Beyond Interval Uncertainty in Describing Statistical Characteristics: Case of Normal Distributions
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.
KeywordsCumulative Distribution Function Fuzzy Number Quadratic Equation Interval Uncertainty Sample Standard Deviation
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