Abstract
The Weibull distribution in which all the three parameters, scale η, shape β and location γ, 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 represents 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.
