title: Robust Fitting of a Weibull Model with Optional Censoring.
abstract: The Weibull family is widely used to model failure data, or lifetime data, although the classical two-parameter Weibull distribution is limited to positive data and monotone failure rate. The parameters of the Weibull model are commonly obtained by maximum likelihood estimation; however, it is well-known that this estimator is not robust when dealing with contaminated data. A new robust procedure is introduced to fit a Weibull model by usingL2distance, i.e. integrated square distance, of the Weibull probability density function. The Weibull model is augmented with a weight parameter to robustly deal with contaminated data. Results comparing a maximum likelihood estimator with anL2estimator are given in this article, based on both simulated and real data sets. It is shown that this newL2parametric estimation method is more robust and does a better job than maximum likelihood in the newly proposed Weibull model when data are contaminated. The same preference forL2distance criterion and the new Weibull model also happens for right-censored data with contamination.
authors.affiliation: Rice University, Department of Statistics, 6100 Main St. MS-138, Houston, TX 77005, U.S.A.
authors.forename: Jingjing
authors.initials: J
authors.lastname: Yang
authors.forename: David W
authors.initials: DW
authors.lastname: Scott
keywords: Contamination; L2 distance; Maximum likelihood; Right-censored data; Robust estimator; Weibull distribution