Likelihood-based confidence interval for the ratio of scale parameters of two independent Weibull distributions

The Weibull distribution is widely used in lifetime data analysis. For example, in studies on the time to the occurrence of tumors in human populations or in laboratory animals, the time of occurrence of tumors is generally assumed to be distributed as a Weibull distribution. Moreover, in engineering, the voltage levels at which failure occurred in electrical cable insulation has been shown to be distributed as a Weibull distribution. When comparing two independent Weibull distributions, it is often assumed that only the scale parameter is altered. In this paper, we propose a simple and accurate procedure to obtain inference concerning the ratio of the two scale parameters of two independent distributions. The performance of the proposed method is assessed through Monte Carlo simulation studies. The numerical results show that the proposed method is extremely accurate even for very small samples. The method is applied to a set of real-life data.