Talk:Copula (probability theory)

Rewrite
Hello everyone.

I intend to do a complete rewrite of this article in the near future. My main aim is to transform this article into a mathematically precise and concise article covering the main aspects of multivariate copulas. The bivariate case will be used for illustration. please feel free to join the effort and/or comment.

Philtime (talk) 14:29, 15 May 2011 (UTC)


 * Reverted changes: see WP:NOTTEXTBOOK. If you want an artcle on the mathematics of copulas, then start a new one. JA(000)Davidson (talk) 08:50, 16 May 2011 (UTC)


 * I find it quite rude to simply revert without proper reasoning. the article, as it is now contains a lot of inconsistent and wrong bullshit. it cannot be read by anyone if he/she is not already familiar with copulas. I truly intend to improve this article by making it mathematically precise. please tell me precisely what you did not like with my version, so I/we can improve the article. From your statement "mathematics of copulas", I guess you have no experience with copulas at all? I can point you to dozends of articles which show you that copulas are a topic showing up in all areas of probability thery, not only statistics. Philtime (talk) 14:48, 16 May 2011 (UTC)


 * I found it very rude of you to have not only renamed the article but also to ahve deleted a lot of material without any discussion at all. If you do that sort of thing you will most certainly be reverted. It is clear from your statements about making this article "mathematically precise" that you have no idea of what makes suitable articles on Wikipedia. It is a lot more important that the article should have at least some parts that are understandable by the general reader than that they should be "mathematically precise" and hence. I see also from your statements about a lot of probability theory being involved with copulas, and hence that it is a proability theory topic that you don't have any understanding of statistics, not do you undrerstand that "proability theory" is only a small relatively unimportant part of statistics. The entire reason that copulas have any importance at all is because of their importance to applied statistics. JA(000)Davidson (talk) 08:18, 17 May 2011 (UTC)

Since I was e-mailed with a prompt to comment on this, I would just say that Wikipedia's standard for maths-type articles is set out at Manual of Style (mathematics). This starts by saying how articles should be organised and emphasizes the need to start with widely-understandable stuff. It seems to me that the original and present versions meet this criterion, whereas the version left by Philtime did not ... placing hard maths in the lead seems unacceptable. The original at least had some background on uses and why the topic is important at the start of the article. The standard suggests that an article can be ordered, placing the technically sophisticated stuff at the end. If some understandable-but-not-including-every-little-detail maths can be used to outline some of what is going on, all well and good. The article need not actually include "every little detail" stuff, but it would be good to indicate the status of what is said and provide citations for more complete details. If "every little detail" is to be included then there is no reason to try to avoid repetition by making the "easy stuff" unreadable by forcing the detail in too early. But read Manual of Style (mathematics). Melcombe (talk) 15:27, 18 May 2011 (UTC)


 * Hi melcombe, thank you very much for your constructive comments. I'll work over my edits in the near future according to the stated manual. Philtime (talk) 16:40, 21 May 2011 (UTC)

Comment by Hsfrey
I would just like to point out that nowhere in the introduction does the article say what a copula IS.

It says what it can be used for, and what the word is derived from, and then launches into a comment about another undefined specialized mathematical term, "marginal distribution function". It adds the vague statement that the copula "describes the dependence structure between the components", without giving the slightest indication of HOW it describes it, but we are then told that "copulas are popular", still without knowing what they ARE.

Then comes the post-graduate Math Seminar, designed more for an "Obfuscated Code" contest than for the general internet user.

Who does Wikipedia think its audience is?

Hsfrey (talk) 02:55, 22 August 2011 (UTC)


 * hi Hsfrey. thanks for your comment. I wrote most of the content presently present at the page. Would be happy to further improve the page. I wrote most of the text under the assumption that the reader knows about 1) probability, 2) random vectors, and 3) multivariate cumulative distribution functions. Unfortunately, its quite difficult to grasp the idea of a copula without knowing these three concepts. Please feel free to comment and suggest improvements. regards Philtime (talk) 18:59, 22 August 2011 (UTC)


 * I think what Hsfrey was trying to say back in 2011 is that the first sentence of the article should be a statement of the form "X is Y" as in "The Queen Mary is a ship" or "A rabbit is a kind of mammal". Normally I would just fix it, but in this case I have no idea what the general kind of mathematical thing a copula is. Here's a stab at one that's well-formed, if not factually correct:


 * "In probability theory and statistics, a copula is a kind of distribution function. Copulas are used to describe the dependence between random variables. They are named for their resemblance to linguistic copulas."


 * Jer ome (talk) 09:28, 22 April 2012 (UTC)

Comment by Etorkia on Excel Articles
Hi Everybody:

I put the link back for the correlation videos in because it is not commercial content nor advertising (though it is on a commercial site), but rather a series of how-to videos and comparisons of the top tools in an unbiased and noncommercial way. Most users that are directed from this link like and consume the articles we offer (very low bounce rate and multiple page views)- tools we present are just as important to the practitioner as theory presented in your excellent article. If you have any questions or suggestions to make the content more appropriate, please let me know. I would not want to jeopardize the quality of the work you are doing.

Best regards,

Etorkia (talk) 18:48, 15 September 2011 (UTC)

Move proposal
Hi. I would like to propose to move this article either to Copula (mathematics) or Copula (probability theory).

Reasons:
 * Copulas (the way they are presented here) do fit to almost none of the methodologies described on Statistics.
 * The copula page does not state anything about estimation, hypothesis testing, Null hypothesis, Error, Interval estimation, Significance. And these terms are "Key terms used in statistics" according to Statistics.
 * Copulas are rather a construction from probability theory: It's constructed, defined and described as a transformation of a probability measure on $$\mathbb{R}^d$$ to $$[0,1]^d$$.
 * From an acedemic point of view, copulas are interesting because they allow for an abstract separation of dependence structure and marginal distributions. Estimation and testing are seconary.

Philtime (talk) 17:26, 23 July 2011 (UTC)


 * Given the reaction above, I think you should go through the formal procedures described at Requested moves for "controversial moves". If this were to go through, doing so would have the benefit of getting an admin to do the renaming properly in the case that the move is to a name that has an existing history. Melcombe (talk) 09:19, 25 July 2011 (UTC)


 * Ok, I will do that, as soon as I find the time. Thanks for your comment. Philtime (talk) 07:37, 26 July 2011 (UTC)


 * striked through as formal move request is opened below. Philtime (talk) 19:17, 26 July 2011 (UTC)

Requested move

 * The following discussion is an archived discussion of a requested move. Please do not modify it. Subsequent comments should be made in a new section on the talk page. No further edits should be made to this section. 

The result of the move request was: moved to Copula (probability theory). Favonian (talk) 09:03, 9 August 2011 (UTC)

Copula (statistics) → Copula (probability theory) – Reasons: . Relisted and three projects notified. Favonian (talk) 08:28, 2 August 2011 (UTC) Philtime (talk) 19:12, 26 July 2011 (UTC)
 * Copulas (the way they are presented here) do fit to almost none of the methodologies described on Statistics.
 * The copula page does not state anything about estimation, hypothesis testing, Null hypothesis, Error, Interval estimation, Significance. And these terms are "Key terms used in statistics" according to Statistics.
 * Copulas are rather a construction from probability theory: It's constructed, defined and described as a transformation of a probability measure on $$\mathbb{R}^d$$ to $$[0,1]^d$$.
 * From an academic point of view, copulas are interesting because they allow for a separation of dependence structure and marginal distributions. Statistical aspects are secondary.


 * Agree. Sounds entirely sensible to me. Qwfp (talk) 08:25, 2 August 2011 (UTC)


 * Note: links to this discussion have been posted on WT:WPM, WT:PROBAB and WT:WPSTAT. — Favonian (talk) 08:28, 2 August 2011 (UTC)
 * Agree with reasoning presented above. CRGreathouse (t | c) 14:42, 2 August 2011 (UTC)
 * The above discussion is preserved as an archive of a requested move. Please do not modify it. Subsequent comments should be made in a new section on this talk page. No further edits should be made to this section.

Continuous or strictly increasing CDFs?
The article states that the inverse probabilities can be found from the uniform random vector and marginal CDFs, F. From the article, "The inverses are unproblematic as the F_i were assumed to be continuous." However, isn't what's required to find X given u and F a strictly increasing distribution function? Jerkmonster (talk) 13:53, 15 February 2012 (UTC)


 * "Strictly increasing" on its own won't work ... consider any singly or doubly bounded distribution, for which the CDF is constant outside the range of the distribution (and for which copula's still work). In particular, the uniform distribution on (0,1) is a viable candidate. And viable distributions can have internal ranges where the CDF is constant. What is needed is that for any u in (0,1) there is a value x such that F(x)=u ... which doesn't hold for distributions having discontonuities in their CDF's. Melcombe (talk) 14:23, 15 February 2012 (UTC)


 * Maybe also consider the "generalized inverse", as given in any textbook on probability theory. Philtime (talk) 19:29, 15 February 2012 (UTC)

examples
This article need some simple examples.64.228.220.16 (talk) 08:36, 1 June 2013 (UTC)

Archimedean generators and inverses
The section on Archimedean copulas introduces the concept using generators and their (generalized) inverse in one sense (i.e., that used by, e.g., Nelsen), but appears to switch the roles in the table. For example, the independence copula can be written $$C(u,v) = \exp{-\left(-\ln{u}-\ln{v}\right)}$$. I would consider the generator to be $$-\ln{u}$$, and its inverse to be $$\exp{-t}$$, consistent with the initial definition in the section. I recognize, however, there are advantages to reverse the roles, such as when using the inverse Laplace transform to create (inverse) generators, and assessing the maximum dimensionality.

Is there a concensus as to which is the generator and which is the inverse? If there is, it would be preferable to use this convention in the article. In either case, however, the article should (a) be consistent, and (b) mention the other convention. Lovibond (talk) 21:10, 5 August 2013 (UTC)

Neutrality
Hello, I added a "neutrality disputed" tag to this article. The final few sentences of the third paragraph which state that copulas created an "evaluation culture", etc. are hardly neutral. A reference to a clearly non-neutrally written article from a sociologist is not sufficient to justify the word choice in these sentences. In fact, as is discussed later in the article, non-normal copulas do exist and are frequently used. I'd suggest that they should be removed. — Preceding unsigned comment added by 209.147.144.8 (talk) 00:44, 13 November 2013 (UTC)

Confusing headings: Definition and Mathematical Definition
I really don't understand the distinction between "Definition" and "Mathematical Definition" (currently the headings of the first two sections). What's a non-mathematical definition? Which definition is in fact the defintion of "copula" - for surely there is one? Or if there are two competing definitions, how do they differ? It would be very helpful if someone who understands copulas thoroughly could clarify these sections. Perhaps a single formal defintion and an explanatory informal section would be good. — Preceding unsigned comment added by 213.162.121.50 (talk) 23:43, 15 February 2015 (UTC)

Dr. Winkelmann's comment on this article
Dr. Winkelmann has reviewed this Wikipedia page, and provided us with the following comments to improve its quality:

"I think that this is a nice entry.

Only suggestion: it is a bit awkward to have separate sections "1. Mathematical definition" and "2. Definition". These should be integrated into a single section."

We hope Wikipedians on this talk page can take advantage of these comments and improve the quality of the article accordingly.

We believe Dr. Winkelmann has expertise on the topic of this article, since he has published relevant scholarly research:


 * Reference : Rainer Winkelmann, 2011. "Copula bivariate probit models: with an application to medical expenditures," ECON - Working Papers 029, Department of Economics - University of Zurich.

ExpertIdeasBot (talk) 16:56, 27 July 2016 (UTC)

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Added two items to the application section
Hi, I have added two items to the section listing applications of the copula. I feel that the application of coupla in Medicine and Ranking of electrical motors should be moved within the application section of Signal processing. It is coz in both these applications, n-dimensional electrical signals are being processed. Any suggestions? Thanks Earthianyogi (talk) 00:56, 8 April 2020 (UTC)

Merged "Copulas in signal processing"
Hi, My article on Copula in Signal Processing (https://en.wikipedia.org/wiki/Draft:Copulas_in_signal_processing) was rejected, and I was asked to merge it with this copula article by :. Therefore, I have added two new sub-sections within 'Signal Processing' section. Thank you. Earthianyogi (talk) 18:24, 12 April 2020 (UTC)

Maximal Couplings
The maximal coupling is related: https://colcarroll.github.io/couplings/static/maximal_couplings.html this would be a good example. Who could add it? https://books.google.de/books?id=8e45DwAAQBAJ&pg=PA232 give the formal definition of the maximal coupling Biggerj1 (talk) 21:27, 26 December 2023 (UTC)