The Weibull distribution plays a central role in modeling duration data. Its maximum likelihood estimator is very sensitive to outliers. We propose three robust and explicit Weibull parameter estimators: the quantile least squares, the repeated median and the median/Q n estimator. We derive their breakdown point, influence function, asymptotic variance and study their finite sample properties in a Monte Carlo study. The methods are illustrated on real lifetime data affected by a recording error.

a b s t r a c tThis paper presents a new method for robust online variability extraction in time series. The proposed estimator is simultaneously highly robust and efficient. We derive its breakdown point, influence function, and asymptotic variance and study the finite sample properties in a simulation study.