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 r(1)(th) ordered value and the corresponding estimate, using all r > r(1) observed values in the Type II censored sample of size n greater than or equal to r. Critical values for conducting the test are given for 10 less than or equal to n less than or equal to 100 and various r and n(1). The choice of n(1) 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.