Assessing the Value of the Threshold Parameter in the Weibull Distribution Using Bayes Paradigm

The Weibull distribution represents a wide variety of situations. Usually, the distribution is considered as a two-parameter family with a scale, and a shape parameter. If, however, the given data reflect additional information in the form of a minimum guarantee, a positive value away from zero, it is better to go for a three-parameter model with the additional parameter known as the threshold. The threshold parameter is often very important, but increases the complexity of the model. Arbitrarily going for the three-parameter form is not advisable unless it is really required by the data. This article attempts to make a simulation-based Bayesian study for checking if the threshold parameter can be taken to be zero or positive in situations representing the two models. We study the compatibility of the models for the given data set. We conduct the posterior simulation in each case using Gibbs sampling.