On the Limiting Distribution of the 3 Parameter Weibull Distribution

The Weibull distribution plays a very important role in the engineering field, especially when we deal with the breakdown voltage or the lifetime of an insulation. This paper derives mainly three conclusions about the parameter and the percentile point estimations in the case we must search for the three Weibull parameters.(1) When all the three parameters tend to infinite values, we could use the extended maximum likelihood estimate for the percentile point estimator. However, the limiting form of the Weibull distribution transfigures to the double exponential distribution. Thus, it is the proper way in handling the data that they are extracted from the double exponential distribution.(2) We can judge whether the data are subjected to the Weibull or the double exponential distribution by using the skewness and the number of sample size.(3) Even if the data are extracted from the Weibull distribution, we can treat them as the data extracted from the double exponential distribution if the shape parameter of the Weibull distribution is large in some extent.