46. Weibull Distribution

  1. Catherine Forbes1,
  2. Merran Evans1,
  3. Nicholas Hastings2 and
  4. Brian Peacock3

Published Online: 16 DEC 2010

DOI: 10.1002/9780470627242.ch46

Statistical Distributions, Fourth Edition

Statistical Distributions, Fourth Edition

How to Cite

Forbes, C., Evans, M., Hastings, N. and Peacock, B. (2010) Weibull Distribution, in Statistical Distributions, Fourth Edition, John Wiley & Sons, Inc., Hoboken, NJ, USA. doi: 10.1002/9780470627242.ch46

Author Information

  1. 1

    Monash University, Victoria, Australia

  2. 2

    Albany Interactive, Victoria, Australia

  3. 3

    Brian Peacock Ergonomics, SIM University, Singapore

Publication History

  1. Published Online: 16 DEC 2010
  2. Published Print: 29 NOV 2010

ISBN Information

Print ISBN: 9780470390634

Online ISBN: 9780470627242



  • five-parameter bi-Weibull distribution;
  • parameter estimation;
  • random number;
  • three-parameter Weibull random number generation;
  • variate;
  • Weibull family


The Weibull variate is commonly used as a lifetime distribution in reliability applications. The two-parameter Weibull distribution can represent decreasing, constant, or increasing failure rates. These correspond to the three sections of the “bathtub curve” of reliability, referred to also as “burn-in,” “random,” and “wearout” phases of life. The bi-Weibull distribution can represent combinations of two such phases of life. This chapter illustrates probability density function, distribution function and Hazard function for the Weibull variate. It discusses variate relationships, parameter estimation and random number generation for the Weibull distribution. The negative exponential, two-parameter Weibull, three-parameter Weibull, and bi-Weibull distributions form a family of distributions of gradually increasing complexity.

Controlled Vocabulary Terms

control variate; Weibull distribution