Talk:Vysochanskij–Petunin inequality

I know about the policy No original research, but it might be worth stating that I believe this result can be improved to:


 * $$P(\left|X-\mu\right|\geq \lambda\sigma)\leq\frac{4}{9\lambda^2} $$
 * when $$\lambda \geq 1.38539...$$
 * $$P(\left|X-\mu\right|\geq \lambda\sigma)\leq 1-\left({4 \lambda^2 \over 3(1+\lambda^2)}\right)^2 $$
 * when $$\lambda \leq 1.38539...$$
 * where $$1.38539... = \sqrt{{2 \over 3}+ \sqrt{124 \over 63}\cos \left( {\cos^{-1}\left( \sqrt{847 \over 29791} \right) \over 3} \right)} $$
 * where $$1.38539... = \sqrt{{2 \over 3}+ \sqrt{124 \over 63}\cos \left( {\cos^{-1}\left( \sqrt{847 \over 29791} \right) \over 3} \right)} $$
 * where $$1.38539... = \sqrt{{2 \over 3}+ \sqrt{124 \over 63}\cos \left( {\cos^{-1}\left( \sqrt{847 \over 29791} \right) \over 3} \right)} $$

--Henrygb 01:31, 16 Aug 2004 (UTC)

The title gives one spelling but the article uses a different spelling of Vysochanskiї/Vysochanskij. Moreover, the second spelling does not redirect to the article. Perhaps (a)the second spelling should be made to redirect, and (b)the article should say "(also known as the Vysochanskiї-Petunin inequality)" and then explain the relation between the two spellings. Duoduoduo (talk) 16:08, 1 October 2009 (UTC)

In "unimodal distribution, mean μ and finite, non-zero variance", is the "non-zero variance" really required? It seems to me that a distribution with zero variance must have all probability in a single point, in which case the inequality holds trivially. Howard Landman (talk) 16:07, 30 August 2011 (UTC)


 * If the variance is zero then the probability is 1 for any &lambda; which means the inequality fails 86.178.140.198 (talk) 20:34, 26 March 2012 (UTC)

Fixing this page title to Vysochanskij-Petunin inequality
I personally knew professor Petunin who supervised Mr. Vysochanski on his postgraduate work. They worked on this result for a few years and the original proof of this inequality was not simple but rather quite long and difficult. There is also a translation of this article in Russian Wikipedia with correct original name. In English the most closed translation of this family name would be Vysochanski, however Vysochanskij is also acceptable. I think it is time to fix the name of this already classic inequality.

Unfortunately I do not have permissions to make this fix myself, so I need help Gchoul (talk) 18:51, 17 March 2013 (UTC) You can use the template on this page http://en.wikipedia.org/wiki/Template:Requested_move Pug6666 20:56, 17 March 2013 (UTC)

I have renamed the article from -iї to -ij, as requested by Gchoul. I have also fixed some redirects that went from -ii to -iї, so that they now go direct from -ii to -ij. But now I think this was all a mistake. There are many article in English Wikipedia that use the -ii spelling, listed at Special:WhatLinksHere/Vysochanskij–Petunin_inequality. It would have been better, in my view, to rename this article to Vysochanskii–Petunin inequality. Maproom (talk) 22:06, 17 March 2013 (UTC)

This was not a mistake. First of all "ї" is not an English letter. Neither a Russian one, so the usage of this symbol is senseless in any way. The ending of name Vysochaski is absolutely the same as say Brzhezinski or Levinski. You can write those names with "y" at the end instead of "i", but never with "ї" or "ii". As I mentioned earlier the best here would be Vysochanski, but the original article from a Russian math journal was translated with the name Vysochanskij. That is the only reason why I suggested to use "ij" Thank you for your prompt help

Gchoul (talk) 22:22, 17 March 2013 (UTC)
 * The thing is, we cannot simply take your word for it. The title must reflect what is most commonly accepted. And from my own enquiries, the old title was the most widely accepted, followed by the double 'ii's. P.S. I think for the moment we should resume this conversation on the Help Desk to get as many opinions as we can.  Kinkreet ~&#9829;moshi moshi&#9829;~ 00:29, 18 March 2013 (UTC)

I have read your comments with regards to using name Vysochanskii as the most appropriate one in the article title. What can I say. As you may guess English is not my mother tongue, but I have been living in the English speaking country for 20 years. I have seen hundreds of Russian and Ukrainian family names that have the same ending as Visochanskii (as you suggested ) I have never ever seen such a spelling in my life. Maybe it appeared just recently and I am not aware of it. As I already mentioned I personally knew Dmitri Fedorovich Visochanski for many years, so I know his name in Russian very well and the article in Russian Wikipedia bears a correct name. I raised the issue with English translation only because it looks ridiculous to me. If it does not for English community it is OK. Anyway English does not have an equivalent sound for the ending of this name and for native English speaking person it is very difficult and nearly impossible to pronounce it correctly. And please do not forget that when the article containing this inequality was translated first in English the translator used the name Vysochanskij

Gchoul (talk) 15:51, 18 March 2013 (UTC)

I have no preference for the article personally. I am only looking at this from the objective point of view. The point about you knowing the professor personally, is exactly what Wikipedia tries to avoid, as outlined here, more specifically, this statement "Do not add unsourced material from your personal experience, because that would make Wikipedia a primary source of that material". Personally, I don't really care what the title is, and I don't think many people do, if so they would have voiced an opinion. And I don't want to criticize anyone, but I think a page move should have only been conducted after looking at the guidelines, and not just because someone requested it. That was always my primary concern. I am no expert in this area. I've made my point about using the common name, and I'd like to gracefully bow out of further debates, because I don't think I have any more to contribute to the discussion. Kinkreet~♥moshi moshi♥~ 16:38, 18 March 2013 (UTC)

Agree with you 100%. To put it simple I requested the name change to Vysochanskij not because I personally like it but rather having in mind a consideration that you mentioned.Wikipedia is built first and foremost on reliable sources. The most reliable source in English which actually is used in the references of this article: D. F. Vysochanskij, Y. I. Petunin (1980). "Justification of the 3σ rule for unimodal distributions". Theory of Probability and Mathematical Statistics 21: 25–36. Please agree that it is not a good idea to have 2 different spellings of the name in one article even if it had it for 9 years Gchoul (talk) 18:37, 18 March 2013 (UTC) — Preceding unsigned comment added by Gchoul (talk • contribs)


 * I think we should all agree that it is not good to have two different spellings within one article, and preferably not within the whole English-language Wikipedia. The question is, should we alter this article and its title to the -ii spelling, to be consistent with the other articles; or alter all the other articles to the -ij spelling; or just leave it all inconsistent? Maproom (talk) 18:54, 18 March 2013 (UTC)

I am not sure how the decision is made in Wikipedia, but I what I want is to provide info for the people who care for Wikipedia. If say, you want to make a change to ii across all Wikipedia then what are you going to do with one of the most famous writer's name Dostoyevsky ???

If you really decide to make a change to ii then you will invent a new name Dostoyevskii

Does Wikipedia really want to make a revolution in spelling ?

Now see, the ending of the names Dostoyevsky and Vysochanskij in Russian is absolutely the same so the most correct option in English would be certainly Vysochansky.

I need to repeat here that I would definitely put ending "y" or "i" in this name, but you cannot change the name in the reference. It means that we do not have much choice here and must stick to the name in the reference - Vysochanskij as the only source available.

And one more thing. Please give me an example of the name in Wiki that has "ii" at the end. Maybe there is some misunderstanding in this discussion

Gchoul (talk) 22:51, 18 March 2013 (UTC)


 * Wikipedia policy is to prefer the form that is most usual in modern English-language texts. With Fyodor Dostoyevsky that has been easy to agree on, with Kiev it has been impossible. If I have time, I will look at all the articles that mention Vysochansk??, check all the English-language sources that they cite, and find which spelling is most common. Maproom (talk) 09:41, 19 March 2013 (UTC)

All right. Looks like it is all clear now and it is time to make a summary. Mr. Vysochansy was Ukrainian (although in the USSR everybody was Soviet, but Mr. Vysochansy's mother tongue was Ukrainian). The ending of his family name in Ukrainian is "ський" and in Russian "ский" These endings do sound differently in the two languages. Therefore it will always be an argument what would be better translation them in English. Under this angle you can use "y", "i", "ij", "ii", "yi". English does not have an equivalent sound anyway. Kiev also sounds differently in Russian and Ukrainian. English native speaker can feel the difference and can easily pronounce it in two different ways. So Ukrainians, because it is their capital will always want it to be translated close to Ukrainian, and Russians to a Russian respectively.

13:47, 19 March 2013 (UTC) — Preceding unsigned comment added by Gchoul (talk • contribs)


 * Here is my own summary. What the endings sound like, how they are spelled in Russian, and in Ukrainian, and how Russians, and Ukrainians, would like them to be spelled in the Latin alphabet — these are all irrelevant to Wikipedia policy. What matters is how English-language texts usually spell the name. Maproom (talk) 13:56, 19 March 2013 (UTC)

Fully agree with you. We have got only one source so far that is why I suggested "ij", no matter what I think of it. I also would like to thank all Wikipedia people who contributed to this discussion and made the subject much more clear to me.

Gchoul (talk) 14:00, 19 March 2013 (UTC)


 * I have done some checking. I found only two links from other eng-Wikipedia articles to references containing the name "Vysochansk??". They are
 * http://m.njit.edu/CAMS/Technical_Reports/CAMS02_03/report4.pdf
 * D. F. Vysochanskij, Y. I. Petunin (1980). "Justification of the 3s rule for unimodal distributions". Theory of Probability and Mathematical Statistics 21: 25–36.
 * Both use the -ij spelling.


 * And I googled for "Vysochanskii" etc., with the quotation marks, and found
 * Vysochanskii   17,500 hits
 * Vysochanskiy   14,000 hits
 * Vysochansky     6,930 hits
 * Vysochanski     2,660 hits
 * Vysochanskij    2,130 hits
 * Vysochanskyi      402 hits
 * Maproom (talk) 21:07, 19 March 2013 (UTC)