Fracture statistics: A comparison of the normal, Weibull, and Type I extreme value distributions

1983 ◽  
Vol 54 (1) ◽  
pp. 193-198 ◽  
Author(s):  
R. H. Doremus
Keyword(s):  
Extreme Value ◽  
Type I ◽  
Extreme Value Distributions

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.

An Extreme Value Model for U.S. Hail Size

2017 ◽  
Vol 145 (11) ◽  
pp. 4501-4519 ◽  
Author(s):  
John T. Allen ◽  
Michael K. Tippett ◽  
Yasir Kaheil ◽  
Adam H. Sobel ◽  
Chiara Lepore ◽  
...  
Keyword(s):  
Gumbel Distribution ◽  
The United States ◽  
Value Theory ◽  
Extreme Value ◽  
Extreme Value Distributions ◽  
The Past ◽  
Return Levels ◽  
Data Limitations ◽  
Extreme Value Model ◽  
Value Model

The spatial distribution of return intervals for U.S. hail size is explored within the framework of extreme value theory using observations from the period 1979–2013. The center of the continent has experienced hail in excess of 5 in. (127 mm) during the past 30 yr, whereas hail in excess of 1 in. (25 mm) is more common in other regions, including the West Coast. Observed hail sizes show heavy quantization toward fixed-diameter reference objects and are influenced by spatial and temporal biases similar to those noted for hail occurrence. Recorded hail diameters have been growing in recent decades because of improved reporting. These data limitations motivate exploration of extreme value distributions to represent the return periods for various hail diameters. The parameters of a Gumbel distribution are fit to dithered observed annual maxima on a national 1° × 1° grid at locations with sufficient records. Gridded and kernel-smoothed return sizes and quantiles up to the 200-yr return period are determined for the fitted Gumbel distribution. These results are used to illustrate return levels for hail greater than a given size for at least one location within each 1° × 1° grid box for the United States.

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