Title
Parameter Estimation in the Extreme-Value Distributions

Authors
H. Hirose

Source
International Journal of Modelling and Simulation, Vol.15, No.4, pp.141-147 (1995.12)

Abstract
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.

Key Words
Weibull distribution; Gumbel distribution; Frechet distribution; Generalized extreme-value distribution; Maximum likelihood estimate; Predictor-Corrector Method.

Citation

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