Timeline for What is the distribution of maximum of a pair of iid draws, where the minimum is an order statistic of other minima?
Current License: CC BY-SA 3.0
13 events
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| Aug 9, 2011 at 21:23 | comment | added | OctaviaQ | (...cont) That gave me the exact probabilities for $X_{final}$ being each order stat. Then I used those weights to mix the 5th -8th order statistics for F(x), using a textbook formula to define the order distributions of F(x) (where the pdf of the 4kth order stat of n draws from cdf F(x) = $\frac{n!}{(k-1)!(n-k)!}F(x)^{k-1}(1-F(x))^{n-k}f(x)$ | |
| Aug 9, 2011 at 21:18 | comment | added | OctaviaQ | My brute force method: I figured that $X_{final}$ would be a mixture of predictable weights of order statistics of n*m draws from F(x). For example, for $n=4$ and $m=2$, we start with 8 independent draws from F(x), and $X_{final}$ > the 4th order statistic. To find the PR of it being each order stat 5-8, I wrote a computer script that wrote out every permutation of 1-8, and an algorithm that found $X_{final}$ for each permutation (using the order stats themselves as the comparisons) (cont...) | |
| Aug 9, 2011 at 18:25 | comment | added | Bogdan Lataianu | yes, but there might be some interesting ideas | |
| Aug 9, 2011 at 18:15 | comment | added | OctaviaQ | yeah, I figured it was now irrelevant, since you provided a much better solution. I'll see if I can find what I'd written. | |
| Jul 31, 2011 at 8:54 | comment | added | Bogdan Lataianu | JandR you deleted a comment of yours in which you indicated an ad-hoc method using weights. | |
| Jul 20, 2011 at 20:15 | vote | accept | OctaviaQ | ||
| Jul 20, 2011 at 6:34 | history | tweeted | twitter.com/#!/StackStats/status/93569328003293185 | ||
| Jul 20, 2011 at 0:18 | comment | added | Bogdan Lataianu | may i ask where did you get this problem? | |
| Jul 19, 2011 at 23:49 | answer | added | Bogdan Lataianu | timeline score: 4 | |
| Jul 19, 2011 at 19:16 | history | edited | user88 | CC BY-SA 3.0 |
added 37 characters in body
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| Jul 19, 2011 at 18:33 | answer | added | highBandWidth | timeline score: 1 | |
| Jul 19, 2011 at 18:14 | history | edited | OctaviaQ |
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| Jul 19, 2011 at 18:05 | history | asked | OctaviaQ | CC BY-SA 3.0 |