Timeline for k-secretary problem: not knowing the length of the queue
Current License: CC BY-SA 4.0
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| May 3, 2021 at 12:12 | history | edited | m0ss | CC BY-SA 4.0 |
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| May 3, 2021 at 9:36 | history | edited | m0ss | CC BY-SA 4.0 |
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| May 3, 2021 at 9:31 | history | edited | m0ss | CC BY-SA 4.0 |
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| May 3, 2021 at 9:20 | comment | added | m0ss | @Kernel You are right. I did not fully explain my problem because I did not want to have an answer to be dim. In the case where n<k, assume that it is more or less like a binary scenario. I will update my question now that someone responded and I'll tell the slight difference between my problem and the secretary problem. I should also mention that I'm not a statistician and I want to know the optimal selecting strategy (knowing the stopping index) and use it as an application in another problem. It would be really helpful if you could introduce some papers about this. | |
| May 3, 2021 at 8:27 | comment | added | Kernel | I suppose $k$ is deterministic, so the problem is somewhat ill posed, as in case $n \in[1,\dots,k-1]$ there is no way to win. I do think you would need an assumption on the law of $n$, much like you did, but perhaps something like $n$ being uniform between $[k+1,ck]$ for $c>1$. Even in this case, the events in which $n-k$ is small might still make the whole game really easy to fail, I would suggest start by looking at $n$ uniform in $[c_1 k ,c_2k]$ with $c_2>c_1>1$ and try to obtain the probability of success in terms of $k,c_1,c_2$. | |
| May 3, 2021 at 8:12 | review | First posts | |||
| May 3, 2021 at 8:34 | |||||
| May 3, 2021 at 8:12 | history | asked | m0ss | CC BY-SA 4.0 |