Fitting the three-parameter Weibull distribution with Cross Entropy

Asghar Moeini, Kouroush Jenab*, Mohsen Mohammadi, Mehdi Foumani

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

30 Citations (Scopus)


The Weibull distribution is widely used in applications such as reliability and lifetime studies. Although this distribution has three parameters, for simplicity, literature pertaining to Weibull parameter estimation relaxes one of its parameters in order to estimate the other two. When the three-parameter Weibull distribution is of interest, the estimation procedure is complicated. For example, the likelihood function for a three-parameter Weibull distribution is hard to maximize. In this paper, a Cross Entropy (CE) method is developed in the context of maximum likelihood estimation (MLE) of a three-parameter Weibull distribution. Performing a simulation study, a comparative analysis between the newly developed method and two existing methods is conducted. The results show the proposed method has better performance in terms of accuracy, precision and run time for different parameter settings and sample sizes.

Original languageEnglish
Pages (from-to)6354-6363
Number of pages10
JournalApplied Mathematical Modelling
Issue number9
Publication statusPublished - 1 May 2013
Externally publishedYes


  • Cross Entropy method
  • Maximum likelihood estimation
  • Parameter estimation
  • Weibull probability distribution


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