Timeline for Statistical moments of $\frac X{X + Y}$ when $X$ and $Y$ are two independent random variables with a Beta distribution
Current License: CC BY-SA 4.0
12 events
| when toggle format | what | by | license | comment | |
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| Apr 19, 2023 at 18:05 | history | edited | Michael Hardy | CC BY-SA 4.0 |
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| Jan 12, 2020 at 15:01 | history | edited | Maximilian Janisch | CC BY-SA 4.0 |
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| Nov 20, 2019 at 8:54 | history | edited | Maximilian Janisch | CC BY-SA 4.0 |
added 196 characters in body
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| Nov 20, 2019 at 8:31 | comment | added | Maximilian Janisch | @IosifPinelis You are right - I will fix it | |
| Nov 20, 2019 at 4:35 | comment | added | Iosif Pinelis | @MaximilianJanisch : I think your indicator for the joint pdf of $(X,\frac X{X+Y})$ is incorrect, which leads to having $1+\frac{a\cdot(b-1)}b<0$ under your final integral when $b<1/2$ and $a$ is close to $1$. | |
| Nov 19, 2019 at 17:21 | comment | added | Maximilian Janisch | @MattF. I implemented some of your suggestions | |
| Nov 19, 2019 at 17:20 | history | edited | Maximilian Janisch | CC BY-SA 4.0 |
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| Nov 19, 2019 at 17:20 | comment | added | Kerighan | @MaximilianJanisch To clarify: I don't want to integrate numerically, as I use this formula/distribution as some sort of utility function applied on a lot (I mean a lot) of data. The ideal would be a simple approximation of the moments that can be very quickly computed from the Beta parameters. | |
| Nov 19, 2019 at 17:16 | comment | added | Maximilian Janisch | Hi @Kerighan I agree that this doesn't (fully) answer your question, but I think I'll leave my answer here as it might be useful to other users... As for approximating moments: I suppose that you could approximate them using numerical integration for fixed $\alpha,\beta,\gamma,\delta$. I don't have a good idea if you want an answer for every $\alpha,\beta,\gamma,\delta$ | |
| Nov 19, 2019 at 17:15 | comment | added | user44143 | This would be easier to read replacing $]0,1[$ with $I$, removing most of the $\cdot$'s, replacing $\operatorname{Bet}$ with the more standard $\mathrm{B}$, and replacing $const.$ with the more standard $c$. | |
| Nov 19, 2019 at 16:53 | comment | added | Kerighan | thank you very much for your thorough answer. I came to the same result as you do, but have trouble reducing this expression further (as I feel it could be done, but maybe I'm mistaken) and/or finding/approximating moments. | |
| Nov 19, 2019 at 16:29 | history | answered | Maximilian Janisch | CC BY-SA 4.0 |