Timeline for Expected value of ratio of normal CDFs
Current License: CC BY-SA 3.0
14 events
| when toggle format | what | by | license | comment | |
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| Mar 24, 2016 at 18:24 | history | edited | Bob | CC BY-SA 3.0 | added 9 characters in body |
| Mar 24, 2016 at 18:22 | comment | added | Bob | Yeah, I was afraid there might not be a solution. It's related to this one, stats.stackexchange.com/questions/61080/… But I don't see how to generalize to my setting... | |
| Mar 24, 2016 at 18:21 | comment | added | leonbloy | Ok, it's clear now, it does not look easy. | |
| Mar 24, 2016 at 18:20 | vote | accept | Bob | ||
| Mar 24, 2016 at 18:17 | comment | added | Bob | @leonbloy, It's a ratio of two random variables, $Z_1=\Phi(X+Y)$ and $Z_2=\Phi(X)$ where $\Phi$ is the standard normal cdf function, mapping $\mathbb{R} \to [0,1]$. I want to compute $E(Z_1 / Z_2)$ | |
| Mar 24, 2016 at 18:06 | comment | added | leonbloy | I don't understand your notation. Your are doing a ratio of variables or of distributions? To write "the expected value of $\Phi(X+Y)/\Phi(X)$" makes no sense to me. If you mean the expected value of $Z=(X+Y)/X$, then it reduces to $E(1 +Y/X)=1 + E(Y/X)$ | |
| Mar 24, 2016 at 17:34 | history | edited | Bob | CC BY-SA 3.0 | added 48 characters in body |
| Mar 24, 2016 at 17:34 | comment | added | Bob | Thanks for the thoughts and sorry my notation wasn't super clear. With $\Phi(.)$ I meant the standard normal CDF, whereas $X$ and $Y$ can have any mean or variance. (I'll edit the original question to make it more clear) | |
| Mar 24, 2016 at 16:12 | answer | added | Clarinetist | timeline score: 1 | |
| Mar 24, 2016 at 15:54 | comment | added | Clarinetist | @Henry Ah, that's true. Hmm. I might recommend doing a simulation. | |
| Mar 24, 2016 at 15:53 | comment | added | Henry | @Clarinetist: note that $\Phi(X+Y)$ and $\Phi(X)$ are not independent | |
| Mar 24, 2016 at 15:37 | comment | added | Clarinetist | If by $\Phi(X+Y)$ and $\Phi(X)$ you mean the CDF of $X+Y$ and the CDF of $X$, aren't continuous CDFs uniformly distributed in $[0, 1]$? If my memory is right, your question is equivalent to finding the expected value of a ratio of uniform $[0, 1]$ distributions. | |
| Mar 24, 2016 at 15:10 | review | First posts | |||
| Mar 24, 2016 at 15:17 | |||||
| Mar 24, 2016 at 15:10 | history | asked | Bob | CC BY-SA 3.0 |