Parameter Estimation in
the Extreme-Value Distributions Using the Continuation Method
Authors
H. Hirose
Source
Transactions of Information
Processing Society of Japan, Vol.35 , No.9 , pp.1674-1681 (1994.9)
Abstract
An efficient and stable maximum likelihood parameter
estimation scheme for the three kinds of extreme-value distributions
(the Weibull, the Gumbel and the Frechet) using the generalized
extreme-value distribution and the continuation method is introduced.
As the proposed algorithm can almost always obtain the maximum likelihood
estimates automatically, it is of considerable practical value.
This paper focuses on the Weibull distribution parameter
estimation and shows that using the generalized extreme-value distribution
is better than the Weibull distribution itself and that the continuation
method is more efficient than the grid search method in searching
for parameters globally. The paper also shows that when there are
no finite local maximum likelihood estimates in the Weibull distribution,
it is probable that there are finite local maximum likelihood estimates
in the Fr\'{e}chet distribution; and vice
versa. Only complete data sets are considered in this paper, but
the algorithm can easily be applied to censored data.