are needed in order to provide a well-based decision. ...

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