Employing the approach proposed by Z. Chen for constructing an exact confidence interval for the location parameter, this study has investigated the exact confidence intervals, confidence limits and point estimators for the location parameter μ of the three-parameter Weibull distributions. Statistical simulation was carried out for different selections of i, j and k with specified confidence level and sample size. The critical values (ωα/2 and ω1-α/2 have been found using Mote-Carlo simulation. The optimization of the combination of i, j and k has been discussed. The point estimator for the location parameter of the three-parameter Weibull distributions is explored.
It is observed that the critical values do not depend on the parameters. Simulation results show that the optimization of i, j and k is i=1, k-n and j=[n+2/3]. Compared with the commonly used MLE method, the described method provides a simpler, more accurate and more efficient way to estimate the location parameter of the three-parameter Weibull distributions. The described method yields very good statistical inferences for the location parameter of the three-parameter Weibull distributions.