Inference on the Weibull location parameter

A simple method is proposed for testing the 2-parameter Weibull distribution against the 3-parameter alternative. It is based on the ratio of the maximum likelihood estimate of the shape parameter calculated with the observations censored at the r₁^th ordered value and the corresponding estimate, using all r > r₁ observed values in the Type II censored sample of size n ≥ r. Critical values for conducting the test are given for 10 ≤ n ≤ 100 and various r and n₁. The choice of n₁ in the range 5-9 is found to give nearly maximum power over the range of sample sizes explored. The acceptance region for the test can be translated into a lower confidence interval estimate for the location parameter. Two numerical examples illustrate the calculations.