Talk:Heavy-tailed distribution

message: 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)
thread_title:  Comments from before 13 March 2007 

message: 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)
replies: text: It is quite correct that the log-normal distribution has all its moments.  But the text does NOT say that a heavy-tailed distribution has only its first moment (in fact the Cauchy doesn't even have a finite mean).  Some authors do use the term in this way,but the most common usage, and the one that includes all the distributions implied by the other distributions is the one given at the start of the article: that the moment generating function is not defined for any positive value of the argument (assuming we are talking about a heavy right-tail). This is all clearly explained (I hope) in the introduction.  PoochieR (talk) 09:50, 22 January 2008 (UTC)
thread_title:  Factual error? 

message: 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)
replies: text: I agree with the merge proposal; there appears to be some overlap in terminology. If you consider fat-tailed to be a subtype of heavy-tailed, explaining that in one article is easier because it can be contrasted with other subtypes. If you consider them to be synonyms, there's really no point in having two articles. -- Beland (talk) 15:27, 1 May 2020 (UTC)
thread_title:  Proposal: merge heavy-tails with fat-tails 

message: 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)
thread_title:  Tsallis Distributions 

message: Illustrations would be so helpful here. Anybody? Vegard (talk) 19:25, 10 August 2012 (UTC)
replies: text: Indeed, that's the only way I can think of to explain the concept to non-technical readers. As it stands now, most readers will abandon the article at the beginning of the first section, when the equations start, and the intro doesn't do a good job of explaining the concept in common language. -- Beland (talk) 15:25, 1 May 2020 (UTC)
thread_title:  Illustrations needed! 

message: I believe the exponential should have a leading negative sign, no?
: No, here should not be a leading negative sign. The definition ensures (roughly speaking) that if the distribution is itself exponentail, or has a lighter tail then the limit is finite, so not a heavy distribution. But a distribution such as a Pareto where the tail distribution is a polynomial, then the limit will be infinite, and by the definition it will then be a heavy tailed distribution. AWRichards1 (talk) 21:26, 23 February 2013 (UTC)
thread_title:  Incorrect definition? 

message: 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)
thread_title:  Definition too narrow for practical purposes? 

message: 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)
replies: text: I agree, it would be nice to have a definition in the article. Tilde#As a relational operator does not describe ubiquitously-used definition. I looked into some references, but were not able to find a definition used there either. Nuretok (talk) 19:49, 31 January 2024 (UTC)
thread_title:  Tilde sign not defined