Using the empirical moment generating function in testing for the Weibull and the type I extreme value distributions

Test ◽  
2005 ◽  
Vol 14 (2) ◽  
pp. 417-431 ◽  
Author(s):  
Alejandra Cabaña ◽  
Adolfo J. Quiroz
Keyword(s):  
Generating Function ◽  
Moment Generating Function ◽  
Extreme Value ◽  
Type I ◽  
Extreme Value Distributions ◽  
Empirical Moment Generating Function

scholarly journals Extreme-value distributions for some classes of non-uniformly partially hyperbolic dynamical systems

2009 ◽  
Vol 30 (3) ◽  
pp. 757-771 ◽  
Author(s):  
CHINMAYA GUPTA
Keyword(s):  
Sufficient Conditions ◽  
Extreme Value Distribution ◽  
Extreme Value ◽  
Type I ◽  
Skew Product ◽  
Extreme Value Distributions ◽  
Product System ◽  
Expanding Maps ◽  
Expanding Map ◽  
Product Extension

AbstractIn this note, we obtain verifiable sufficient conditions for the extreme-value distribution for a certain class of skew-product extensions of non-uniformly hyperbolic base maps. We show that these conditions, formulated in terms of the decay of correlations on the product system and the measure of rapidly returning points on the base, lead to a distribution for the maximum of Φ(p)=−log(d(p,p0)) that is of the first type. In particular, we establish the type I distribution for S1 extensions of piecewise C2 uniformly expanding maps of the interval, non-uniformly expanding maps of the interval modeled by a Young tower, and a skew-product extension of a uniformly expanding map with a curve of neutral points.

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