Timeline for Bound on probabilities of the sum of uniform order statistics
Current License: CC BY-SA 3.0
10 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Nov 2, 2017 at 22:04 | vote | accept | guigux | ||
| Nov 1, 2017 at 16:44 | answer | added | Iosif Pinelis | timeline score: 5 | |
| Oct 29, 2017 at 7:01 | comment | added | user64494 | @wolfes: Thank you. I got it, looking in en.wikipedia.org/wiki/Order_statistic . | |
| Oct 29, 2017 at 6:43 | comment | added | wolfies | @user64494 We are interested in the joint pdf of $(X_{(1)}, X_{(2)})$ -- not just the isolated pdf of say $X_{(1)}$ on its own, and $X_{(2)}$ on its own. This is because there is dependency between $X_{(1)}$ and $X_{(2)}$ which your model is not capturing. | |
| Oct 29, 2017 at 6:39 | comment | added | user64494 | @wolfes: Can you base your "this is because it is incorrect to treat your xx as the 1st order statistic and your yy as the second order statistic ... you need the JOINT pdf of the 1st and 2nd order statistics"? TIA. | |
| Oct 29, 2017 at 5:46 | answer | added | wolfies | timeline score: 2 | |
| Oct 29, 2017 at 5:06 | comment | added | wolfies | @user64494 I haven't looked at your Maple work, but your Mathematica working is incorrect: this is because it is incorrect to treat your $x$ as the 1st order statistic and your $y$ as the second order statistic ... you need the JOINT pdf of the 1st and 2nd order statistics. The OP's result seems correct to me, and very neatly stated too. | |
| Oct 28, 2017 at 21:04 | answer | added | user63957 | timeline score: 2 | |
| Oct 28, 2017 at 19:10 | comment | added | user64494 | First, no motivation of the problem is done, Second, your $p_2(u)$ seems to be wrong: both Mathematica dropbox.com/s/1q4ls7jrngmlwqu/OrderStatistic.pdf?dl=0 and Maple dropbox.com/s/5q0inmikpqh40cv/CDF.pdf?dl=0 produce $\frac {17267}{32256}$ for $n=5,u=\frac 1 2$, whereas your formula performs $\frac {285}{512}$. | |
| Oct 28, 2017 at 12:01 | history | asked | guigux | CC BY-SA 3.0 |