Timeline for It is true that $\mathbf X \sim F_X \Rightarrow F_X(\mathbf X) \sim U_{[0;1]}$; does the converse hold for multivariate $\mathbf X$?
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Nov 1, 2017 at 23:18 | history | edited | MInner | CC BY-SA 3.0 |
added 303 characters in body
|
| Oct 30, 2017 at 19:54 | comment | added | whuber♦ | By using copulas, you may restrict your study to the case where the marginals of $X$ are uniform on the interval $[0,1]$. Plotting a few copulas will make the answers immediately apparent: in particular, $\tilde X$ is not necessarily uniform. | |
| Oct 30, 2017 at 19:33 | answer | added | MInner | timeline score: 0 | |
| Oct 18, 2017 at 20:01 | comment | added | whuber♦ | You implicitly assume all variables are non-discrete; for discrete variables, it is not the case that $F_X(X)$ is uniform. Notice that the distribution function implied by "$U_{[0;1]}$" is the identity map on the open interval $(0,1)$. | |
| Oct 18, 2017 at 20:00 | history | edited | MInner | CC BY-SA 3.0 |
deleted 24 characters in body
|
| Oct 18, 2017 at 18:58 | history | asked | MInner | CC BY-SA 3.0 |