Computing Outlier Thresholds under Interval Uncertainty

Abstract

In many application areas, it is important to detect outliers. The traditional engineering approach to outlier detection is that we start with some “normal” values x₁,..., x _n , compute the sample average E, the sample standard variation σ, and then mark a value x as an outlier if x is outside the k₀-sigma interval [E – k₀ · σ, E + k₀ · σ] (for some pre-selected parameter k₀). In real life, we often have only interval ranges [$\underline{x}_{i}$, $\overline{x}_{i}$] for the normal values x₁,..., x _n . In this case, we only have intervals of possible values for the “outlier threshold” – bounds E – k₀ · σ and E + k₀ · σ. We can therefore identify outliers as values that are outside all k₀-sigma intervals.