Timeline for A normal distribution inequality
Current License: CC BY-SA 4.0
42 events
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| Aug 19, 2019 at 19:02 | history | edited | YCor | CC BY-SA 4.0 |
removed capitals from title
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| Aug 19, 2019 at 9:01 | answer | added | Hans | timeline score: 0 | |
| Aug 18, 2019 at 19:59 | vote | accept | Hans | ||
| Jan 10, 2018 at 15:55 | history | edited | Hans | CC BY-SA 3.0 |
deleted 49 characters in body
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| Jan 10, 2018 at 9:17 | vote | accept | Hans | ||
| Aug 18, 2019 at 19:59 | |||||
| Jan 10, 2018 at 9:16 | vote | accept | Hans | ||
| Jan 10, 2018 at 9:17 | |||||
| Jun 5, 2015 at 1:04 | history | edited | Hans | CC BY-SA 3.0 |
deleted 38 characters in body
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| Jun 3, 2015 at 22:02 | answer | added | Iosif Pinelis | timeline score: 6 | |
| Jul 8, 2013 at 12:44 | vote | accept | Hans | ||
| Jan 10, 2018 at 9:16 | |||||
| Jul 8, 2013 at 12:44 | vote | accept | Hans | ||
| Jul 8, 2013 at 12:44 | |||||
| Jul 7, 2013 at 18:30 | history | edited | Hans | CC BY-SA 3.0 |
Added a comma.
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| Jul 7, 2013 at 18:13 | history | edited | Hans | CC BY-SA 3.0 |
Added a proof for $g(x)>0, \forall x\ge\sqrt{\frac{4}{3}}$.
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| Jul 7, 2013 at 14:33 | comment | added | cardinal | @Hans: Yesterday, I was trying to reverse-engineer your problem and found several other representations. Let $U$ be a standard normal random variable. Two equivalent formulations are below (assuming I've done the algebra correctly). First, $\mathbb(E(U - x)\mid U > x) \mathbb E(x-U \mid U < x) \leq 1$. Second, $\left(\int_{-\infty}^x N(u)\,\mathrm d u\right)\left(\int_x^\infty (1-N(u)) \,\mathrm du\right) \leq N(x)(1-N(x))$. | |
| Jul 7, 2013 at 7:44 | answer | added | user64494 | timeline score: -1 | |
| Jul 7, 2013 at 4:46 | comment | added | Hans | @cardinal: I have written out the explicit integral form of $f(x)$. See if you can see any openings. | |
| Jul 7, 2013 at 4:42 | history | edited | Hans | CC BY-SA 3.0 |
Write out integral form of $f(x)$.
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| Jul 6, 2013 at 22:10 | history | edited | Hans |
edited tags
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| Jul 6, 2013 at 21:21 | answer | added | juan | timeline score: 1 | |
| Jul 6, 2013 at 7:00 | answer | added | user64494 | timeline score: -1 | |
| Jul 6, 2013 at 1:31 | comment | added | Hans | @cardinal: You are absolutely right. I had the positive axis of $x$ in mind when proving the upper bound but neglected to write it down. Like you, I am also thinking of looking at the original integral and to see if I can resolve it more elegantly through the original integral itself. I will write the original formulation shortly. | |
| Jul 6, 2013 at 1:27 | history | edited | Hans | CC BY-SA 3.0 |
Specified the domain of the upper bound proof.
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| Jul 5, 2013 at 19:06 | answer | added | cardinal | timeline score: 12 | |
| S Jul 5, 2013 at 14:23 | history | suggested | cardinal |
added arXiv classification tags
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| Jul 5, 2013 at 14:20 | review | Suggested edits | |||
| S Jul 5, 2013 at 14:23 | |||||
| Jul 5, 2013 at 14:19 | comment | added | cardinal | @Hans: Note that the argument for the upper bound, as given, isn't quite correct since $x^2 m (1-m) < n x (1-m)$ holds only for nonnegative $x$. You are saved by the fact that $h(x)$ happens to be an even function, so it suffices to consider only nonnegative $x$. Also, $g$ is even. Could you please edit to specify precisely what truncation of a normal you are considering. Perhaps a somewhat more indirect approach might yield something if we know a little more about the problem you are considering. Cheers. | |
| Jul 5, 2013 at 12:49 | history | edited | Hans | CC BY-SA 3.0 |
Corrected a typo: "f" $\rightarrow$ "h".
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| Jul 5, 2013 at 2:43 | history | reopened |
Yemon Choi Andrés E. Caicedo David E Speyer Gil Kalai Mark Meckes |
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| Jul 4, 2013 at 23:59 | comment | added | Hans | @ToddTrimble et al: I have added the easier upper bound proof and pointed out the difficulty in carrying out the lower bound proof. | |
| Jul 4, 2013 at 23:57 | history | edited | Hans | CC BY-SA 3.0 |
Added proof for the upper bound of $f(x)$.
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| Jul 4, 2013 at 23:51 | history | edited | Hans | CC BY-SA 3.0 |
Added proof for the upper bound of $f(x)$.
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| Jul 3, 2013 at 16:55 | comment | added | Yemon Choi | Posted this meta.mathoverflow.net/questions/223/requests-for-reopen-votes/… on meta | |
| Jul 3, 2013 at 14:57 | comment | added | Todd Trimble | I am inclined to believe this may not be easy, as you say, but if you have a write-up of the results you've obtained so far that you can link to, you might have more success in convincing others that the problem is definitely non-trivial. (This is too far from my areas of research for me to weigh in with any authority, so I won't vote to reopen. I suspect however it might be MO-worthy.) | |
| Jul 3, 2013 at 13:22 | comment | added | Hans | @WillJagy et al: I have edited my original post to describe the problem with accuracy, provide reason for my speculation of its validity, and give more context. This is not an easy problem. There is a subject called normal approximation with Stein's Method. Besides, browsing through the forum, I have seen several other more trivial looking but legitimate posts. I would like to ask for the reason for deeming this question "off topic" and a review of the classification. | |
| Jul 3, 2013 at 5:57 | review | Reopen votes | |||
| Jul 3, 2013 at 18:58 | |||||
| Jul 3, 2013 at 5:01 | comment | added | Hans | @YemonChoi: You are correct in that I have not prove the inequality. I am however pretty confident of its validity judging from the plot I made of the two sides of the inequality. I have edited the post to reflect this discussion. Thank you. | |
| Jul 3, 2013 at 4:57 | history | closed |
Will Jagy user6976 Andrés E. Caicedo Chris Godsil Daniel Moskovich |
Not suitable for this site | |
| Jul 3, 2013 at 4:55 | history | edited | Hans | CC BY-SA 3.0 |
added 109 characters in body
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| Jul 3, 2013 at 4:10 | comment | added | Yemon Choi | When you say "prove the following inequality" - do you mean that you already know the inequality is true? If so, what is your source? If not, then what evidence do you have for why the inequality might be true? | |
| Jul 3, 2013 at 3:53 | history | edited | Hans | CC BY-SA 3.0 |
edited body
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| Jul 3, 2013 at 2:51 | history | edited | Hans | CC BY-SA 3.0 |
added 305 characters in body
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| Jul 3, 2013 at 2:47 | review | Close votes | |||
| Jul 3, 2013 at 4:57 | |||||
| Jul 3, 2013 at 2:24 | history | asked | Hans | CC BY-SA 3.0 |