Timeline for Probability of one binomial variable being greater than another.
Current License: CC BY-SA 2.5
10 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Aug 17, 2010 at 1:31 | answer | added | Tomas | timeline score: 1 | |
| Feb 24, 2010 at 13:45 | vote | accept | user4120 | ||
| Feb 21, 2010 at 4:31 | answer | added | Douglas Zare | timeline score: 5 | |
| Feb 20, 2010 at 22:37 | comment | added | user4120 | Thank you for the clarification. I am interested in the tails, in the sense that I would like a bound that becomes tight as $n$ becomes large. | |
| Feb 20, 2010 at 21:39 | comment | added | Douglas Zare | Yes, the Berry-Esseen theorem can be used to make the normal approximation effective. Whether that helps you a lot or not depends on the type of bound you want. If you can get the probability within 0.01, is that good? Or are you interested in the tails, where the probability might be 10^-6, and being off by a 0.01 is unacceptable? If the latter, then you may want something other than the Berry-Esseen theorem, and other bounds exist for that case. | |
| Feb 20, 2010 at 21:31 | comment | added | user4120 | Yes, X and Y are independent. As to the bounds, I apologize that I don't totally understand the question. What I want to do is find control the probability of the worse coin "beating" the better coin. (i.e. I want to upper bound $Pr(y>x)$ when $y\leftarrow B(n,q), x \leftarrow B(n,p)$ and $q<p$.) The specific application is in a randomized approximation algorithm-- I want to select $n$ to be as low as I can. Thank you for the pointer to the Berry-Esseen theorem. It looks like this can be used to convert Normal approximations into rigorous bounds? | |
| Feb 20, 2010 at 21:03 | comment | added | Douglas Zare | Do you want upper bounds when the probability is large, or upper bounds when the probability is small? The Berry-Esseen theorem tells you how rapidly the normal approximation works, but that might not help if you want tight estimates on the tails. | |
| Feb 20, 2010 at 20:29 | comment | added | Yemon Choi | X and Y are independent, right? | |
| Feb 20, 2010 at 20:25 | answer | added | David Shor | timeline score: 0 | |
| Feb 20, 2010 at 17:28 | history | asked | user4120 | CC BY-SA 2.5 |