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{{About|the extreme value theory in statistics|the result in calculus|extreme value theorem}}
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There are millions of used Leisure Vehicles out there in the market thee days that are making this firm memorable for longer.<br><br>I f for any cause the tire is flawed; we will cowl any defect below normal put on and tear condition. We will ship a replacement, or refund the purchase if we don't have a alternative in stock, we will concern a full refund. This applies to make use of tires only. In case it's worthwhile to order pre-owned tires online, just be sure you ask the vendor to send you detailed footage of the merchandise, for you to decide the situation of the tires, and if they are actually good enough. Discovering quality tires is usually a tricky choice, their are lots of options to choose from and chances are you'll not know the appropriate choice, hopefully this article will help read extra Tire substitute/reimbursement outdoors of 25-mile radius of the Sallas Auto Restore locations. Tire placement and rotation<br><br>Winter tires on the market additionally seem to come reasonably priced in these deals that do not have any latent strings attached with the apparent advantages. The wheels so bought at a discounted value are simply as good in high quality as the new OEM wheels usually are. Being sourced by reputed suppliers, there is an unstated label of assure despite the fact that the purchase may arrive with not more than a warrantee period mentioning sure length of time for harm substitute. These providers function both online and offline, the former being extra popular among folks because of its time saving convenience. Making the very best of these opportunities may be the only regrettable issue in this respect.
{{Expert-subject|Statistics|talk="Models for exceedances"|date=August 2013}}
 
[[File:1755 Lisbon earthquake.jpg|thumb|Extreme value theory is used to model the risk of extreme, rare events, such as the [[1755 Lisbon earthquake]].]]
 
'''Extreme value theory''' or '''extreme value analysis''' ('''EVA''')  is a branch of [[statistics]] dealing with the extreme [[Deviation (statistics)|deviation]]s from the [[median]] of [[probability distribution]]s. It seeks to assess, from a given ordered [[Sample (statistics)|sample]] of a given random variable, the probability of events that are more extreme than any previously observed. Extreme value analysis is widely used in many disciplines, such as structural engineering, finance, earth sciences, traffic prediction, and geological engineering. For example, EVA might be used in the field of [[hydrology]] to estimate the value an unusually large flooding event, such as the [[100-year flood]]. Similarly, for the design of a [[breakwater (structure)|breakwater]], a coastal engineer would seek to estimate the 50-year wave and design the structure accordingly.
 
== Data analysis ==
 
Two approaches exist for practical extreme value analysis. The first method relies on deriving block maxima (minima) series as a preliminary step. In many situations it is customary and convenient to extract the annual maxima (minima), generating an "Annual Maxima Series" (AMS). The second method relies on extracting, from a continuous record, the peak values reached for any period during which values exceed a certain threshold (falls below a certain threshold). This method is generally referred to as the "Point Over Threshold" method (POT) and can lead to several or no values being extracted in any given year.
 
For AMS data, the analysis may partly rely on the results of the [[Fisher–Tippett–Gnedenko theorem]], leading to the [[generalized extreme value distribution]] being selected for fitting.<ref>Fisher and Tippett (1928)</ref><ref>Gnedenko(1943)</ref> However, in practice, various procedures are applied to select between a wider range of distributions. The theorem here relates to the limiting distributions for the minimum or the maximum of a very large collection of [[statistical independence|independent]] [[random variable]]s from the same arbitrary distribution. Given that the number of relevant random events within a year may be rather limited, it is unsurprising that analyses of observed AMS data often lead to distributions other than the generalized extreme value distribution being selected{{Citation needed|date=April 2013}}.
 
For POT data, the analysis involves fitting two distributions: one for the number of events in a basic time period and a second for the size of the exceedances. A common assumption for the first is the [[Poisson distribution]], with the [[generalized Pareto distribution]] being used for the exceedances. Some further theory needs to be applied in order to derive the distribution of the most extreme value that may be observed in a given period, which may be a target of the analysis. An alternative target may be to estimate the expected costs associated with events occurring in a given period.
 
An alternative approach is the [[Power_law#Estimating_the_exponent_from_empirical_data_2|tail-fitting]] approach based on the [[Pickands–Balkema–de Haan theorem]].<ref>Pickands (1975)</ref><ref>Balkema and de Haan (1974)</ref> This concentrates on the distribution of the size of an event, given that one has occurred.
 
==Applications==
Applications of extreme value theory include predicting the probability distribution of:
* Extreme [[flood]]s
* The amounts of large [[insurance]] losses
* [[Equity risk]]s
* Day to day [[market risk]]
* The size of [[freak wave]]s
* Mutational events during [[evolution]]
* Large [[wildfire]]s<ref>Alvardo (1998, p.68.)</ref>
* It can be applied to some characterization of the distribution of the maxima of incomes, like in some surveys done in virtually all the National Offices of Statistics
* Estimate fastest time humans are capable of running the [[100 metres]] sprint.<ref>{{Citation | last = | first =  | authors = J.H.J. Einmahl & S.G.W.R. Smeets | title = Ultimate 100m World Records Through Extreme-Value Theory | journal = CentER Discussion Paper, Tilburg University,  | volume = 57| issue =  | pages = | year = 2009 | url=http://arno.uvt.nl/show.cgi?fid=95436| accessdate =  2009-08-12}}</ref>
* Pipeline failures due to [[pitting corrosion]].
 
==History==
 
The field of extreme value theory was pioneered by
[[Leonard Tippett]] (1902–1985).  Tippett was employed by the British Cotton Industry Research Association, where he worked to make cotton thread stronger.  In his studies, he realized that the strength of a thread was controlled by the strength of its weakest fibres. With the help of [[R. A. Fisher]], Tippet obtained three asymptotic limits describing the distributions of extremes. [[Emil Julius Gumbel]] codified this theory in his 1958 book ''Statistics of Extremes'', including the [[Gumbel distribution]]s that bear his name.
 
A summary of historically important publications relating to extreme values theory can be found on the article [[List of publications in statistics#Extreme value theory|List of publications in statistics]].
 
== Univariate theory ==
 
Let <math>X_1, \dots, X_n</math> be a sequence of [[independent and identically distributed]] variables with distribution function ''F'' and let <math>M_n =\max(X_1,\dots,X_n)</math> denote the maximum.
 
In theory, the exact distribution of the maximum can be derived:
:<math>
\begin{align}
\Pr(M_n \leq z) & = \Pr(X_1 \leq z, \dots, X_n \leq z) \\
& = \Pr(X_1 \leq z) \cdots \Pr(X_n \leq z) = (F(z))^n.
\end{align}
</math>
 
The associated [[indicator function]] <math>I_n = I(x_n>z)</math> is a [[Bernoulli process]] with a success probability <math>p(z)=(1-F(z))</math> that depends on the magnitude <math>z</math> of the extreme event. The number of extreme events within <math>n</math> trials thus follows a [[binomial distribution]] and the number of trials until an event occurs follows a [[geometric distribution]] with expected value and standard deviation of the same order <math>O(1/p(z))</math>.
 
In practice, we might not have the distribution function <math>F</math> but the [[Fisher–Tippett–Gnedenko theorem]] provides the following asymptotic result
 
If there exist sequences of constants <math>a_n>0 </math> and <math>b_n\in \mathbb R </math> such that
 
:<math> \Pr\{(M_n-b_n)/a_n \leq z\} \rightarrow G(z) \propto \exp \left[-(1+\zeta z)^{-1/\zeta} \right] </math> 
 
as <math>n \rightarrow \infty</math> where <math>\zeta</math> depends on the tail shape of the distribution.
When normalized, ''G'' belongs to one of the following non-[[degenerate distribution]] families:
 
[[Weibull distribution|Weibull law]]: <math> G(z) = \begin{cases} \exp\left\{-\left( -\left( \frac{z-b}{a} \right) \right)^\alpha\right\} & z<b \\ 1 & z\geq b \end{cases}</math>
when the distribution of <math>M_n</math> has a light tail with finite upper bound.  Also known as Type 3.
 
[[Gumbel distribution|Gumbel law]]: <math> G(z) = \exp\left\{-\exp\left(-\left(\frac{z-b}{a}\right)\right)\right\}\text{ for }z\in\mathbb R.</math> when the distribution of <math>M_n</math> has an exponential tail. Also known as Type 1
 
[[Frechet distribution|Fréchet Law]]: <math> G(z) = \begin{cases} 0 & z\leq b \\ \exp\left\{-\left(\frac{z-b}{a}\right)^{-\alpha}\right\} & z>b. \end{cases}</math> when the distribution of <math>M_n</math> has a heavy tail (including polynomial decay).  Also known as Type 2.
 
In all cases, <math>\alpha>0</math>.
 
==See also==
* [[Generalized extreme value distribution]]
* [[Pareto distribution]]
* [[Large deviation theory]]
* [[Weibull distribution]]
* [[Extreme risk]]
* [[Extreme weather]]
* [[Fisher–Tippett–Gnedenko theorem]]
 
{{More footnotes|date=September 2010}}
 
==Citations==
{{Reflist}}
 
==References==
* {{Citation | url = http://www.fas.org/irp/agency/dod/jason/statistics.pdf | format = PDF | title = Statistics of Extreme Events with Application to Climate | last = Abarbane | first = H. | last2 = Koonin | first2 = S. | last3 = Levine | first3 = H. | last4 = MacDonald | first4 = G. | last5 = Rothaus | first5 = O. | journal = JASON | volume = JSR-90-30S | date = January 1992 | accessdate = 2011-10-11}}
* {{Citation | url = http://www.vetmed.wsu.edu/org_nws/NWSci%20journal%20articles/1998%20files/Special%20addition%201/v72%20p66%20Alvarado%20et%20al.PDF | format = PDF | title = Modeling Large Forest Fires as Extreme Events | last = Alvarado | first = Ernesto | last2 = Sandberg | first2 = David V. | last3 = Pickford | first3 = Stewart G. | journal = Northwest Science | volume = 72 | date = Special Issue 1998 | pages = 66–75 | accessdate = 2009-02-06
}}
* Balkema A. and [[Laurens de Haan]] (1974) ''Residual life time at great age'', Annals of Probability, '''2''', 792–804.{{doi|10.1214/aop/1176996548}}{{jstor|2959306}}
* Burry K.V. (1975). ''Statistical Methods in Applied Science''. John Wiley & Sons.
* Castillo E. (1988) ''Extreme value theory in engineering.'' Academic Press, Inc. New York.
* Coles S. (2001) ''An Introduction to Statistical Modeling of Extreme Values''. Springer, London.
* Embrechts P., Klüppelberg C. and Mikosch T. (1997) ''Modelling extremal events for insurance and finance''. Berlin: Spring Verlag
* Fisher R.A. and Tippett L.H.C. (1928) ''Limiting forms of the frequency distribution of the largest and smallest member of a sample'', Proc. Cambridge Phil. Soc., '''24''', 180–190.
* Gnedenko B.V. (1943) ''Sur la distribution limite du terme maximum d'une serie aleatoire'', Annals of Mathematics, '''44''', 423–453.
* {{Citation | url = http://archive.numdam.org/article/AIHP_1935__5_2_115_0.pdf | format = PDF | title = Les valeurs extrêmes des distributions statistiques | last = Gumbel | first = E.J. | journal =  Ann. Inst. Henri Poincaré | volume = 5 | year =  1935 | pages = 115–158 | accessdate = 2009-04-01 | issue = 2
}}
* {{Citation | first=Emil J. | last = Gumbel | origyear=1958 |year = 2004| title=Statistics of Extremes | publisher = Dover |location = Mineola, NY |isbn=0-486-43604-7 | url=http://books.google.com/?id=kXCg8B5xSUwC&lpg=PP1&dq=Statistics%20of%20Extremes%20gumbel&pg=PP1#v=onepage&q=}}
* Leadbetter M.R., Lindgren G. and Rootzen H. (1982) ''Extremes and related properties of random sequences and processes.'' Springer-Verlag, New York.
* Lindgren G. and Rootzen H. (1987) ''Extreme values: Theory and technical applications''. Scandinavian Journal of Statistics, Theory and Applications 14:241–279.
* Novak S.Y. (2011) ''Extreme value methods with applications to finance''. Chapman & Hall/CRC Press, London. ISBN 978-1-4398-3574-6
* Pickands J. (1975) ''Statistical inference using extreme order statistics'', Annals of Statistics, '''3''', 119–131.
 
==External links==
* [http://www.approximity.com/papers/evt_wp.pdf ''Extreme Value Theory can save your neck'' Easy non-mathematical introduction (pdf)]
* [http://www.bankofcanada.ca/wp-content/uploads/2010/01/wp00-20.pdf ''Steps in Applying Extreme Value Theory to Finance: A Review'']
* [http://www.numdam.org/item?id=AIHP_1935__5_2_115_0 ''Les valeurs extrêmes des distributions statistiques'' Full-text access to conferences held by E. J. Gumbel in 1933–34, in French (pdf)]
 
{{DEFAULTSORT:Extreme Value Theory}}
[[Category:Actuarial science]]
[[Category:Statistical theory]]
[[Category:Emergency management]]
[[Category:Extreme value data]]
[[Category:Tails of probability distributions]]

Latest revision as of 01:05, 19 December 2014

I purchased four Bridgetsone Turanza Serenity Plus 235/fifty five 17 "V" rated tires at Costco, Rohnert Park, Ca. for my 2009 Hyundai Azera sedan - I waited the 1.5 hours for mounting and 'STATIC' balancing. Got up to sixty five mph and very unhealthy steering wheel shake.

2004 - 2014 Efficiency Plus Tires. All rights reserved. Efficiency Plus Tire is proud to offer the trade's most interesting brands of custom tires, customized wheels, tires and wheels packages, and sizzling rod components and equipment for the automotive and truck fanatic. Discount tires for automotive, mild truck, SUV, and customized vehicles. When in search of protection against bruising, puncturing, and sidewall splitting, the LTB tires are the perfect buy a Jeep owner could make. With its amplified lugs for stronger on- and off-street traction, this product proves to be an even more aggressive bias tire than previous fashions. Its durability and self-cleaning elements are its greatest strengths. Shopper Guide to Tires Uses of Scrap Rubber Tires days in the past Mavis Discount Tire, Yonkers

Low profile auto tires are some of the widespread new fads inside the automobile business. The tires aren't restricted to simply race cars anymore. For more information about purchase tires look at the web-site. Low profile tires are actually being match on all the things from sports coupes to family sedans. Due to the modern car tires there's a number of considerations wanted to be addressed. read more All-Terrain T/A KO Tires by BFGoodrich Truck Tires A Cheap Solution to Redo a Room to a Music Theme How A lot Do Cheap Suspended Ceiling Tiles Value? Low-cost & Straightforward Washing Machine Restore Find out how to Build a Complete Tile Bathe for Low-cost How to Make a Cheap Brass Cleaner and Shiner With No Salt Low cost Fun Stuff to Do at Teenage Events Tips on how to Hold a Cheap Curtain Bracket How to Make a Cardboard High Hat With Low cost Supplies Low cost Do-it-yourself Ground Blinds

Truck tire load score index is the assigned numbers delegated to a tire that may let you know the safe load that can be used for a tire Once more use moderation when choosing this, however know first what kind of load you will be utilizing with the tires The upper the number the higher the load you can have (in fact the more expensive it's). Beneath-inflation allows tire sidewalls to flex, cracking the rubber on the flex point. The constant flexing causes tires to run hot, shortening tire life and welcoming a blowout. Depending on the tires , one can use the ATV for numerous functions. Because the ATV is designed for off-street use, corresponding to on sand, gravel, mud or snow, much is determined by the type of tires one uses in an ATV. Used Tractor Tires — Name To Verify Availability

Quite often consumers are uncertain how you can learn or interpret specifications on a tire side wall. This drawback is compounded by the Trailer Tire Business's use of three totally different size identification methods on trailer tires. The following are examples and explanations of tire code. Along with being the OE tires for the Lotus Exige, Yokohama Tires ' flagship ADVAN line is now unique equipment on many different world's quickest and most prestigious automobiles, such as the Bentley Continental GT, Bentley's Continental Flying Spur, the Lotus Elise , 2006 Porsche 911 Carrera four, and Lexus GS300 and GS430. 1500 Aug 14 22" lexani wheels and tires 5x120 of my bmw 745li $1500 (fremont / union city / newark) auto parts - by proprietor Featured Used Tire Brands

John Crean, a well-known automotive character created his new venture in the RVs on the market enterprise in 1950 with the title of Fleetwood RVs. The corporate has created many of the fashions and also has gained greater popularities within the RV lovers. In 2007, the company was introduced as the No.1 model of Recreational Automobiles manufacturing. The company has just lately filed bankruptcy and has closed down the travel trailer section to provide. There are millions of used Leisure Vehicles out there in the market thee days that are making this firm memorable for longer.

I f for any cause the tire is flawed; we will cowl any defect below normal put on and tear condition. We will ship a replacement, or refund the purchase if we don't have a alternative in stock, we will concern a full refund. This applies to make use of tires only. In case it's worthwhile to order pre-owned tires online, just be sure you ask the vendor to send you detailed footage of the merchandise, for you to decide the situation of the tires, and if they are actually good enough. Discovering quality tires is usually a tricky choice, their are lots of options to choose from and chances are you'll not know the appropriate choice, hopefully this article will help read extra Tire substitute/reimbursement outdoors of 25-mile radius of the Sallas Auto Restore locations. Tire placement and rotation

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