Timeline for When $(X_1-X_0, X_1-X_2)\sim (X_2-X_0, X_2-X_1)\sim(X_0-X_1, X_0-X_2)$?
Current License: CC BY-SA 4.0
23 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Dec 25, 2021 at 14:02 | history | bumped | CommunityBot | This question has answers that may be good or bad; the system has marked it active so that they can be reviewed. | |
| Aug 23, 2021 at 1:03 | history | bumped | CommunityBot | This question has answers that may be good or bad; the system has marked it active so that they can be reviewed. | |
| Mar 22, 2021 at 18:04 | history | bumped | CommunityBot | This question has answers that may be good or bad; the system has marked it active so that they can be reviewed. | |
| Nov 20, 2020 at 22:06 | history | bumped | CommunityBot | This question has answers that may be good or bad; the system has marked it active so that they can be reviewed. | |
| S Oct 15, 2020 at 17:06 | history | bounty ended | CommunityBot | ||
| S Oct 15, 2020 at 17:06 | history | notice removed | CommunityBot | ||
| Oct 9, 2020 at 15:00 | history | tweeted | twitter.com/StackStats/status/1314581402466357250 | ||
| Oct 7, 2020 at 15:40 | history | edited | Star | CC BY-SA 4.0 |
added 44 characters in body
|
| S Oct 7, 2020 at 15:30 | history | bounty started | Star | ||
| S Oct 7, 2020 at 15:30 | history | notice added | Star | Canonical answer required | |
| Oct 7, 2020 at 15:26 | history | edited | Star | CC BY-SA 4.0 |
deleted 111 characters in body
|
| Dec 12, 2018 at 15:51 | comment | added | Star | If you have time to provide an answer, I'd be glad to accept it. Thanks | |
| Dec 12, 2018 at 15:46 | comment | added | Star | Yes, thanks, I totally understand. I modified it just because I received confusing comments and I though of clearing them up by slightly changing my question. | |
| Dec 12, 2018 at 15:43 | comment | added | guy | @user Sorry, I’m not going to go back over your modified question :) I thought the original one was clear enough. | |
| Dec 12, 2018 at 9:05 | history | edited | Star | CC BY-SA 4.0 |
added 52 characters in body
|
| Dec 12, 2018 at 8:59 | comment | added | Star | @guy: thanks, I had to modify slightly my question given the confusion in the comments. Could you explain why $G_1=G_2$? Thanks. I can see that my condition implies $X_1-X_0 \sim X_2-X_0\sim X_0-X_1$ and $X_1-X_2 \sim X_2-X_1\sim X_2-X_0$. Why this implies $X_1-X_0\sim X_1-X_2$? | |
| Dec 12, 2018 at 8:58 | history | edited | Star | CC BY-SA 4.0 |
added 18 characters in body
|
| Dec 12, 2018 at 8:52 | history | edited | Star | CC BY-SA 4.0 |
added 18 characters in body
|
| Dec 11, 2018 at 21:39 | answer | added | Dilip Sarwate | timeline score: 1 | |
| Dec 11, 2018 at 21:13 | comment | added | Dilip Sarwate | Since CDFs are right-continuous functions, your symmetry condition insists that the CDF be continuous at $0$ and have value $\frac 12$ at $0$. @Kodiologist: There exist joint CDFs for random vectors, for example, $F_{X.Y}(x,y) = P\{X \leq x, Y \leq y\}$ where the comma is commonly used to mean intersection. Easier to read than the more formal $$F_{X.Y}(x,y) = P\left(\{X \leq x\}\cap \{Y \leq y\}\right)$$ but YMMV.... | |
| Dec 11, 2018 at 19:23 | comment | added | guy | If $X_1$ is not degenerate, then a necessary condition is that the correlation between $X_1$ and $X_2$ is $0.5$. In the special case where $(X_1, X_2)$ is a bivarate normal this, with the additional requirement that the mean is $(0,0)$, is both necessary and sufficient. It is easy to find counterexamples to sufficiency in the general case (e.g., if $X_1$ and $X_2$ are Rademacher variables then this is not sufficient). Additionally, note that it is necessary that $G_1 = G_2$. | |
| Dec 11, 2018 at 19:19 | comment | added | Kodiologist | Random vectors with more than one dimension don't have CDFs. There are marginal CDFs for the coordinates, but no one CDF for the whole joint distribution. | |
| Dec 11, 2018 at 18:52 | history | asked | Star | CC BY-SA 4.0 |