Timeline for Distribution of ratio between complex Gaussian and Chi-square R.V.s
Current License: CC BY-SA 4.0
16 events
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| Feb 1, 2019 at 20:08 | history | edited | Felipe Augusto de Figueiredo | CC BY-SA 4.0 |
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| Jan 9, 2018 at 11:14 | vote | accept | Felipe Augusto de Figueiredo | ||
| Jan 7, 2018 at 18:57 | history | edited | Felipe Augusto de Figueiredo | CC BY-SA 3.0 |
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| Jan 7, 2018 at 18:51 | history | edited | Felipe Augusto de Figueiredo | CC BY-SA 3.0 |
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| Jan 7, 2018 at 17:43 | comment | added | Iosif Pinelis | @FelipeAugustodeFigueiredo : Of course, the mere rescaling by a constant factor (say $k>0$) does not make it easier or harder to find the pdf: the pdf of $kY$ is $\frac1k\,f_Y(\frac yk)$, where $f_Y(y)$ is the pdf of a random variable $Y$. | |
| Jan 7, 2018 at 17:31 | comment | added | Iosif Pinelis | @FelipeAugustodeFigueiredo : I suggest you restore the original definition of $z$ -- but, just in the captions to your pictures, replace z by Mz. | |
| Jan 7, 2018 at 16:24 | comment | added | ofer zeitouni | Asymptotically it converges to Gaussian, as I indicated. I do not know about corrections that eventually vanish in the limit. | |
| Jan 7, 2018 at 15:52 | comment | added | Felipe Augusto de Figueiredo | @oferzeitouni, thanks for your comment. Your are right, $z$ indeed is missing the $M$ term as you suggested. If you check my simulation script, you will see that $M$ is part of the $z$ ratio. Do you think now with $M$ it is easier to find the p.d.f of this ratio? | |
| Jan 7, 2018 at 15:46 | history | edited | Felipe Augusto de Figueiredo | CC BY-SA 3.0 |
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| Jan 7, 2018 at 15:27 | comment | added | ofer zeitouni | $z$ itself converges to $0$. You probably mean $Z=Mz$. Since $\sum_{i=1}^M |x_i|^2/M\to 2$, you get that $Z$ converges to a (constant multiple of) a standard complex Gaussian. If you mean to ask something else, please update. | |
| Jan 7, 2018 at 13:09 | history | edited | Felipe Augusto de Figueiredo | CC BY-SA 3.0 |
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| Jan 7, 2018 at 13:02 | history | edited | Felipe Augusto de Figueiredo | CC BY-SA 3.0 |
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| Jan 7, 2018 at 11:56 | history | edited | Felipe Augusto de Figueiredo | CC BY-SA 3.0 |
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| Jan 7, 2018 at 3:06 | history | edited | Iosif Pinelis |
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| Jan 7, 2018 at 2:59 | answer | added | Iosif Pinelis | timeline score: 4 | |
| Jan 6, 2018 at 20:04 | history | asked | Felipe Augusto de Figueiredo | CC BY-SA 3.0 |