Estimating Parameters of Gumbel Distribution using the Methods of Moments, probability weighted Moments and maximum likelihood

We derive here estimators for the parameters of the Gumbel distribution using three estimating methods, namely, the probability weighted moments, the moment and the maximum likelihood methods. Furthermore, we compare the performance of these estimators using simulations. Both integer and non-integer...

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Main Authors: Mahdi, Smail, Cenac, Myrtene
Format: Artículo
Language: Español
Published: 2015
Online Access: http://revistas.ucr.ac.cr/index.php/matematica/article/view/259
http://hdl.handle.net/10669/12905
Summary: We derive here estimators for the parameters of the Gumbel distribution using three estimating methods, namely, the probability weighted moments, the moment and the maximum likelihood methods. Furthermore, we compare the performance of these estimators using simulations. Both integer and non-integer orders are considered in the probability weighted moments method. Overall, the results show that the probability weighted moments method outperforms the other methods in the estimation of both $\alpha$ and $\epsilon$ parameters.