Timeline for PDF of $R$ given that $R^2 = C^2 + S^2$, with $C = \sum_{j=1}^{n}{\cos \theta_j}$ and $S = \sum_{j=1}^{n}{\sin \theta_j}$ for a small $n$
Current License: CC BY-SA 4.0
13 events
| when toggle format | what | by | license | comment | |
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| Dec 1, 2019 at 17:27 | vote | accept | Felipe Augusto de Figueiredo | ||
| Nov 30, 2019 at 22:40 | comment | added | Felipe Augusto de Figueiredo | @IosifPinelis, no problem, thanks for the clarification. | |
| Nov 30, 2019 at 22:28 | comment | added | Iosif Pinelis | @FelipeAugustodeFigueiredo : I meant the distribution of the distance of the random point from the origin, rather than the distribution of the random point itself. Sorry about that confusion. This is now corrected. | |
| Nov 30, 2019 at 22:24 | history | edited | Iosif Pinelis | CC BY-SA 4.0 |
added 30 characters in body
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| Nov 30, 2019 at 21:59 | comment | added | Carlo Beenakker | see mathoverflow.net/q/347317/11260 for a clarification. | |
| Nov 30, 2019 at 9:39 | comment | added | Felipe Augusto de Figueiredo | My question above comes from the fact that after running some matlab simulations I noticed that the distributions does not look the same (even though the derived PDF fits the (C,S) distribution ). Please, see the matlab script I created for plotting both distributions. pastebin.com/DX6UsNiM and the generated figures can be seen at docs.google.com/document/d/… | |
| Nov 29, 2019 at 22:33 | comment | added | Felipe Augusto de Figueiredo | Dear, I have checked your answer with some sumulations and it is correct, however, I'd like to understabd this step "distribution of the random point (C,S) is the same as that of (1,0)+(cosU,sinU)" better. Could you explain how you that (C,S) is equal to (1,0)+(cosU,sinU), please? | |
| Nov 29, 2019 at 22:29 | vote | accept | Felipe Augusto de Figueiredo | ||
| Dec 1, 2019 at 17:27 | |||||
| Nov 29, 2019 at 17:12 | comment | added | Felipe Augusto de Figueiredo | @MickyboYakari, thanks! | |
| Nov 29, 2019 at 17:10 | comment | added | Mickybo Yakari | This is the indicator (or characteristic) function of a set. See en.wikipedia.org/wiki/Indicator_function for clarification. | |
| Nov 29, 2019 at 15:27 | comment | added | Felipe Augusto de Figueiredo | Dear, thanks for your answer. One question, what does the number "1" mean in the $f_R(r)$ expression, just before the limits of r? It also appears for the case when $n$ is large. Is that a typo?Thanks a lot! | |
| Nov 29, 2019 at 14:14 | history | edited | Iosif Pinelis | CC BY-SA 4.0 |
added 609 characters in body
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| Nov 29, 2019 at 13:44 | history | answered | Iosif Pinelis | CC BY-SA 4.0 |