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. ( I ) 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 distribu-tion
is large in some extent.
The paper written in English is available
upon request.