Computing Higher Moments under Interval Uncertainty

Abstract

Higher central moments M _h = $\frac{1}{n}$ · $\sum\limits^{n}_{i=1}$ (x _i  − E)^h are very useful in statistical analysis: the third moment M₃ characterizes asymmetry of the corresponding probability distribution, the fourth moment M₄ describes the size of the distribution’s tails, etc. To be more precise, skewness M₃/σ³ is used to characterize asymmetry, and kurtosis M₄/σ⁴ – 3 is used to characterize the size of the tails (3 is subtracted so that kurtosis is 0 for the practically frequent case of a normal distribution).