Beyond Interval Uncertainty in Describing Statistical Characteristics: Case of Normal Distributions

  • Hung T. Nguyen
  • Vladik Kreinovich
  • Berlin Wu
  • Gang Xiang
Part of the Studies in Computational Intelligence book series (SCI, volume 393)

Abstract

In the previous two chapters, we considered the case when, in addition to the bounds on the cumulative distribution function F(x), we also have additional information about F(x) – e.g., we know that F(x) is smooth (differentiable), and we know the bounds on the derivative of F(x). Sometimes, we have even more information about F(x); we may even know the analytical expression for F(x) – with the parameters which are only known with uncertainty. For example, in practice, when the observed signal is caused by a joint effect of many small components, it is reasonable to assume that the distribution is normal – but the parameters of this normal distribution are only known with uncertainty. Such a situation is analyzed in this chapter.

Keywords

Cumulative Distribution Function Fuzzy Number Quadratic Equation Interval Uncertainty Sample Standard Deviation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Hung T. Nguyen
    • Vladik Kreinovich
      • Berlin Wu
        • Gang Xiang

          There are no affiliations available

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