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Statistical Methods for Fuzzy Data by Reinhard Viertl

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17.3 Continuous case

For continuous stochastic models X ~ f(·|θ), θ ∈ Θ with continuous parameter Θ and fuzzy a posteriori density π*(·|D*) on the parameter space Θ, the fuzzy predictive density f*(·|D*) of X is defined by the generalization of the standard predictive density:

Unnumbered Display Equation

where the integral is the generalized integral defined in Section 3.6.

Remark 17.3:

f*(·|D*) is a fuzzy density in the sense of Definition 8.1 from Section 8.1.

Example 17.2

In continuation of Example 16.1 the calculation of the fuzzy predictive density f*(·|*) can be calculated.

In Figure 17.2 some δ-level curves of f*(·|*) are depicted for the fuzzy sample x1*,…,x8* from Figure 16.1. The combined fuzzy sample * is constructed by the minimum combination rule.

Figure 17.2 δ-level curves of f*(·|*).

c17f002.eps

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