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Histogram-Covering Approach to Verify Model Reliability
Chongfu Huang and Dongyun Jia

In statistics viewpoint, it is impossible to precisely estimate a probability distribution of a population with a sample whose size is less than the population’s size. In general, with histogram method, estimates resulted from different samples are different, whose cover would reflect the scattering of estimates. Meanwhile, a fuzzy probability distribution would reflect the fuzziness of the probability estimate. According to the consistency principle of possibility/probability, we infer that the model used for calculating fuzzy probabilities is reliable if the fuzzy probability distribution is consist with the cover of histograms, which is a class of probability distributions of the probabilities that the event occurs in intervals. In this paper, with simulation results, we verify that the interior-outer-set model is basically reliable.

Keywords: Probability, possibility, fuzzy probability, reliability, histogram, interior-outer-set model

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