Estimation of lower percentiles under a Weibull distribution

We discuss here the estimation of lower percentiles by assuming a Weibull distribution. A log-transformation is made with the Weibull distribution to a smallest extreme value distribution. The location parameter of SEV is re-parameterized by a particular 100pth percentile and the scale parameter of the transformed distribution is assumed to be nonconstant. Statistical inference about the model parameters will be addressed on the basis of the maximum likelihood estimation. And the corresponding confidence intervals of the percentiles are computed based on the normal approximation method. An illustrative example and a simulation study will be presented to show the appropriateness of the method. The simulation study shows that the lower percentile re-parameterization model gives more accurate lower percentile estimates than the commonly used location assumption model.