Talk:Extreme value theory

Possible Copyright Infringement

The line

Extreme value distributions are the limiting distributions for the minimum or the maximum of a very large collection of random observations from the same arbitrary distribution.

comes from:

http://www.itl.nist.gov/div898/handbook/apr/section1/apr163.htm

I'm not sure if it is legal, I can't find copyright information. --206.191.28.13 00:26, 16 August 2007 (UTC)[reply]

Can we just put it in quotes? — Preceding unsigned comment added by Jeantoilliez (talk • contribs) 18:04, 4 January 2012 (UTC)[reply]

Use in financial applications

I suggest that the section recently added (now called "Use in financial applications") should be deleted. It relies on the single reference given which seems to me to be flawed as:

it doesn't contain any explicit evidence for its claims;
it provides no details of any analyses that might actually have been done and hence there is no possibility of assessing whether such analyses are even close to valid applications of extreme value theory;
there are no details of the extent of any data that might have been analysed.

A more reasonable explanation for supposed failures of extreme value theory is that the outcomes experienced represent effcts caused by non-stationarity (typically excluded by applications of extreme value theory) (recent changes to systems for paying bonuses), which might just mean that someone applied some model derived from extreme value theory when they shouldn't - which is not the fault of the theory. Melcombe (talk) 16:11, 16 July 2008 (UTC)[reply]

Agree, removed section. It was based on a single, rather non-scientific reference. Besides, the argument didn't make any sense to begin with. It merely claimed there were two observations not predicted by the theory, which of course is not enough to undermine the theory. Barcturus (talk) 20:58, 20 November 2008 (UTC)[reply]

correction

In references "Burry" should be "Bury" —Preceding unsigned comment added by 65.19.54.30 (talk) 01:47, 1 May 2009 (UTC)[reply]

Approaches

Can someone please clarify the meaning of the word "models" in the phrase "only a few models are needed". Sniedo (talk) 00:23, 5 July 2009 (UTC)[reply]

Here "model" would mean a family of probability distributions used to model the actual probability distribution of whatever extreme events are being studied. It seems implicit in the context that that only univariate extremes are being studied, as what is said is not really true of the multivariate case. Melcombe (talk) 08:33, 6 July 2009 (UTC)[reply]

This section says that "for any well-behaved initial distribution (i.e., F(x) is continuous and has an inverse), only a few models are needed,". This could too easily be taken to mean that if F(x) is continuous and has an inverse then the distribution of the maximum of n independent draws can be translated and rescaled to one of the 3 standard models (given below in the Univariate Theory section). But this is not the case: there are counterexamples in von Mises, and in the book by de Hahn and Ferreira. What we need is something more like "if the distribution of the maximum of n independent draws can be translated and rescaled to tend to some limiting form, then that limiting form must be one of the 3 standard models given below." Perhaps also in the Univariate Theory section after the explanation about a_n and b_n it should be added, "But there are initial distributions F for which no such sequences a_n and b_n exist." Fathead99 (talk) 18:25, 3 February 2011 (UTC)[reply]

Misleading use of the word "extreme"

In normal English, an "extreme value" may be understood to mean one that is very severe, or has an unusually harmful impact, or is a very long way from normal values. That is not what it means in mathematics; it simply means either the maximum or minimum value of a set. In some cases they may be "extreme" in the layman's sense but in other cases they may be practically indistinguishable from typical values. e.g. if the values in a set of data are {0.99999, 1, 1, 1, 1, 1.00001} then the extreme values are 0.99999 and 1.00001.

I believe that the head of this article makes precisely this mistake when it says:

Extreme value theory is important for assessing risk for highly unusual events, such as 100-year floods.

This sentence isn't actually wrong, but it gives a misleading impression. It is true that extreme value theory is used to model such rare, high-impact events. However it is also used to model very commonplace and lower impact events, such as sporting records (the maximum value of a series of sports results) and equipment service lives (the minimum value of the component failures times of a number of components, assuming they are roughly i.i.d.)

This impression is enhanced by the list of applications, which is dominated by rare, alarming events:

Extreme floods; The amounts of large insurance losses; Equity risks; Day to day market risk; The size of freak waves; Mutational events during evolution; Large wildfires[1]; 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-meter sprint.; Pipeline failures due to pitting corrosion

The theory can be used for analysing freak waves but it is just as applicable to analysing, say, "the most probable largest wave in the next hour" -- even though that probably won't be a "freak". Similarly, in analysis of pitting corrosion (where presumably the system is considered to fail once the fastest growing pit breaks through the wall) pipelines are just a particularly dramatic example; leaks in metal roofs would be equally applicable and far more common.

Anyway, I think we should clean up the misleading impression that this theory is principally about disasters. -- 203.20.101.203 (talk) 01:35, 23 August 2010 (UTC)[reply]

195.59.68.205 (talk) 14:17, 30 October 2015 (UTC) I have to disagree. Extreme should indeed be understood as unusually high (or low) events. EVA purpose is to extrapolate from observed level to unobserved level. This theory is usefull when we do not have enough data to observe extremely rare event. If the event you are trying to characterize (say the leek in a roof) is observed several time (which is probably the case in your example as we probably recorded many many roof leaks for example) then there is no point in using EVA as you can easily determine the whole probability ditribution and there is no need to focus on the tail. Once again "extreme" here specifically refers to "highly unusual events" (compared to the one we have been able to record). — Preceding unsigned comment added by 195.59.68.205 (talk) 14:16, 30 October 2015 (UTC)[reply]

The user 195.59.68.205 is providing the more correct interpretation. EVT's goal is not concerned with the impact of the largest event in a relatively small window (e.g.: the largest micro-earthquake that happened in the past 24 hours in Netherlands is not of much interest; but the largest earthquake in the past 400 years is) Mcrt007 (talk) 01:52, 11 December 2018 (UTC)[reply]

Referring to a missing section

"A summary of historically important publications relating to extreme values theory can be found on the article List of publications in statistics." - no such section exists on that page. — Preceding unsigned comment added by 193.11.155.128 (talk) 12:26, 3 August 2011 (UTC)[reply]

"Models for exceedances"

The article stated: For a start, significant differences among the genomes of human individuals are on the order of 0.1%^[1] For an indication of the thoroughness of a test of 0.1% of one's DNA, consider that 0.1% of one's DNA represents the contribution of each of one's 1024 10th generation ancestors. This 0.1% value allows for the possibility that a very few of them are the same people, not uncommon among small populations not traveling much. For 0.1% to represent some ethnic trace, say, it must show certain known complex patterns within 3 million pairings of 4 chemical bases (3 billion constituting the full human genome), i.e. several known complex patterns out of 4^3000000 possible, which is much less likely to occur, by chance, than a monkey typing one of the 154 Shakespeare's sonnets (~500 characters each, and ignoring all but 26 letters + space = 27): 154 / 27⁵⁰⁰ = 154 / 3¹⁵⁰⁰.

I see neither a source nor its being an application of extreme value theory. Actually, it looks like original research. -- Zz (talk) 10:29, 5 August 2013 (UTC)[reply]

Extreme value assessment need not require a distribution, rather, in simplest form, one can refer to another more "known" extreme value. As for WP:OR, see WP:CALC under it, which covers mere arithmetic (no algebra here). Attleboro (talk) 18:10, 5 August 2013 (UTC)[reply]

The article is not about "extreme value assessment", whatever that may be, but about extreme value theory. There is nothing in your paragraph which refers to it or applies it. I am pretty sure you do not even know what it is. Further, you have gone far beyond simple calculations with your attempts at analogies in unencyclopedic wording, and you try to come up with conclusions, and you pass judgment. For any of this, you need sources. -- Zz (talk) 09:38, 6 August 2013 (UTC)[reply]

From the lead, the theory "seeks to assess, ... the probability of events that are more extreme than any previously observed." That's actually overstated, but this article is not simply about the theory. Rare event redirects here, too. Perhaps, that should have its own article linking to this one. Anyway, the reason for the monkey idea is its continued use in popular press, ease of calculation, by arithmetic alone, and useful comparison in a practical problem, "How rare is it for 2 people to be genetically the same, by chance?" i.e. rarer than a monkey typing... Attleboro (talk) 21:56, 6 August 2013 (UTC)[reply]

I assume your intent is good. Unfortunately, it is unencyclopedic, too. Yet, the redirection of rare event to the article should be reconsidered. -- Zz (talk) 09:57, 7 August 2013 (UTC)[reply]

We disagree as to whether this is "unencyclopedic." It's no more unencyclopedic than Infinite monkey theorem in popular culture and uses that popular image of a practically impossible event to illustrate the much greater impossibility of an event that's worth considering. A probabilist should weigh in here. Attleboro (talk) 17:34, 7 August 2013 (UTC)[reply]

Your contribution is original research. End of story. -- Zz (talk) 13:27, 8 August 2013 (UTC)[reply]

Ich glaube nicht, weil es so üblich und einfach ist, i.e., too common and simple. Attleboro (talk) 19:14, 8 August 2013 (UTC)[reply]

It is not, as explained here. Original research, and you do not want to let go, because it is your pet theory at the time being. For me, the discussion has ended. Attempts to reintroduce the content might find your account listed on certain pages here. -- Zz (talk) 12:09, 12 August 2013 (UTC)[reply]

It adds nothing to repeat an explanation that I showed you was refuted in the leading part of the article. Formalizing extreme value assessment (or analysis, interchangeable here) is the entire purpose of concocting special distributions for those extreme values. Attleboro (talk) 20:02, 12 August 2013 (UTC)[reply]

References

^ See lead paragraph of "Human genome."

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[1] See lead paragraph of "Human genome."

[1]