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Robust Fitting of a Weibull Model with Optional Censoring.

Authors
  • Yang, Jingjing1
  • Scott, David W
  • 1 Rice University, Department of Statistics, 6100 Main St. MS-138, Houston, TX 77005, U.S.A.
Type
Published Article
Journal
Computational statistics & data analysis
Publication Date
Nov 01, 2013
Volume
67
Pages
149–161
Identifiers
PMID: 23888090
Source
Medline
Keywords
Language
English
License
Unknown

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 using L2 distance, 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 an L2 estimator are given in this article, based on both simulated and real 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 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.

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