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Statistical Methods for Fuzzy Data by Reinhard Viertl

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Chapter 11

a. For n fuzzy observations xi* with corresponding characterizing functions ξi (·), i = 1(1)n the characterizing function μ (·) of the fuzzy sample mean can be calculated using the δ-cuts to obtain the characterizing function of and then take the scalar multiplication of fuzzy numbers from Section 3.3.

b. There are two possibilities to estimate the median: The first is to use the smoothed empirical distribution function nsm(·). If the corresponding 0.5 fractile exists, this can be used as estimator for the median. The second possibility is based on the fuzzy valued empirical distribution function n* (·) from Section 6.1. The fuzzy estimate of the median is the fuzzy fractile q0.5* from Section 6.2.

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