Markov Chain Monte Carlo Methods for Parameter Estimation of a New Modified Weibull Distribution

The Markov Chain Monte Carlo (MCMC) method is first applied to estimate the parameters of a new modified Weibull distribution based on a complete sample while the Maximum Likelihood Estimation (MLE) has been used for its parameter estimation of three parameters in this paper. Details of the implementation of the Bayesian parameter estimation of the modified Weibull distribution based on a MCMCmethod are elaborated and a numerical example is presented to illustrate the methods of inference discussed in this paper. In addition, a simulation study is provided, and the differences between the estimates obtained by the two algorithms are examined. Thus, it is concluded that MCMC is a better choice than MLE for the parameter estimation of the modified Weibull distribution.