gumbel law
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2019 ◽  
Vol 42 (1) ◽  
pp. 21-32 ◽  
Author(s):  
Abdelghani Bekhira ◽  
Mohammed Habi ◽  
Boutkhil Morsli

Abstract During the last few years, the City of Bechar in Algeria has witnessed some extreme events, such as the great flood of the year 2008 in which an exceptional amount of rain was recorded with a flow rate of 830 m3∙s−1 (hwater = 4 m, b = 200 m); similar flooding also occurred in 2012 and 2014. The problem is that most of the City of Bechar has an urban sprawl that extends to the banks of Wadi Bechar, which represents a huge risk for the lives of the inhabitants of the region. The present work aims to assess the flood risk through flood hazard mapping. This method consists in determining the flow rates for the return periods of 25 years (Q25 = 388.6 m3∙s−1, hwater = 3.5 m, b = 200 m, Sspot = 55.35 ha), 50 years (Q50 = 478.3 m3∙s−1, hwater = 5 m, b = 200 m, Sspot = 66.48 ha) and 100 years (Q100 = 567.3 m3∙s−1, hwater = 7 m, b = 200 m, Sspot = 133 ha). For this, it is necessary to adjust the flow rates using Gumbel law along with some computer supports such as HEC-RAS, HEC-GeoRAS and ArcGis for mapping the event. Finally, this work enables us to determine the zones exposed to risk of flooding and to classify them according to the flood water height.


2010 ◽  
Vol 42 (02) ◽  
pp. 460-488 ◽  
Author(s):  
Anthony G. Pakes

This paper gives easy proofs of conditional limit laws for the population size Z t of a critical Markov branching process whose offspring law is attracted to a stable law with index 1 + α, where 0 ≤ α ≤ 1. Conditioning events subsume the usual ones, and more general initial laws are considered. The case α = 0 is related to extreme value theory for the Gumbel law.


2010 ◽  
Vol 42 (2) ◽  
pp. 460-488 ◽  
Author(s):  
Anthony G. Pakes

This paper gives easy proofs of conditional limit laws for the population size Zt of a critical Markov branching process whose offspring law is attracted to a stable law with index 1 + α, where 0 ≤ α ≤ 1. Conditioning events subsume the usual ones, and more general initial laws are considered. The case α = 0 is related to extreme value theory for the Gumbel law.


1977 ◽  
Vol 47 (6) ◽  
pp. 389-394 ◽  
Author(s):  
A. Barella ◽  
J. M. Tura ◽  
J. P. Vigo

The influence of rotor diameter on separation between two successive belts, belt length, and belt nature were studied. It was concluded that when rotor diameter increases, both length of belt and belt separation increase, and the tightness of their coiling round the yarn core decreases. The study of statistical distributions of the considered parameters—belt separation, number of belts in a given length, and belt length—shows that the phenomenon follows the Gumbel law in the first case, the Poisson law in the second case, and the lognornal law in the third case.


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