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This article was the subject of a Wiki Education Foundation-supported course assignment, between 27 August 2021 and 19 December 2021. Further details are available
on the course page. Student editor(s):
Jimyzhu.
Above undated message substituted from Template:Dashboard.wikiedu.org assignment by PrimeBOT ( talk) 23:15, 16 January 2022 (UTC)
This material was originally taken from the long-range dependency article, which conflated long-range dependent processes and the heavy-tailed distributions that can arise from them as if they were the same thing. -- The Anome 23:56, 23 November 2006 (UTC)
I propose to redirect the Heavy-tailed distribution article name to the power law article (note that the editors of the power laws article are in the process of producing a dramatically better version that is currently public). The new power-laws article covers both power-law functions and power-law distributions (including distributions with power-law tails), and so information on Heavh-tailed distribution would naturally fit as as a subsection of that topic. In fact, it would be nice to have a section there on the relationship between power-tail tails and extreme value theory. Paresnah 20:14, 13 March 2007 (UTC)
The examples seem to be wrong. The text states that a heavy-tailed distribution has no moments beyond the first one. However, the lognormal and Cauchy distribution are listed. These have moments. -- Zz ( talk) 15:58, 15 January 2008 (UTC)
Although there are essentially three different usages of the term heavy-tailed in probability theory, this article deals with the most general definition. The term fat-tail doesn't have a similiar rigourousness of definition. The current fat-tail article deals only with regularly varying distributions with finite mean, ad as such is dealing with a narrow though important subclass of heavy-tailed distributions. Fat-tails could well be merged with power laws, but this article, dealing as it does with heavy-tailed Weibull, log-normal and other non-power law distributions is logically independent. PoochieR ( talk) 07:00, 17 June 2008 (UTC)
@ User:PoochieR The fat tail article defines fat tails as synonymous with power law tail, but there's no source to that. Lbertolotti ( talk) 23:38, 21 November 2014 (UTC)
I've seen the term fat/heavy tails used to mean fatter than the normal distribution. I know I've seen it used that way in robust statistics. (See These lecture notes, which refer to the double exponential distribution as having heavy tails) and it's implicit in the discussion on the fat tail page itself, since the reason why heavy-tailed distributions are an issue is that using the normal distribution causes you to underestimate the risk of catastrophic losses. I edited the article to mention the usage, though perhaps the article should be revised more extensively. -- Walt Pohl ( talk) 13:30, 8 March 2010 (UTC)
Article does not define what it means by a heavy distribution, or a heavy tail. Recursion results. ᛭ LokiClock ( talk) 08:29, 11 June 2010 (UTC)
Tsallis distributions are often used for their heavy/fat tails. They should be mentioned here as well. Purple Post-its ( talk) 14:32, 27 June 2011 (UTC)
@ User:Purple Post-its does the Tsallis Distributions satisfies the subexpoentiality property? Lbertolotti ( talk) 23:35, 21 November 2014 (UTC)
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Illustrations would be so helpful here. Anybody? Vegard ( talk) 19:25, 10 August 2012 (UTC)
I believe the exponential should have a leading negative sign, no?
I think we get unbounded behavior for any nonzero distribution give the current limiting definition proposed in the 'Definition of Heavy-tailed...'
Reviewed the references, the definition of heavy tailed in terms of the limit is not cited as an if and only if statement. Rather it is mentioned as a one way implication, hence I am not sure if there is an equivalence between those two definitions. Tried to prove it, no luck though hence I consulted the references and this was what I saw.
The practical use of heavy tailed distributions is to model processes that produce rare, extreme events. However, you can have distributions that have finite tails that produce such data. For example, mix a U(-1,1) with a U(-10000, 10000), with mixing probability .0001 on the U(-10000, 10000). This distribution produces rare (1 in 10000) values that are extremely far from the common (-1,1) range, and hence should qualify as a "heavy-tailed" distribution. So it seems that the insistence on infinite tails is not helpful for practical uses, because it eliminates a very large class of useful distributions. After all, many real processes produce data that are both bounded and outlier-prone. BigBendRegion ( talk) 15:43, 29 July 2018 (UTC)
The article often uses the tilde symbol. I think it might mean that the ratio becomes equal in the infinite limit, or something like that. But it's not defined and this makes parts of the article impossible to understand. Its meaning needs to be stated. Nathaniel Virgo ( talk) 04:00, 30 January 2024 (UTC)
![]() | This article is rated Start-class on Wikipedia's
content assessment scale. It is of interest to the following WikiProjects: | ||||||||||||||||||||
|
This article was the subject of a Wiki Education Foundation-supported course assignment, between 27 August 2021 and 19 December 2021. Further details are available
on the course page. Student editor(s):
Jimyzhu.
Above undated message substituted from Template:Dashboard.wikiedu.org assignment by PrimeBOT ( talk) 23:15, 16 January 2022 (UTC)
This material was originally taken from the long-range dependency article, which conflated long-range dependent processes and the heavy-tailed distributions that can arise from them as if they were the same thing. -- The Anome 23:56, 23 November 2006 (UTC)
I propose to redirect the Heavy-tailed distribution article name to the power law article (note that the editors of the power laws article are in the process of producing a dramatically better version that is currently public). The new power-laws article covers both power-law functions and power-law distributions (including distributions with power-law tails), and so information on Heavh-tailed distribution would naturally fit as as a subsection of that topic. In fact, it would be nice to have a section there on the relationship between power-tail tails and extreme value theory. Paresnah 20:14, 13 March 2007 (UTC)
The examples seem to be wrong. The text states that a heavy-tailed distribution has no moments beyond the first one. However, the lognormal and Cauchy distribution are listed. These have moments. -- Zz ( talk) 15:58, 15 January 2008 (UTC)
Although there are essentially three different usages of the term heavy-tailed in probability theory, this article deals with the most general definition. The term fat-tail doesn't have a similiar rigourousness of definition. The current fat-tail article deals only with regularly varying distributions with finite mean, ad as such is dealing with a narrow though important subclass of heavy-tailed distributions. Fat-tails could well be merged with power laws, but this article, dealing as it does with heavy-tailed Weibull, log-normal and other non-power law distributions is logically independent. PoochieR ( talk) 07:00, 17 June 2008 (UTC)
@ User:PoochieR The fat tail article defines fat tails as synonymous with power law tail, but there's no source to that. Lbertolotti ( talk) 23:38, 21 November 2014 (UTC)
I've seen the term fat/heavy tails used to mean fatter than the normal distribution. I know I've seen it used that way in robust statistics. (See These lecture notes, which refer to the double exponential distribution as having heavy tails) and it's implicit in the discussion on the fat tail page itself, since the reason why heavy-tailed distributions are an issue is that using the normal distribution causes you to underestimate the risk of catastrophic losses. I edited the article to mention the usage, though perhaps the article should be revised more extensively. -- Walt Pohl ( talk) 13:30, 8 March 2010 (UTC)
Article does not define what it means by a heavy distribution, or a heavy tail. Recursion results. ᛭ LokiClock ( talk) 08:29, 11 June 2010 (UTC)
Tsallis distributions are often used for their heavy/fat tails. They should be mentioned here as well. Purple Post-its ( talk) 14:32, 27 June 2011 (UTC)
@ User:Purple Post-its does the Tsallis Distributions satisfies the subexpoentiality property? Lbertolotti ( talk) 23:35, 21 November 2014 (UTC)
![]() | It is requested that a mathematical diagram or diagrams be
included in this article to
improve its quality. Specific illustrations, plots or diagrams can be requested at the
Graphic Lab. For more information, refer to discussion on this page and/or the listing at Wikipedia:Requested images. |
Illustrations would be so helpful here. Anybody? Vegard ( talk) 19:25, 10 August 2012 (UTC)
I believe the exponential should have a leading negative sign, no?
I think we get unbounded behavior for any nonzero distribution give the current limiting definition proposed in the 'Definition of Heavy-tailed...'
Reviewed the references, the definition of heavy tailed in terms of the limit is not cited as an if and only if statement. Rather it is mentioned as a one way implication, hence I am not sure if there is an equivalence between those two definitions. Tried to prove it, no luck though hence I consulted the references and this was what I saw.
The practical use of heavy tailed distributions is to model processes that produce rare, extreme events. However, you can have distributions that have finite tails that produce such data. For example, mix a U(-1,1) with a U(-10000, 10000), with mixing probability .0001 on the U(-10000, 10000). This distribution produces rare (1 in 10000) values that are extremely far from the common (-1,1) range, and hence should qualify as a "heavy-tailed" distribution. So it seems that the insistence on infinite tails is not helpful for practical uses, because it eliminates a very large class of useful distributions. After all, many real processes produce data that are both bounded and outlier-prone. BigBendRegion ( talk) 15:43, 29 July 2018 (UTC)
The article often uses the tilde symbol. I think it might mean that the ratio becomes equal in the infinite limit, or something like that. But it's not defined and this makes parts of the article impossible to understand. Its meaning needs to be stated. Nathaniel Virgo ( talk) 04:00, 30 January 2024 (UTC)