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The return rate in imprecision risk may be described as a fuzzy probabilistic set [Piasecki, 2011a]. On the other side, in [Piasecki, Tomasik 2013] is shown that the Normal Inverse Gaussiandistribution is the best matching probability distribution of logarithmic returns on Warsaw Stock Exchange. There will be presented the basic properties if imprecise return with the Normal Inverse Gaussian distribution of future value logarithm. The existence of distribution of expected return rate is discussed. All obtained results may be immediately applied for effectiveness analysis at risk of uncertainty and imprecision [Pi-asecki, 2011c]
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