A successful maximum likelihood parameter estimation
scheme for the three kinds of extreme-value distributions (the Weibull,
Gumbel and Frechet) using the generalized extreme-value distribution
and the predictor-corrector method is introduced in this paper.
The paper focuses on the Weibull distribution parameter estimation
and shows that using the generalized extreme-value distribution
is better than using the Weibull distribution itself. As the proposed
algorithm can successfully obtain the maximum likelihood estimates
in a certain restricted parameter domain, it is of practical value.
The paper also shows that when there are no finite maximum likelihood
estimates in the Weibull distribution, it is probable that there
are finite maximum likelihood estimates in the Fr\'{e}chet distribution,
but not decisively so. Only complete data sets are considered in
this paper.
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