The fallacy of large shape parameters when using the two-parameter weibull distribution

摘要

The Weibull distribution is used to characterize the parameters of survival data. However, the two-parameter version of the Weibull model does not include a shift parameter. As the first breakages are sometimes occurring far from 0, the shape of the 2-parameter Weibull distribution must be extreme to accommodate such data. Here we show that Weibull distributions with extreme shapes are degenerate distributions which do not contain information about shape anymore. Because of this, any 2- parameter Weibull distribution with large shape parameter can be mimicked by another large-shaped distribution. The argument is further illustrated with simulated results. We present simple solutions to detect and avoid such situations.