The Weibull distribution is the widely used distribution not only in reliability but also in many other fields. There are two parameterized forms of this distribution which are most frequently used. As we will show in the paper, these forms indeed affect Bayesian inference via Markov chain Monte Carlo methods. Although our study suggests the ways to successfully apply Bayesian inference mainly via Hamiltonian Monte Carlo, any other Markov chain Monte Carlo methods can easily be adopted. Maximum likelihood estimators using cross-entropy method is also given along with Bayesian estimators. A simulation study has also been conducted to compare the parameter estimation of the two forms. A real data set is given in order to demonstrate the suggested ways for the Weibull distribution.