Timeline for Deriving the distribution of standardized variables with empirical mean and standard deviation
Current License: CC BY-SA 4.0
13 events
| when toggle format | what | by | license | comment | |
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| Nov 14 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. | |
| Jul 17 at 21:06 | 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. | |
| Mar 19 at 21:03 | 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. | |
| Feb 21 at 14:34 | comment | added | Iosif Pinelis | "the joint distribution marginalized over the $z_j$, $j\ne i$" ... The joint distribution of what random variables? What could "marginalized over the $z_j$, $j\ne i$" possibly mean? Also, again, in what terms do you want to describe the distribution you are interested in? Here, you may want to say: the pdf of $z_i$, for each $i$ --which is, by symmetry, the same as the pdf of $z_1$. Or you may want to say: the joint pdf of $z_1,\dots,z_{N-1}$. Or something else -- expressed in standard, common terminology. | |
| Feb 21 at 10:20 | comment | added | user1172131 | @IosifPinelis I'm interested in the p.d.f. of $z_i$, i.e. the joint distribution marginalized over the $z_j$ , $j \neq i$ | |
| Feb 20 at 20:42 | comment | added | Iosif Pinelis | @user1172131 : This depends on what you mean by "to get the joint distribution". The joint distribution is a measure. In what terms do you want to describe it? For instance, it could be described in terms of the joint pdf of $z_1,\dots,z_{N-1}$. You still have not answered my previous question. | |
| Feb 20 at 15:15 | comment | added | user1172131 | @IosifPinelis is it even possible to get the joint distribution of $(z_1, \dots, z_N)$? Eq.(1) seems to be a non invertible transformation (i.e. null Jacobian) | |
| Feb 18 at 20:03 | answer | added | Christian Remling | timeline score: 0 | |
| Feb 18 at 1:04 | comment | added | Iosif Pinelis | Do you want to find the distribution of each $z_i$ or the joint distribution of $(z_,1,\dots,z_N)$? | |
| Feb 17 at 17:04 | comment | added | Anthony Quas | That is, the sphere of radius $\sqrt N$ | |
| Feb 17 at 16:21 | comment | added | Anthony Quas | I believe that you are precisely sampling a uniform point on the intersection of the unit sphere with the plane $x_1+\ldots+x_N=0$. | |
| Feb 16 at 17:41 | history | edited | YCor | CC BY-SA 4.0 |
removed capitals from title
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| Feb 16 at 17:34 | history | asked | user1172131 | CC BY-SA 4.0 |