# Talk:Fat-tailed distribution

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## Black-Scholes

The Black-Scholes model assumes the log-return (equivalent to an interest rate for a stock) has a normal distribution. This gives the price a log-normal distribution. The log-normal is heavy-tailed (but is not included in your definition of fat-tailedness). Data shows that the log-returns have heavier tails than the normal distribution, and this makes the price even heavier than log-normal. This may lead to either under- or over-pricing of an option. PoochieR (talk) 08:18, 23 June 2008 (UTC)

## Proposal: merge Fat Tail with Power Law

I propose to redirect the fat tail 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 fat tails 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, if you guys would like to write it.

Paresnah 20:14, 13 March 2007 (UTC)

## Comments from before 13 March 2007

I believe Fat tail and Heavy tail are the same concept. Heavy tail redirects to Long-range dependency, but this page is more about statistical network simulation than statistical finance.

Fat tail and Heavy Tail are the same concept, however Heavy Tail is more politically correct.

I disagree with the above poster.

1. The article does a good job at explaining in laymans terms the key idea of fat-tails in probability distributions: that extreme events can occur much more frequently than modelling would suggest. It also makes good reference to the origin of the concept in finance theory.

2. Whilst political correctness can be an important issue in relation to some terms (e.g "master-slave" rather than "primary-secondary" etc), I would suggest that the term "fat" is not beyond the realm of correctness. This phenomenon has been known as a fat tail in finance theory for at least thirty years now (since the work of Eugene Fama and Benoit Mandlebrot, if not before) and I don't see the need to post-edit wikipedia to change this term when mainstream academic journals remain quite happy to accept this term.

3. The article on Long Range Dependency is heavily mathematically orientated, and not an appropriate introduction to the concept of "fat tail" events for a layman or casual browser. I would suggest keeping and expanding this entry and including a link to the Long Range Dependency article for those who wish to delve further into the mathematical aspects.

203.192.146.185 02:53, 18 October 2006 (UTC) David Peterson

I also disagree with the suggestion that this topic should be merged with long range dependences. Fat/heavy tails are NOT the same as long range dependence. You can have a sequence of heavy tailed r.v.s that are independent, and thus there is no dependence (long range or short range). You can have light tailed distributions with long range dependence, e.g. an ARIMA model with Gaussian innovations. The most complex case is where you have heavy tails long range dependence. While there can be a connection, the topics are distinct and should have separate entries, with a cross reference.

147.9.55.178 18:51, 2 November 2006 (UTC)John Nolan (jpnolan@american.edu)

Fat tail has more to do with Kurtosis than with Long Range Dependency.--190.10.30.192 03:03, 22 December 2006 (UTC)

I agree that fat tail and long range dependecy are two completely different topics (and that fat-tail and heavy tail are indeed synonomous) and therefore that it is odd that heavy tail redirects to the page on long-range dependency. What - I believe - has much more merit is merging the Fat tail page with the distinct heavy-tailed distribution page

## Illustrations Wanted for the Less Mathematically Knowledgeable

It might help to have some illustrations of a group of normal and another of more heavy tailed curves for the mathematically less educated though this would have to be conceptually sophisticated.

I would also suggest expanding the discussion of the concept of "pseudo-normal" curves that are, or may be actually transient cases, determined by temporary circumstances, of fatter tailed curves. In fact, many superficially normal distributions in nature and, (as noted) finance, may fall into this category, so it would behoove students not to naively make the error of taking apparently normal distributions found in data as being fixed and immutable, without close analysis of the level or probability that the underlying curve type governing the probabilities might be something else....as a number of financial people, from whom I have gotten the idea, have been stressing very strongly of late.FurnaldHall (talk) 10:04, 26 November 2008 (UTC)

Thanks, FurnaldHall. I would like to see a Plain English explanation at the top and perhaps a simple Cartesian graph or two - that would really help. 123.24.170.25 (talk) 10:54, 11 April 2009 (UTC)
Agree, and it would be easy to do for a knowledgeable editor. I added a reqdiagram tag to this talk page, for what it's worth. Tempshill (talk) 19:39, 26 June 2009 (UTC)
I agree. The term "fat tail" sounds like it is derived from the appearance of a graph, and the article is way too technical and jargon-filled; I think only a statistician could glean any meaning from it.--Humanist Geek (talk) 00:06, 9 August 2010 (UTC)
Added a link to a diagram showing a number of different curves (and removed reqdiagram tag). Egmason (talk) 04:50, 29 August 2010 (UTC)

## Section Deleted: Fat Tails in Geopolitics

I really don't think that this section adds anything to the article. It's just an advert for the book's article, which is itself an AfD. The idea isn't a bad one, but a hefty section based on a single book is rather much. Of course, making the article for the book the "main article" for the section really didn't help. The main article for a section should have the same title as the section itself, in my opinion. If there isn't enough information to have an article on the subject, then don't use the {{main|}} markup at all.

Oops! Forgot to sign!--Proginoskes (talk) 17:07, 10 February 2009 (UTC)

## "posits events"?!

Surely the normal distribution doesn't "posit" any events. It might deal with them, but it, being a concept,is entirely neutral as to whether events occur and therefore can not "posit" them.

Let's look for some more accurate use of language. This is about mathematics, after all. — Preceding unsigned comment added by 94.116.120.252 (talk) 20:30, 4 July 2012 (UTC)

## Thin tailed distribution

So the opposite of fat tails is a distribution that has exponential tails? (ex: normal) Lbertolotti (talk) 10:35, 11 July 2013 (UTC)