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

Abstract

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.

Keywords:

• three-parameter Weibull distribution
• confidence interval
• upper confidence limit
• point estimation
• Monte Carlo simulation

Acknowledgements

The authors are grateful to an anonymous referee and the editor for their helpful suggestions that greatly improved the original manuscript. The research of Zhenmin Chen is supported by the research fund provided by the College of Arts and Sciences at the Florida International University, USA.