Timeline for Normality of the sum of uniformly distributed random variables
Current License: CC BY-SA 4.0
13 events
| when toggle format | what | by | license | comment | |
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| Oct 17, 2019 at 20:15 | comment | added | Mateusz Kwaśnicki | This looks a little bit like the Metropolis-Hastings algorithm, with uniform jumps. The rejection mechanism is of course much different, but still I find the two somewhat analogous. | |
| Oct 17, 2019 at 15:49 | history | edited | Anthony Quas | CC BY-SA 4.0 |
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| Oct 15, 2019 at 6:21 | comment | added | Anthony Quas | @MichaelHardy: I haven't seen conditoinal convergence in probability before. On the other hand, what I'm doing here is a version of my favourite party trick: essentially using extra randomness (in this case the $N$ which is the target random variable) to build something doing what you want (Notice that the $N$ once built in to the $Z$'s is obtained from the $Z$'s rather than the other way around). I have generally done things a bit like this in dynamical systems, where I call the technique "Coupling and Splicing". The symmetry is a bonus making things work out nicely. | |
| Oct 15, 2019 at 4:07 | comment | added | Michael Hardy | ok, I have this open-ended question: When does conditional convergence occur in the theory of probability? (I wonder if I've seen it before.) | |
| Oct 15, 2019 at 4:03 | comment | added | Michael Hardy | Amazing. I would have guessed that what was asked for cannot be done. $\qquad$ | |
| Oct 14, 2019 at 21:13 | vote | accept | Iosif Pinelis | ||
| Oct 14, 2019 at 18:27 | comment | added | Anthony Quas | @IosifPinelis : I tried to expand the explanation in the way that you suggested. | |
| Oct 14, 2019 at 18:26 | comment | added | Anthony Quas | @MattF. : Sorry. I have no idea what the joint pdf looks like. (I do know the marginal PDFs though!) | |
| Oct 14, 2019 at 18:24 | history | edited | Anthony Quas | CC BY-SA 4.0 |
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| Oct 14, 2019 at 15:05 | comment | added | Iosif Pinelis | Very nice! However, it may seem unclear when you write "by symmetry (under replacing each random variable by its negation)" but actually (of course) do not negate the $Z_i$'s. Can you detail this symmetry consideration? | |
| Oct 14, 2019 at 9:05 | comment | added | user44143 | Can you clarify — what is the pdf for the sequence $u_1, u_2, \ldots$? | |
| Oct 14, 2019 at 8:12 | history | edited | Anthony Quas | CC BY-SA 4.0 |
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| Oct 14, 2019 at 8:05 | history | answered | Anthony Quas | CC BY-SA 4.0 |