Efficient estimation of the Weibull shape parameter based on a modified profile likelihood. (English) Zbl 1014.62025

Summary: The maximum likelihood estimator of the Weibull shape parameter can be very biased. An estimator based on the modified profile likelihood is proposed and its properties are studied. It is shown that the new estimator is almost unbiased with relative bias being less than \(1\%\) in most of the situations, and it is much more efficient than the regular MLE. The smaller the sample or the heavier the censoring, the more efficient is the new estimator relative to the regular MLE.


62F10 Point estimation
62N02 Estimation in survival analysis and censored data
65C05 Monte Carlo methods