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Note that this is not the same as the so called WeiBayes model. The so called WeiBayes model is really a one-parameter Weibull distribution. It assumes a fixed value (constant) for the shape parameter and solves for the scale parameter. The Weibull-Bayesian model in Weibull++ is actually a true WeiBayes model and offers an alternative to the one-parameter Weibull by including the variation and uncertainty that is present in the prior estimation of the shape parameter.

The Weibull-Bayesian distribution and its characteristics are presented in detail in the Weibull-Bayesian Analysis section in Chapter 8.