User talk:Loraof

Dear Mister Loraof,

Do you think Enough source to convert Dao's theorem on six circumcenters associadted with a cyclic hexagon From wiki Viet Nam to English?

https://vi.wikipedia.org/wiki/%C4%90%E1%BB%8Bnh_l%C3%BD_%C4%90%C3%A0o_v%E1%BB%81_s%C3%A1u_t%C3%A2m_%C4%91%C6%B0%E1%BB%9Dng_tr%C3%B2n

Main source

1. Dergiades, Nikolaos (2014). “Dao’s Theorem on Six Circumcenters associated with a Cyclic Hexagon”. Trong Yiu, Paul. Forum Geometricorum (PDF) 14. tr. 243–246. ISSN 1534-1178. Truy cập , MR3260500

2. Telv, Cohl (2014). “A Purely Synthetic Proof of Dao’s Theorem on Six Circumcenters Associated with a Cyclic Hexagon”. Trong Yiu, Paul. Forum Geometricorum (PDF) 14. tr. 261–264. ISSN 1534-1178. Truy cập , MR3267837

3. X(3649) = KS(INTOUCH TRIANGLE), http://faculty.evansville.edu/ck6/encyclopedia/ETCPart3.html#X3649

4. Grégoire Nicollier, Two six-circle theorems for cyclic pentagons, Forum Geometricorum, 16 (2016) 347--354.

5. http://www.cut-the-knot.org/m/Geometry/AnotherSevenCircles.shtml

6. Nguyen Ngoc Giang, The extension from a circle to a conic having center: The creative method of new theorems, International Journal of Computer Discovered Mathematics, pp.21-32.

7. Ngo, Quang Duong (2016). “Ngo Quang Duong, Some problems around the Dao's theorem on six circumcenters associated with a cyclic hexagon configuration”. Trong Deko, Dekov. International Journal of Computer Discovered Mathematics (PDF) 1. tr. 25–39. ISSN 2367-7775

8. http://mathoverflow.net/questions/234053/daos-theorem-on-six-circumcenters-associated-with-a-cyclic-hexagon — Preceding unsigned comment added by 222.252.34.231 (talk) 17:40, 29 December 2016 (UTC)

I cannot get into reference 3 because the website has a problem. Numbers 5 and 8 are not reliable sources. Number 4 barely mentions the case of hexagons. Numbers 6 and 7 are in a journal I'm not familiar with, and I don't know if it is a reliable source. References 1 and 2 look good. So I now have no opinion about the answer to your question.

I would mention that if you do create an article for the theorem, I don't think you should draw the six circumcircles as tangent to each other--I don't think that they are tangent in general. Loraof (talk) 20:22, 29 December 2016 (UTC)

But I got into reference 3; first I got only a part of that long page, and then, after waiting a minute, I got the whole page, with X(3649). Boris Tsirelson (talk) 20:32, 29 December 2016 (UTC)

I still get an error message saying "webpage crashed". It appears to be a page on a triangle center, but how does that relate to the point of concurrency in Dao's cyclic hexagon? Loraof (talk) 20:47, 29 December 2016 (UTC)

Thank to Dear Mister Loraof.

if cyclic hexagon ABCDEF degenerated to ACE (A=B, C=D, E = F) then AOa, BOb, COc are concurrent at X(3649) so X(3649) of GHI = X(54) of ACE, so the theorem is a generalization of Kosnita theorem.

3 wrote^[1]:

X(3649) = KS(INTOUCH TRIANGLE)

Trilinears f(a,b,c) : f(b,c,a) : f(c,a,b), where f(a,b,c) = bc(b + c)(2a + b + c)(a - b + c)(a + b - c)

                       = g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = (b + c)(2a + b + c)(a - b + c)(a + b - c)

Barycentrics af(a,b,c) : bf(b,c,a) : cf(c,a,b) Two proofs of Dao's theorem about cyclic hexagons were published in 2014: Nikolaos Dergiades's Dao's Theorem on Six Circumcenters Associated with a Cyclic Hexagon and Telv Cohl's A Purely Syntheitc Proof of Dao's Theorem on Six Circumcenters Associated with a Cyclic Hexagon. In the degenerate case that the hexagon is the intouch triangle A'B'C', the triangle of the circumcenters of AB'C', A'BC', A'B'C is perspective to A'B'C' with perspector X(3649). (Dao Thanh Oai, Francisco Javier Garcia Capitan, ADGEOM #1718, September 16, 2014)

X(3649) lies on these lines: 1,30 7,21 10,12 11,113 55,3487 57,191 140,3336 145,388 354,946 396,2306 429,1835 553,1125 940,1406 962,3303 1056,2098 1086,1193 1100,1839 1317,1365 1358,2795 1360,1367 1411,2647 1749,3337 1834,2650 1852,1870 1901,2294 3318,3324

There are two author ask me that, they give two new papers on this theorem will appear in April 2017. So we will waiting these papers. Thank to You very much for your helping. 113.189.226.37 (talk) 13:13, 8 March 2017 (UTC)

Dear Mister Loraof,

There are two new papers on the Dao's theorem on six circumceneters:

http://geometry-math-journal.ro/pdf/Volume6-Issue1/6.pdf

http://geometry-math-journal.ro/pdf/Volume6-Issue1/4.pdf

So now, the Theorem appear in three Journals and Kimberling center with some papers, with some good review, do you think it is enough reliable source to convert Dao's theorem on six circumcenters from wiki Viet Nam to English? — Preceding unsigned comment added by 27.72.247.152 (talk) 16:42, 31 March 2017 (UTC)

Dear Mister Loraof,

[1]-Nguyen Van Linh, Another synthetic proof of Dao's generalization of the Simson line theorem, Forum Geometricorum, 16 (2016) 57--61. http://forumgeom.fau.edu/FG2016volume16/FG201608.pdf

[2]-Nguyen Le Phuoc and Nguyen Chuong Chi (2016). 100.24 A synthetic proof of Dao's generalisation of the Simson line theorem. The Mathematical Gazette, 100, pp 341-345. doi:10.1017/mag.2016.77. https://www.cambridge.org/core/journals/mathematical-gazette/article/div-classtitle10024-a-synthetic-proof-of-daoandaposs-generalisation-of-the-simson-line-theoremdiv/9CE7AA808F87FF05E290A7ED641FE9C4

[3]-Leo Giugiuc, A proof of Dao’s generalization of the Simson line theorem, tạp chí Global Journal of Advanced Research on Classical and Modern Geometries, ISSN: 2284-5569, Vol.5, (2016), Issue 1, page 30-32 http://geometry-math-journal.ro/pdf/Volume5-Issue1/4.pdf

[4]-Tran Thanh Lam, ANOTHER SYNTHETIC PROOF OF DAO’S GENERALIZATION OF THE SIMSON LINE THEOREM AND ITS CONVERSE, Global Journal of Advanced Research on Classical and Modern Geometries, ISSN: 2284-5569, Vol.5, (2016), Issue 2, page 89-92 http://geometry-math-journal.ro/pdf/Volume5-Issue2/3.pdf

[5]-Ngo Quang Duong, A generalization of the Simson line theorem, Forum Geometricorum, to appear in Forum Geometricorum.

[6]-Three other proof by Telv Cohl, Luis Gonzalez, Tran Thanh Lam, A Generalization of Simson Line http://www.cut-the-knot.org/m/Geometry/GeneralizationSimson.shtml

[7]-Another proof https://www.artofproblemsolving.com/community/c6h1075523p5181203 — Preceding unsigned comment added by 113.189.226.37 (talk) 16:51, 7 March 2017 (UTC)

Hi. Thank you for your recent edits. Wikipedia appreciates your help. We noticed though that when you edited Degeneracy (mathematics), you added a link pointing to the disambiguation page Parallel. Such links are almost always unintended, since a disambiguation page is merely a list of "Did you mean..." article titles. Read the FAQ • Join us at the DPL WikiProject.

It's OK to remove this message. Also, to stop receiving these messages, follow these opt-out instructions. Thanks, DPL bot (talk) 10:04, 14 March 2017 (UTC)

Hi. Thank you for your recent edits. Wikipedia appreciates your help. We noticed though that when you edited Hyperbola, you added a link pointing to the disambiguation page Relativity. Such links are almost always unintended, since a disambiguation page is merely a list of "Did you mean..." article titles. Read the FAQ • Join us at the DPL WikiProject.

It's OK to remove this message. Also, to stop receiving these messages, follow these opt-out instructions. Thanks, DPL bot (talk) 09:55, 21 March 2017 (UTC)

Hi Loraof,

The point of the text you changed is that determinacy is a field of study, not simply a mathematical property. I'm sure the text can be improved, but I would like it to focus on the field of study. Any suggestions? --Trovatore (talk) 22:05, 24 March 2017 (UTC)

Hi. Thank you for your recent edits. Wikipedia appreciates your help. We noticed though that when you edited Saddle point, you added a link pointing to the disambiguation page Lagrangian. Such links are almost always unintended, since a disambiguation page is merely a list of "Did you mean..." article titles. Read the FAQ • Join us at the DPL WikiProject.

It's OK to remove this message. Also, to stop receiving these messages, follow these opt-out instructions. Thanks, DPL bot (talk) 09:58, 12 April 2017 (UTC)

Sorry, I don't get it: how can the sentence "the system constraint for all projects is identified as are the resources" possibly be grammatically correct? IMO it should be either "the system constraint for all projects is identified as the resources" or "the system constraint for all projects are the resources". --Martin de la Iglesia (talk) 17:46, 23 April 2017 (UTC)

I would prefer to include a comma for clarity: "the system constraint for all projects is identified, as are the resources"; but some editors don't like to use as many commas as I do. The sentence as I have it means "the system constraint for all projects is identified, and the resources are identified." Note that the constraint is an equality or inequality, whereas the resources are physical entities or amounts. Loraof (talk) 17:54, 23 April 2017 (UTC)

OK, I get it now, but I'd strongly suggest to change the sentence so that its meaning becomes clearer. How about "...the system constraint for all projects as well as the resources are identified"? --Martin de la Iglesia (talk) 14:53, 24 April 2017 (UTC)

OK, but I would use commas around "as well as the resources" to give " the system constraint for all projects, as well as the resources, are identified" Loraof (talk) 15:08, 24 April 2017 (UTC)

A disciplinary discussion in which you may become involved, or may wish to comment, is at WP:ANI here regarding possible disciplinary action against User:The Banner for edit warring at Peacock Alley (restaurant). Akld guy (talk) 01:14, 19 July 2017 (UTC)

The only thing is that he misrepresents your stance, by claiming you said anything about "defunct restaurant" while you were responding on "former restaurant". The Banner talk 02:09, 19 July 2017 (UTC)

Hi. Thank you for your recent edits. Wikipedia appreciates your help. We noticed though that when you edited Dutch Ceylon, you added a link pointing to the disambiguation page Creole (check to confirm | fix with Dab solver). Such links are almost always unintended, since a disambiguation page is merely a list of "Did you mean..." article titles. Read the FAQ • Join us at the DPL WikiProject.

It's OK to remove this message. Also, to stop receiving these messages, follow these opt-out instructions. Thanks, DPL bot (talk) 10:52, 10 October 2017 (UTC)

Dear Loraof, I just read the article [] and I'm not quite sure, but maybe you're the main author of the section "History and origin of term". Right? It says

The term "bubble", in reference to financial crisis, originated in the 1711–1720 British South Sea Bubble, and originally referred to the companies themselves, and their inflated stock, rather than to the crisis itself. This was one of the earliest modern financial crises; other episodes were referred to as "manias", as in the Dutch tulip mania. The metaphor indicated that the prices of the stock were inflated and fragile – expanded based on nothing but air, and vulnerable to a sudden burst, as in fact occurred.

Unfortunately there's no source and I'm curious who said that. If I get this correctly, the Term and concept of the "bubble" has been used since the 18th century, since the South Sea Bubble, in an economic context. is that correct? Or do we use this Term later for things like the Mississippi scandal and the crisis around the South Sea Company?

Thank you very much! :)

14:21, 24 October 2017 (UTC)Daktylo (talk)

Sorry, I didn’t write that and am not familiar with it. Loraof (talk) 15:16, 24 October 2017 (UTC)

Hi. Thank you for your recent edits. An automated process has detected that when you recently edited Price signal, you added links pointing to the disambiguation pages Consumption and Production (check to confirm | fix with Dab solver). Such links are usually incorrect, since a disambiguation page is merely a list of unrelated topics with similar titles. (Read the FAQ • Join us at the DPL WikiProject.)

It's OK to remove this message. Also, to stop receiving these messages, follow these opt-out instructions. Thanks, DPL bot (talk) 20:22, 7 December 2017 (UTC)

Hi here, I'm currently on travel, and will be back at home at the beginning of New Year. Please let me look at your question at that time, and than decide what to do, ok? With regards --Qniemiec (talk) 18:24, 26 December 2017 (UTC)

Okay. Have a good holiday! Loraof (talk) 18:26, 26 December 2017 (UTC)

Hi there, I've just found some free moments to re-read your posting, and to comment it, so please take a look at what I wrote, ok? Maybe its a misunderstanding. However, of course, the diagram will look different if the data cloud will change its shape - in my picture it rather tends towards high values of ${\displaystyle \rho }$, while being rather circular with ${\displaystyle \rho }$ tending towards zero, to diagram might change the way you proposed. Greetings --Qniemiec (talk) 14:31, 4 January 2018 (UTC)

Hi, please take a look at my answer to your last posting, and let me know if my current understanding of the issue is correct, ok? Greetings --Qniemiec (talk) 20:22, 4 January 2018 (UTC)

Hi, just uploaded the redrawn version of the diagram we spoke about. Hope that now everything is ok. Thank you for the advice. --Qniemiec (talk) 23:44, 4 January 2018 (UTC)

Hi, you wrote "I would note, though, that your yellow caution above is incorrect—on my screen the red “y=...” version shows as the steeper one. But on the page Pearson correlation coefficient the new version shows." I think this comes due to some delay in Wikimedia's/Wikipedia's effort to update all links to a given new file - e.g. after uploading a new version of a picture or diagram it often takes some time until the updated version finally appears on screen, so in the beginning I often panicked thinking that I've uploaded the old version again. And as far as it concerns thanking, I should also thank you for this valuable hint. So have a good time and New Year! --Qniemiec (talk) 00:03, 5 January 2018 (UTC)

PS. I seem to be right with my delay hypothesis: Just took a look at the French Wikipedia article on regression, where my picture also appears, and when first opening the page, still the old image appeared. So I reloaded the page once more with my browser, and not earlier than after that reload the new version showed up. Greetings --Qniemiec (talk) 00:20, 5 January 2018 (UTC)

PS². Hi, it's me once more. Provided that ${\displaystyle \rho ^{2}={\frac {\sigma _{xy}}{\sigma _{x}^{2}}}\cdot {\frac {\sigma _{xy}}{\sigma _{y}^{2}}}<1}$, this leads - as you explained - to ${\displaystyle {\frac {\sigma _{xy}}{\sigma _{x}^{2}}}<{\frac {\sigma _{y}^{2}}{\sigma _{xy}}}}$, i.e. the slope of the x-versus-y correlation line must always be steeper than the one of the y-versus-x line. Ok, at least in case of positive correlations. But what about negative ones? In that case the 2nd inequation would be wrong, so - in order to be more exact - shouldn't we better work with absolute values then? I.e. ${\displaystyle |{\frac {\sigma _{xy}}{\sigma _{x}^{2}}}|<|{\frac {\sigma _{y}^{2}}{\sigma _{xy}}}|}$. Although this won't immediately affect my drawing, I'd like to know whether my way of understanding is correct. Greetings --Qniemiec (talk) 22:09, 5 January 2018 (UTC)

Yes, that looks correct. A few months ago I augmented a passage in Pearson correlation coefficient#Geometric interpretation to say

”For uncentered data, there is a relation between the correlation coefficient and the angle φ between the two regression lines, y = g_x(x) and x = g_y(y), obtained by regressing y on x and x on y respectively. (Here φ is measured counterclockwise within the first quadrant formed around the lines' intersection point if r > 0, or counterclockwise from the fourth to the second quadrant if r < 0.”

So the rho < 0 case has both curves negatively sloped in the second and fourth quadrants, with the “y=...” line flatter. But I doubt that adding another drawing to make this point would be insightful. Loraof (talk) 22:39, 5 January 2018 (UTC)

In the article linear differential equations I think it was you who edited the current version of the first paragraph, in which I found the phrase: "They equate 0 to a polynomial that is linear in the value and various derivatives of a variable;". Is this phrase correct? I honestly cannot understand what is meant here. Thanks. Conjugado (talk) 20:12, 25 January 2018 (UTC)

The value 0 (zero) equals the value of a polynomial which is a constant plus (another constant times the value y of a variable) plus (another constant times the derivative of y with respect to an independent variable) plus possibly other terms involving second , third, etc. derivatives of y with respect to the independent variable. In this context y refers both to a function y(t) of the independent variable t and to the value of that function.

I’ll think about the wording and rewrite the sentence in the article if I can improve it. Thanks for bringing it to my attention. Loraof (talk) 23:22, 25 January 2018 (UTC)

I came here to look for the background of your edits at linear differential equations and noticed the misplaced ref. I apologize for my efforts to repair this. You are certainly free to revert all my edits on your TP. Purgy (talk) 13:13, 26 January 2018 (UTC)

Hi, regarding the graph, have you tried to draw it on Octave? Often the whole code from Matlab works, but you could need to install a package (to get empirical cdf). There's also Scilab that has a Matlab-Scilab converter. If you generate new random samples, that could suffice. Ideally the author of the graph would save it with a better resolution, like nagual wrote. But having graphs drawn with free softwares could be a better alternative than matlab, more accessible (easier to perform later fixes by others). Yaḥyā ‎ (talk) 16:44, 28 January 2018 (UTC)

Thanks, @Yahya Talatin:. Unfortunately, I have zero graphing skills, so I have to leave graphing to others. Loraof (talk) 17:15, 28 January 2018 (UTC)

Alright, I'll do it if there is consensus. Just to be sure that I understand what you want; you want a new set (of 20) that represent what we would usually expect (last value <3). Just a word of caution though, it could be that the author of the picture chose a set where the last value is unusually that far to make it more obvious that there is less clustering on these regions. If you, nagual or other users agree on the ranges... I could provide a couple of randomized sets (that end within that range), and you could decide the one that is more acceptable for you all. Yaḥyā ‎ (talk) 19:11, 28 January 2018 (UTC)

After running it several time, I couldn't reproduce (on Octave) a value of 3.5; it usually does not go beyond this. I guess this suggest that the author run it continuously until he finds that one for a purpose (to highlight the clustering variation). Yaḥyā ‎ (talk) 20:11, 28 January 2018 (UTC)

The purpose of this graph, which I presume was made specifically for the article Empirical distribution, is not to show clustering – it’s just to show the relation of the empirical step function to the population distribution function (namely that the former approximates the latter). So I think the picture you just linked looks good. Can you replace the old one with this one? Thanks. Loraof (talk) 20:38, 28 January 2018 (UTC)

OK, how's this? Yaḥyā ‎ (talk) 23:44, 28 January 2018 (UTC)

Looks great! Can you make the curve a more vivid color? Loraof (talk) 00:02, 29 January 2018 (UTC)

I will ask nagual for that, stuff that concern personal tastes (like colors) I prefer leaving it to someone else. Yaḥyā ‎ (talk) 00:11, 29 January 2018 (UTC)

New graph

In my opinion, the new graph lacks the randomness of the current graph. Re-running the code until you find one that 'looks random' is more akin to a sort of subjective pseudorandomness. The original complaint with the image was that the curve appears to reach (or 'touch') y=1. However, this is also true of the two graphs linked to above. Now you've decided that there shouldn't be a sample at x>3 in order to satisfy your own expectations, which seems a bit misguided to me. I'm sure one of the mathematicians among us can calculate the exact probability of finding a sample >3 in a sample size of 20, and it isn't 0. While you're focussing your attention on the top end of the graph you don't seem the least bit bothered by the fact that the low end has the converse 'problem' – that none of the graphs have a sample at x<-2, making all of them subjectively a little right heavy. Of course, they're not, they're just random. That's the thing about randomness.

Anyway, I've been asked to colour the graphs provided and I'll do that. I assume everyone's happy with the pale green curve? But I would suggest that you link to this discussion from WT:MATH and get a broader consensus before changing the graph. I'll be back here shortly when I've finished the new graph... nagualdesign 10:05, 29 January 2018 (UTC)

I've just spent the last hour redrawing the graph and Photoshop crashed! I'll do it again in a while, after I've calmed down. nagualdesign 11:12, 29 January 2018 (UTC)

Hi nagual, I'd say the probability of having above 3 is pretty much rare. See here: 68–95–99.7_rule#Table_of_numerical_values, assuming variance of 1. I might be missing something, but I wasn't able to reproduce the original samples range. Yaḥyā ‎ (talk) 12:58, 29 January 2018 (UTC)

Well, of course it's pretty rare, you can see that by looking at the line. My point was that it's non-zero, but I'll leave it to others to decide which graph is more appropriate. Compared to the old graph I think it looks contrived, but the new graph is much higher resolution at least. Now that I have a Photoshop file with everything on separate layers I can make any changes to colour etc. if necessary. (By the way, I credited you in the file description, Yaḥyā. ) nagualdesign 14:23, 29 January 2018 (UTC)

I've left a note at WT:MATH. At this point altering the samples, as well as the step function, would be very straightforward, as would changing any of the colours. nagualdesign 14:34, 29 January 2018 (UTC)

But as I mentioned above, this graph exists for only one reason: to give a visual impression of how an empirical frequency distribution can approximate a population distribution function. All we need is a generic-looking population function and a logically possible empirical function that approximates it.

This means (1) the empirical function must not have any horizontal values greater than the value (if there exists one) at which the population curve hits (and for visual clarity, appears to hit) a height of 1, and (2) the empirical function must not have any horizontal values below the value (if there exists one) at which the population function hits (and for visual clarity, appears to hit) a height of 0. These are logical requirements, and don’t involve merely satisfying my own expectations. And there’s nothing innately relevant about x=–2 or x=3 here (and it doesn’t matter whether there’s a zero or positive probability of x > 0).

Also, both the graphs shown above do look very random. Maybe it would look nicer if the whole image would be stretched horizontally in both directions.

Note further that in between the lowest and highest values of the empirical curve, the empirical curve should be sometimes above and sometimes below the smooth population curve, because any well-designed sampling process will have that feature. So that feature of the old graph needs to be restored. Loraof (talk) 18:04, 29 January 2018 (UTC)

Thus, what remains to do is: (a) make the curves intersect each other in at least several places, (b) stretch the whole diagram horizontally, and (c) re-color more vividly. Thanks, both of you! Loraof (talk) 18:11, 29 January 2018 (UTC)

When I say that the new graph doesn't look random I'm referring to the fact that the space between samples, from left to right, gets progressively smaller until x=0, then gets progressively larger, with only maybe 3 data points (out of 20) where this isn't the case. That is the opposite of random. I may as well have faked it by making every step cross the curve.

These are logical requirements, and don’t involve merely satisfying my own expectations. No they are not logical requirements, as pure logic would dictate that samples could exist anywhere within the range of the graph and have nothing to do with how it looks (subjectively). And these graphs have indeed been made to satisfy your specific requirements. You expressed your expectations to Yaḥyā who ran the code repeatedly until he got one that would satisfy you.

Moreover, you're now asking for a set of samples where the step function crosses the curve a few times. I can see why you'd want that but, again, that isn't random. If you asked me to toss a coin ten times and it came up H,H,H,H,H,H,T,H,T,H you'd probably think that wasn't quintessentially random, but it's actually just as likely as H,T,T,H,T,H,H,H,T,H or any other combination. Human perception of randomness is typically rather flawed and involves considerable bias, as you have amply demonstrated. If you want to avoid bias it's better to just run the code once and be satisfied with whatever it spits out. What would be even better is if the step function was generated on the fly each time the article is visited, but I'm not sure that's possible.

I'd like to hear more opinions from other editors before I make further changes to the images. nagualdesign 19:03, 29 January 2018 (UTC)

OK, I will wait and do what is decided. I can run (in another software though) a conditional randomization, but I don't think nagual will like that. :) For what it is worth nagual, some statistics course books also seem to do what he wants (like choosing the good apple from a couple of bad ones...). Here we have an expression for that: Arrangé avec le gars des vues. :) Yaḥyā ‎ (talk) 19:37, 29 January 2018 (UTC)

Thinking of it, seems similar to a photographer who takes a couple of pictures and pick the one that seems more appealing. Yaḥyā ‎ (talk) 20:15, 29 January 2018 (UTC)

• @Nagualdesign: Any distribution function that is not a single point mass describes a random variable. So of course it is random in the sense of portraying a random variable. Your statement that the observations are farther apart far to the left and far to the right is not “the opposite of random”, as you put it – that spacing just reflects the feature that is uni-modal. Lots of random variables have cdf’s that look this way. For example, a random variable with a normal distribution, the most used distribution, is unimodal, and a typical sample will have observations bunched more near the center. It appears to me that you are thinking about a uniform distribution, which has no tendency to bunch; you appear to be thinking incorrectly that that is the only thing that is a random variable.

I suspect that part of nagual’s confusion lies in the fact that laypeople sometimes use the word “random” for a specifically uniform distribution, while in statistics, such as here, the word “random” pretty much only arises in the context of “random variable”.

Yes, the relation I mentioned above between the two curves is a logical requirement, for the simple reason that it is impossible to observe a sample unit drawn from the population and have that sample unit be a larger value than any value in the population. There is no speculation here, and frankly this should be obvious to anyone who has ever learned about cdf’s. Loraof (talk) 20:40, 29 January 2018 (UTC)

Well you assumed wrongly. I understand the mathematics; that this is a normal distribution. I've been running numbers on Wolfram Alpha and other websites all afternoon. Generally speaking, the samples should bunch in the middle, but you often get 2 or more clusters, as we see in the original graph. The new graph, as I said, hardly deviates from the curve at all. In such a small sample (20) you normally get more bona fide randomness. nagualdesign 20:53, 29 January 2018 (UTC)

(edit conflict) Maybe we’ve been talking past each other. In any event, we don’t need the example to be normally distributed. If it is normal, then as long as the curve is drawn thin enough, it will be clear, from what the reader can see at a glance, that the empirical cdf hits a height of 1 whereas the population cdf never does, so it’s fine, and it will be clear that going leftward the empirical cdf hits 0 whereas the population cdf never does. But we don’t need the normal cdf – any valid cdf will do for the purposes of the article that this graph is for. It might or might not be an easier graphing task to use a bounded one, in which case as I’ve said above, we have to be careful at both ends. Loraof (talk) 22:38, 29 January 2018 (UTC)

Random graph

<div style="position: relative; top: -Script error: No such module "MjolnirPants".px; left: -Script error: No such module "MjolnirPants".px; width: 2500px">

The blue step function graph shows an empirical distribution function. The grey bars represent the observations in the sample corresponding to the sample’s empirical distribution function, and the green curve, which asymptotically approaches a height of 1 without reaching it, is the true cumulative distribution function. (Click here to load a new graph.)

There's some further discussion taking place on my talk page about creating a set of images and a function that picks one of those at random. nagualdesign 22:27, 29 January 2018 (UTC)

This morning I wrote some JavaScript that randomly generates a 'sheet' of 100 graphs, which I've saved as a single PNG file and uploaded (see right). User:MjolnirPants is going to write a script that will randomly select one of those graphs to display as a thumbnail, which will look something like the image below that.

Take a look at the graphs and let me know what you think. Also, please check the gaussian() function (below) to see if I've coded it correctly, if you can. In JavaScript, Math.random() gives you random number between 0 and 1 with uniform distribution, and you have to do a bit of mathematical jiggery-pokery to get a normal distribution, if that makes sense. nagualdesign 12:09, 30 January 2018 (UTC)

function gaussian() {
  // Generate a random number, mean=0, standard deviation=1
  return Math.sqrt(-2*Math.log(Math.random()))*Math.cos((2*Math.PI)*Math.random());    
}

MjolnirPants has finished the code, which you can now see to the right, and I've added it to the article. Do let us know what you think. Cheers. nagualdesign 16:15, 30 January 2018 (UTC)

Thanks to all of you for the work you’ve put in on this! The graph that’s now in the article is easy to read. My only concern is that a reader seeing it might get the false impression that the blue one has to be below the green one until the last step. If a substantial number of your 100 graphs show at least one crossing that is not near the ends, I think we ought to go with one of those. We do not have to use a graph that was obtained by random selection from these 100 – we just need one that gives a good generic idea without leaving any false impressions for the casual reader. Loraof (talk) 17:36, 30 January 2018 (UTC)

They all give a good generic idea without leaving any false impressions, since they're the real deal. The whole point of this endeavour is that cherry picking one that you (or anyone else) think is somehow quintessential, and exemplifies the right sort of step function more that any other, is completely misguided. As you can see by looking at File:ECDF-100.png, very few of them conform to the aesthetic ideals that you were aiming for with this graph, which is hardly random at all.

Looking at the first couple of dozen graphs I notice that as many of them have a step function that's above the curve as below the curve, which is exactly what we'd expect. The idea of being able to Click here to load a new graph is specifically to dispel any misapprehensions that any single graph on its own might otherwise impart, but in a way that removes any possibility of bias on our part.

There's no reason to treat casual readers as laypeople who ought to be handled using "lies-to-children", especially when it comes to topics like empirical distribution functions. Similarly, we don't dumb down articles on quantum wave functions and suchlike, as the people who read those articles are likely to have a keen sense of comprehension. I expect most of them will be in higher education. nagualdesign 18:10, 30 January 2018 (UTC)

If I were to pick one graph that somehow exemplifies the step function it would be the one on the third row, sixth from the left. It's got a nice s-curve to it and it crosses the green line multiple times. The one next to it (fifth from the left) isn't bad either. However, these two graphs only constitute 2% of those available, and the other 98% don't look very much like them, so they're not really representative at all. Do you see what I mean? nagualdesign 18:35, 30 January 2018 (UTC)

How about the one in row 3, column 7 – does that look more representative? It’s got places where it’s easy to see at a glance (even on a small computer screen) that the blue curve is sometimes above and sometimes below the green one, so it satisfies my concern. Loraof (talk) 18:50, 30 January 2018 (UTC)

I thought this might interest you; I altered the code so that instead of drawing graphs it just ran the numbers, so I was able to get some reasonable statistics based on a large number of runs:

The calculations were done in 3 batches. The first batch (10s) were based on 1000 graphs each. The second and third batches (100s and 1000s) were based on 100 graphs each. The final batch took a minute and a half to compute! I'm not sure what it means. I thought the Average/samples would converge on a number but they just seem to keep dropping. nagualdesign 00:41, 6 February 2018 (UTC)

It’s interesting that the average number of crossings as a ratio to the sample size decreases monotonically as the sample size increases. Loraof (talk) 02:42, 6 February 2018 (UTC)

Hi. Thank you for your recent edits. An automated process has detected that when you recently edited State-space representation, you added a link pointing to the disambiguation page Matrix (check to confirm | fix with Dab solver). Such links are usually incorrect, since a disambiguation page is merely a list of unrelated topics with similar titles. (Read the FAQ • Join us at the DPL WikiProject.)

It's OK to remove this message. Also, to stop receiving these messages, follow these opt-out instructions. Thanks, DPL bot (talk) 09:38, 10 February 2018 (UTC)

An automated process has detected that when you recently edited Reciprocal polynomial, you added a link pointing to the disambiguation page Characteristic (check to confirm | fix with Dab solver).

(Opt-out instructions.) --DPL bot (talk) 09:18, 20 February 2018 (UTC)

An automated process has detected that when you recently edited Discount function, you added a link pointing to the disambiguation page Consumption (check to confirm | fix with Dab solver).

(Opt-out instructions.) --DPL bot (talk) 09:14, 14 March 2018 (UTC)

An automated process has detected that when you recently edited Controlling for a variable, you added a link pointing to the disambiguation page Regression (check to confirm | fix with Dab solver).

(Opt-out instructions.) --DPL bot (talk) 09:23, 2 May 2018 (UTC)

An automated process has detected that when you recently edited Rational expectations, you added a link pointing to the disambiguation page Consumption (check to confirm | fix with Dab solver).

(Opt-out instructions.) --DPL bot (talk) 09:24, 25 May 2018 (UTC)

High, Loraof! I have seen your edit re math and I bring to your attention an aspect which should be prezented in athe article Mathematician. I heve opened a discussion on talk:Mathematician about the employability of math graduates and mathematicians. Your feedback is appreciated.--5.2.200.163 (talk) 16:20, 30 May 2018 (UTC)

An automated process has detected that when you recently edited Mean squared error, you added a link pointing to the disambiguation page Cross-validation (check to confirm | fix with Dab solver).

(Opt-out instructions.) --DPL bot (talk) 09:03, 15 June 2018 (UTC)

Hello Loraof,

Since you've worked on a range of interesting articles, I'm messaging to ask if you'd be interested in updating any of them and subjecting them to academic peer review via the WikiJournal of Science.

Peer-reviewed articles are dual-published both as standard academic PDFs, as well as into Wikipedia. This improves the scientific accuracy of the encyclopedia, and rewards academics with citable, indexed publications. It is also a good way to gt outside feedback on existing Wikipedia content.

Let me know if it's the sort of thing that you might be interested in and I'm happy to give more info. T.Shafee(Evo&Evo)^talk 11:10, 28 October 2018 (UTC)

Further info:

• Wikipedia:WikiJournal_article_nominations
• Shafee, Thomas; Mietchen, Daniel; Su, Andrew I. (2017). "Academics can help shape Wikipedia". Science. 357 (6351): 557.2–558. doi:10.1126/science.aao0462. ISSN 0036-8075.
• Shafee, Thomas (2017). "Health Libraries - Wikipedia-integrated publishing: a comparison of successful models". Health Inform. 27 (2).
• Editorial board (2018-06-01). "The aims and scope of WikiJournal of Science". WikiJournal of Science. 1 (1): 1. doi:10.15347/wjs/2018.001. ISSN 2470-6345.{{cite journal}}: CS1 maint: unflagged free DOI (link)

Hi Loraof

We're working to measure the value of Wikipedia in economic terms. We want to ask you some questions about how you value being able to edit Wikipedia.

Our survey should take about 10-15 minutes of your time. We hope that you will enjoy it and find the questions interesting. All answers will be kept strictly confidential and will be anonymized before the aggregate results are published. Regretfully, we can only accept responses from people who live in the US due to restrictions in our grant-based funding.

As a reward for your participation, we will randomly pick 1 out of every 5 participants and give them $25 worth of goods of their choice from the Wikipedia store (e.g. Wikipedia themed t-shirts). Note that we can only reward you if you are based in the US.

Click here to access the survey: https://mit.co1.qualtrics.com/jfe/form/SV_eXJcEhLKioNHuJv

Thanks

Avi

Researcher, MIT Initiative on the Digital Economy --Avi gan (talk) 05:15, 15 December 2018 (UTC)

What do you know about this article: Redacted? The referencing needs some cleanup, and it's citing redacted, among other somewhat dodgy things that would generally be associated with self-promotional articles. Ping me when responding or drop a message on my talk page. Thanks. — Insertcleverphrasehere ^{(or here)}_{(click me!)} 19:13, 15 December 2018 (UTC)

@Insertcleverphrasehere:Yes, it is me. I was aware that someone was writing an article about me, and I’ve stayed completely out of it. Yes, the author that you’ve apparently been communicating with has a conflict of interest, having co-authored with me.

As for the content of the article, which I’ve only seen just now in clicking there from your message, at a minimum it needs to have my two wikipedia pseudonyms removed and the incorrect place of birth removed. Also, the redlink to Distributed lags should be corrected to Distributed lag. Loraof (talk) 19:33, 15 December 2018 (UTC)

I've removed the wikipedian information, and will request revision deletion of the page history of that page as well as the last couple edits to this page. — Insertcleverphrasehere ^{(or here)}_{(click me!)} 19:37, 15 December 2018 (UTC)

Loraof, Sorry about all of this... looks like everything is sorted now. Cheers, — Insertcleverphrasehere ^{(or here)}_{(click me!)} 23:26, 15 December 2018 (UTC)

In this edit, is plainly a mistake to insist that ${\textstyle \mathbf {A} }$ be a ${\textstyle p\times p}$ matrix rather than ${\textstyle q\times p}$ for some positive integer ${\textstyle q}$. One has

${\displaystyle {\begin{aligned}{\text{constant (i.e. non-random) }}&\mathbf {A} \in \mathbb {R} ^{q\times p}.\\[5pt]{\text{constant }}&\mathbf {a} \in \mathbb {R} ^{q\times 1}\quad {\text{(with }}q{\text{ not }}p.)\\[5pt]{\text{random }}&\mathbf {X} \in \mathbb {R} ^{p\times 1}.\\[5pt]&\operatorname {var} (\mathbf {X} )=\Sigma \in \mathbb {R} ^{p\times p}.\\[5pt]{\text{random }}&\mathbf {AX} +\mathbf {a} \in \mathbb {R} ^{q\times 1}.\\[5pt]&\operatorname {var} (\mathbf {AX} +\mathbf {a} )=\mathbf {A} \operatorname {var} (X)\mathbf {A} ^{\rm {T}}=\mathbf {A} \Sigma \mathbf {A} ^{\rm {T}}\in \mathbb {R} ^{q\times q}.\end{aligned}}}$

I fixed this in a recent edit. Michael Hardy (talk) 20:10, 22 December 2018 (UTC)

http://geometry-math-journal.ro/pdf/Volume7-Issue2/5.pdf

http://forumgeom.fau.edu/FG2015volume15/FG201509.pdf

http://www.journal-1.eu/2018/Dao-Perspective-Triangles.pdf

http://faculty.evansville.edu/ck6/encyclopedia/IndexOfTrianglesReferencedInETC.html — Preceding unsigned comment added by 117.6.129.14 (talk) 04:06, 29 December 2018 (UTC)

Re Walras's law, see MOS:POSS. Dicklyon (talk) 04:56, 28 January 2019 (UTC)

Thanks for making this change at Genderless language; it's much better (and accurate) now, thanks. It still needs a reference, though; can you find one and add a citation? Articles of all sorts on language-related topics tend to be full of original research and unsubstantiated allegations, because everybody feels like an expert in their own language, which, to some extent, they are. But it also means that editors sometimes feel they don't need to add citations to reliable sources for something they "know" is true; however, Wikipedia's verifiability policy requires this. I try to add citations in all my changes to articles about language, even if I "know it to be true", and I hope you can do the same to help keep the encyclopedia articles on language in good condition. Thanks, and happy editing! Mathglot (talk) 20:59, 14 February 2019 (UTC)

@Mathglot: Actually I think I didn’t add any assertions to that passage – I just tried to transform wording that was difficult to follow into clear wording. I’ll add a citation-needed tag to the passage for now, and if I can come up with citations I’ll add them. Loraof (talk) 22:10, 14 February 2019 (UTC)

Yes, I see your point; there weren't really any assertions relative to genderless language itself added. And it is easier to follow now, so thanks for that. I guess what I was considering an "assertion", was that pretty minor issue of converse vs. inequality (or subset), not really a new assertion. I just have a pet peeve in general about language-related articles being replete with OR; if we followed Verfiability policy properly, huge chunks of many language articles would just be wiped out, even if they might be correct—but, without the citations, we don't know that. So, I might've been oversensitive about your change, which in fact, improves the article. I hope in general, you'll help push for accountability in language articles (I see that you've edited a few of them), so don't hesitate to slap {{cn}} tags on things that need citations,and if they're not provided after being tagged for a while, be bold and delete them. Thanks, Mathglot (talk) 22:35, 14 February 2019 (UTC)

An article you recently created, Exogenous and endogenous variables, does not have enough sources and citations as written to remain published. It needs more citations from reliable, independent sources. (?) Information that can't be referenced should be removed (verifiability is of central importance on Wikipedia). I've moved your draft to draftspace (with a prefix of "Draft:" before the article title) where you can incubate the article with minimal disruption. When you feel the article meets Wikipedia's general notability guideline and thus is ready for mainspace, please click on the "Submit your draft for review!" button at the top of the page. CASSIOPEIA^(talk) 04:03, 6 March 2019 (UTC)

Please see:

https://vi.wikipedia.org/wiki/%C4%90%E1%BB%8Bnh_l%C3%BD_t%C3%A1m_%C4%91%C6%B0%E1%BB%9Dng_tr%C3%B2n — Preceding unsigned comment added by 117.6.86.35 (talk) 14:46, 10 April 2019 (UTC)

A discussion is taking place as to whether the article Gaels of Scotland is suitable for inclusion in Wikipedia according to Wikipedia's policies and guidelines or whether it should be deleted.

The article will be discussed at Wikipedia:Articles for deletion/Gaels of Scotland until a consensus is reached, and anyone, including you, is welcome to contribute to the discussion. The nomination will explain the policies and guidelines which are of concern. The discussion focuses on high-quality evidence and our policies and guidelines.

Users may edit the article during the discussion, including to improve the article to address concerns raised in the discussion. However, do not remove the article-for-deletion notice from the top of the article. ThoughtIdRetired (talk) 17:55, 23 June 2019 (UTC)

5 Sources: Crux, Forum geometricorum, Arxvi, international journal of geometry, International Journal of Computer Discovered Mathematics

https://vi.wikipedia.org/wiki/%C4%90%E1%BB%8Bnh_l%C3%BD_t%C3%A1m_%C4%91%C6%B0%E1%BB%9Dng_tr%C3%B2n 14.248.84.234 (talk) 02:17, 30 September 2019 (UTC)