Comparisons of outlier detection procedures in weibull or extreme-value distribution

Abstract

We carried out an empirical performance study of outlier detection procedures for Weibull or extreme–value distributions using a mixture model in which a known number of randomly chosen observations are contaminated. Procedures studied were: L(L') based on leaps (differences of adjacent observations divided by expectation), V, Q and W (Mann, 1982), R₁(R'₁), R₂(R'₂), R₃(R'₃) (Dixon, 1950) and G(G') (Grubbs, 1950). Percentage points for statistics L(L'), R₁(R'₁), R₂(R'₂), R₃(R'₃) and G(G') were computed empirically for the extreme-value distribution and are tabulated. The procedures L(L') (or equivalently in power V) performed best, with few exceptions, for the contaminated model tested. The Grubb statistic G' performed well in testing for lower outliers. Mann's W , which was best for the labeled slippage was substantially poorer than the others for the mixture model. Dixon's R₁(R'₁)is recommended as a generally useful test for sample sizes in the range investigated (n=5,20)

Keywords:

• outlier detection
• extreme-value
• distribution
• Weibull distribution
• Dixon's statistics
• Grubb's statistic