An upper confidence limit on the maximum of m future observations from a Type 1 extreme value distribution

Biometrika ◽  
1972 ◽  
Vol 59 (2) ◽  
pp. 475-477 ◽  
Author(s):  
CHARLES E. ANTLE ◽  
FRED RADEMAKER
Keyword(s):  
Confidence Limit ◽  
Extreme Value Distribution ◽  
Extreme Value ◽  
Value Distribution ◽  
Upper Confidence Limit

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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