Maximum Likelihood Estimates for Parameters of themth Extreme Value Distribution

1977 ◽  
Vol 16 (3) ◽  
pp. 251-254 ◽  
Author(s):  
S. K. LeDuc ◽  
D. G. Stevens
Keyword(s):  
Maximum Likelihood ◽  
Extreme Value Distribution ◽  
Extreme Value ◽  
Value Distribution ◽  
Maximum Likelihood Estimates

scholarly journals A New Numerical Algorithm of Three Parameter Generalized Extreme Value Distribution of Wind Speed

2021 ◽  
Vol 248 ◽  
pp. 01023
Author(s):  
Ye Tao
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Numerical Algorithm ◽  
Shape Parameter ◽  
Extreme Value Distribution ◽  
Likelihood Estimation ◽  
Extreme Value ◽  
Value Distribution ◽  
Generalized Extreme Value Distribution ◽  
Generalized Extreme Value

Maximum likelihood estimation method is used to solve the problem of parameter estimation of three-parameter generalized extreme value distribution. Based on the theory of order reducing，a new numerical algorithm is presented to resolve the problem of maximum likelihood estimation of three-parameter generalized extreme value distribution．Firstly，the shape parameter is assumed to be known and ternary likelihood equations can be transferred into binary ones that are solved with the dichotomy．And then，scale and location parameters are the functions of shape parameter. Further，the maximum likelihood function is described as a unitary function of shape parameter. The optimal estimation of shape parameters can be obtained by applying dichotomy again.

On The Use of The Extreme Value Distribution in Reliability Analysis and Design

1976 ◽  
Vol 98 (3) ◽  
pp. 1080-1085 ◽  
Author(s):  
P. H. Wirsching ◽  
L. H. Jones
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimators ◽  
Extreme Value Distribution ◽  
Monte Carlo Study ◽  
Extreme Value ◽  
Value Distribution ◽  
Method Of Moment ◽  
Analysis And Design ◽  
Simpler Algorithm

Use of the Type 1 Extreme Value Distribution of Maxima to design engineering problems is reviewed. Results of a Monte Carlo study of the statistical behavior of the distribution parameter estimators are summarized. The study compares behavior of the method of moment and maximum likelihood estimators, and the results suggest that the method of moment estimators, a simpler algorithm, is but slightly less efficient than the maximum likelihood estimators. An example is given to illustrate how a design engineer uses these results to translate observations into an estimate of “reliability” or “risk”. Moreover, a scheme for obtaining approximate confidence intervals on reliability is presented.

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