Computing Mean, Variance, Higher Moments, and Their Linear Combinations under Interval Uncertainty: A Brief Summary

Abstract

In the previous chapters, we described several results and algorithms for computing:

• the mean E,

• the variance V = σ² = $\frac{1}{n}$ · $\sum\limits^{n}_{i=1}{(x_{i} - E)}^{2}$,

• more generally, higher central moments M _h = $\frac{1}{n}$ · $\sum\limits^{n}_{i=1}{(x_{i} - E)}^{h}$ and

• statistically useful linear combinations of these characteristics – such as the lower and upper endpoints of the confidence interval L = E – k₀ · σ and U = E + k₀ · σ, where the parameter k₀ is usually taken as k₀ = 2, k₀ = 3, and k₀ = 6.