scholarly journals Existence and consistency of the maximum likelihood estimators for the extreme value index within the block maxima framework

Bernoulli ◽  
2015 ◽  
Vol 21 (1) ◽  
pp. 420-436 ◽  
Author(s):  
Clément Dombry
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimators ◽  
Extreme Value ◽  
Extreme Value Index ◽  
Block Maxima

scholarly journals On the Maximum Likelihood Estimation of Extreme Value Index Based on k-Record Values

2020 ◽  
Vol 2020 ◽  
pp. 1-9
Author(s):  
Abderrahim Louzaoui ◽  
Mohamed El Arrouchi
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Maximum Likelihood Estimator ◽  
Likelihood Estimation ◽  
Record Values ◽  
Extreme Value ◽  
Extreme Value Index ◽  
Likelihood Estimator ◽  
Consistent Solution ◽  
Strongly Consistent

In this paper, we study the existence and consistency of the maximum likelihood estimator of the extreme value index based on k-record values. Following the method used by Drees et al. (2004) and Zhou (2009), we prove that the likelihood equations, in terms of k-record values, eventually admit a strongly consistent solution without any restriction on the extreme value index, which is not the case in the aforementioned studies.

Application of Extreme Value Statistics to Annual Maximum Magnitudes in Jordan Employing a Mixture Distribution

1999 ◽  
Vol 15 (4) ◽  
pp. 711-724 ◽  
Author(s):  
Abdallah I. Husein Malkawi ◽  
Fayez A. Abdulla ◽  
Samer A. Barakat ◽  
Mohanned S. Al-Sheriadeh
Keyword(s):  
Maximum Likelihood ◽  
Simplex Method ◽  
Mixture Distribution ◽  
Maximum Likelihood Estimators ◽  
Extreme Value ◽  
Annual Maximum ◽  
Maximum Earthquake Magnitude ◽  
Newton Raphson ◽  
Maximum Earthquake ◽  
Raphson Method

The concept of extreme value mixture distribution (EVmix) has been implemented in this study to estimate maximum earthquake magnitude occurrence. The EVmix model is applied to annual maximum earthquake magnitude occurrence in Jordan and conterminous regions spanning over the period 1918 to 1997. The maximum likelihood method, in conjunction with the two optimization methods, was employed for determining the statistical parameters of the Gumbel's asymptotic distribution, i.e., GI, and the extreme value distributions EVIII and EVmix. The Simplex method of Nelder and Mead (1965) was found to be more successful in obtaining the maximum likelihood estimators of the three given distributions than the Newton-Raphson method. The difficulties inherent to the Newton-Raphson method were overcome by the Simplex method. It is shown in this study that the EVmix model fits the observed annual maxima far better than GI and EVIII models. In addition, the maximum likelihood estimators obtained using the Simplex method were used to calculate the earthquake risk for a given return period and a design lifetime of structures.

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