Timeline for Finding the sum of realizations of normal random variables equalling zero
Current License: CC BY-SA 3.0
11 events
| when toggle format | what | by | license | comment | |
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| Jun 13, 2014 at 9:32 | comment | added | ws6079 | @Thomas sorry for not stating my question clearly. Your answer is still helpful and you should leave it in if you don't mind. | |
| Jun 13, 2014 at 9:24 | comment | added | Thomas | Now that the question changed, my answer does not fit anymore. Should I delete it? In the beginning it looked like you wanted to draw independent numbers whose linear combination is always zero, which you can't. You can however draw n-1 independent numbers and make statements about the distribution of the linear combination in my answer. | |
| Jun 13, 2014 at 9:07 | comment | added | ws6079 | @JuhoKokkala yes the second sentence exactly - thanks for understanding :) | |
| Jun 13, 2014 at 8:51 | comment | added | Juho Kokkala | If they are independent, the linear combination is not be guaranteed to be 0 (unless all $c_i$s are 0). Or are you perhaps looking for the conditional distribution of the $Z_i$s conditional on the linear combination equaling 0 (so that conditional distributions will not be standard normal, only the 'unconditional' are)? | |
| Jun 13, 2014 at 8:45 | comment | added | ws6079 | @JuhoKokkala for my scenario I know that the $z_n$ are uncorrelated and independent (for the unconditional case) | |
| Jun 13, 2014 at 8:43 | comment | added | ws6079 | Right, my problem is that I can not get the distribution of $z_n$ to meet my constraint (zero mean and unit-variance) | |
| Jun 13, 2014 at 8:42 | comment | added | Juho Kokkala | Without additional assumptions about the joint distribution of $z_1,\ldots,z_{n-1}$ (namely, that they are multivariate normal), the linear combination may be non-normal. | |
| Jun 13, 2014 at 8:40 | comment | added | Thomas | Yes, right. I removed "standard". | |
| Jun 13, 2014 at 8:39 | history | edited | Thomas | CC BY-SA 3.0 |
deleted 9 characters in body
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| Jun 13, 2014 at 8:39 | comment | added | Juho Kokkala | A linear combination of standard normals is not guaranteed to be standard normal. | |
| Jun 13, 2014 at 8:33 | history | answered | Thomas | CC BY-SA 3.0 |