Statistical inference about the location parameter of the three-parameter Weibull distribution

Exact confidence intervals, confidence limits and point estimators for the location parameter μ of the three-parameter Weibull distributions have been investigated in the literature. One of the purposes of this paper is to find the best selection of i, j and k for the approach given by Chen [Z. Chen, Exact confidence intervals and joint confidence regions for the parameters of the Weibull distributions, Int. J. Reliab., Qual. Safety Eng. 11 (2004), pp. 133–140.] for constructing an exact confidence interval of the location parameter μ. Statistical simulation has been conducted to find the optimal combination. The critical values of the pivotal quantity ω are obtained. The point estimation for the location parameter of the three-parameter Weibull distributions is also discussed. Compared with the commonly used maximum likelihood estimation method, the method introduced in this research provides a simpler, more accurate and more efficient way to estimate the location parameter of the three-parameter Weibull distributions.