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The Weibull distribution in which all the three
parameters, scale eta, shape beta and location gamma, are unknown
is widely used, but its property still remains unrevealed. For instance,
some data case has infinity parameters. The Weibull distribution
does not seem to express the data correctly in the case. However,
the other distribution does it well if we reconsider that the Weibull
distribution is derived from the extreme-value distributions. The
Gumbel (doubly exponential) distribution has finite parameters and
repre-sents the case. In the paper, I will describe the three, (1)
the derivation of the Weibull distribution from the extreme-value
distribution, (2) maximum likelihood parameter estimation, and (3)
the way of dealing with the Weibull distribution in the generalized
extreme-value distribution.
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