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The Weibull distribution, with shape parameter $k>0$ and scale parameter$\lambda>0$, is one of the most popular parametric distributions in survivalanalysis with complete or censored data. Although inference of the parametersof the Weibull distribution is commonly done through maximum likelihood, it iswell established that the maximum likelihood estimate of the shape parameter isinadequate due to the associated large bias when the sample size is small orthe proportion of censored data is large. This manuscript demonstrates how theBayesian information-theoretic minimum message length principle coupled with asuitable choice of weakly informative prior distributions, can be used to inferWeibull distribution parameters given complete data or data with type Icensoring. Empirical experiments show that the proposed minimum message lengthestimate of the shape parameter is superior to the maximum likelihood estimateand appears superior to other recently proposed modified maximum likelihoodestimates in terms of Kullback-Leibler risk. Lastly, we derive an extension ofthe proposed method to data with type II censoring.

Minimum message length inference of the Weibull distribution with complete and censored data