Standard Article

Weibull Distribution

  1. John P. Klein1,
  2. Per Kragh Andersen2,
  3. Niels Keiding3

Published Online: 15 JUL 2005

DOI: 10.1002/0470011815.b2a11083

Encyclopedia of Biostatistics

Encyclopedia of Biostatistics

How to Cite

Klein, J. P., Andersen, P. K. and Keiding, N. 2005. Weibull Distribution. Encyclopedia of Biostatistics. 8.

Author Information

  1. 1

    Medical College of Wisconsin, Milwaukee, WI, USA

  2. 2

    University of Copenhagen, Copenhagen, Denmark

  3. 3

    University of Copenhagen, Copenhagen, Denmark

Publication History

  1. Published Online: 15 JUL 2005

Abstract

Properties and derivations of the Weibull distribution are discussed. The Weibull distribution is shown to arise as a limiting distribution of the minimum of n independent random variables. A derivation based on a model for carcinogenesis is presented. The Weibull distribution is shown to fall in both the proportional hazards and accelerated failure-time class of models.

Keywords:

  • two-parameter Weibull;
  • hazard plots;
  • multistage model of carcinogenesis;
  • extreme-value distribution;
  • accelerated failure-time model;
  • proportional hazards model