Timeline for Distribution and moments of ratio of two beta variables?
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
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| Jul 19, 2019 at 17:29 | comment | added | wolfies | @user14330 says; "The first raw moment of the ratio should be 1." ... It appears that your hypothesis is that if $X$ and $Y$ are iid random variables, then $E[X/Y] = 1$. Unfortunately, your hypothesis is wrong. | |
| Jul 19, 2019 at 16:01 | history | edited | YCor | CC BY-SA 4.0 |
added main question
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| Jul 19, 2019 at 15:39 | comment | added | user143306 | Sorry - it might be a stupid observation, but I struggle to see how the above expression is correct. If we have $a=c$ and $b=d$, The first raw moment of the ratio should be 1. And the above formula does not satisfy this. For example, for $a=b=c=d=2$ and $k=1$, I get: $$ \dfrac{B(2+1,2)B(2-1,2)}{B(2,2)B(2,2)} = 1.5 $$ What am I doing wrong? For the Euler Beta function I am using this in the scipy implementation | |
| Nov 8, 2013 at 6:45 | vote | accept | Aryeh Kontorovich | ||
| Nov 7, 2013 at 16:32 | answer | added | wolfies | timeline score: 8 | |
| Nov 7, 2013 at 10:05 | comment | added | Aryeh Kontorovich | I've located the paper, so now the only question is: what is known about the moments of this ratio? | |
| Nov 7, 2013 at 9:42 | history | asked | Aryeh Kontorovich | CC BY-SA 3.0 |