Timeline for How well can we approximate a given continuous random variable by a weighted sum of several i.i.d uniform variables?
Current License: CC BY-SA 4.0
5 events
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| Jun 12, 2021 at 0:08 | comment | added | RyanChan | @losifPinelis Thanks for your comment. I will post a new question separately. | |
| Jun 11, 2021 at 14:07 | comment | added | Iosif Pinelis | @RyanChen : I think that, even if the additional log-concavity condition is imposed, there will be no approximation in general. However, to prove that, one will probably need to use some properties of the convolution of uniform distributions that are much less trivial than the log-concavity. So, I believe the question with the additional log-concavity condition should be posted separately, especially given that your posted question has been answered. | |
| Jun 11, 2021 at 7:40 | comment | added | RyanChan | @losifPinelis Thanks. We further assume that $S$ is a given log-concave distribution. How to approximate $S$ by the weighted sum of i.i.d. uniform random variables and find the optimal weighting factors? Of course, the asymptotic analysis is welcome. | |
| Jun 10, 2021 at 14:06 | history | edited | Iosif Pinelis | CC BY-SA 4.0 |
added 31 characters in body
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| Jun 10, 2021 at 13:32 | history | answered | Iosif Pinelis | CC BY-SA 4.0 |