Robust Fitting of a Three-Parameter Weibull Model for Contaminated Survival Data with Optional Censoring

• Activity Number: 690
• Type: Contributed
• Date/Time: Thursday, August 8, 2013 : 10:30 AM to 12:20 PM
• Sponsor: Section on Statistical Computing
• Author(s): Jingjing Yang*+ and David Scott
• Companies: Rice University and Rice University
• Keywords: Weibull distribution ; L2 distance ; Robust estimator ; Maximum likelihood ; Right censored data ; Contamination

Abstract

The Weibull family is widely used to model failure data, or lifetime survival data, although the classical two-parameter Weibull distribution is limited with positive data and monotone failure rate. The parameters of the Weibull model are commonly obtained by maximum likelihood estimation; however, some unreasonable estimates may result when dealing with contaminated data. We introduce a new robust way to fit Weibull model by using L2 distance, i.e. integrated square distance of the Weibull probability density function. A new three-parameter Weibull model is proposed in this paper to robustly deal with contaminated data. Results comparing a maximum likelihood estimator with an L2 estimator are given in this article, based on both real and simulated data sets. It is shown that this new L2 parametric estimation method is more robust and does a better job than maximum likelihood in the newly proposed three-parameter Weibull model when data are contaminated. The same preference for L2 distance criterion and the new Weibull model also happens for right censored data with contamination.