Timeline for Independence between $X_{n-k:n}$ and $\sum\limits_i Y_{n-i:n}-Y_{n-k:n}$
Current License: CC BY-SA 4.0
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| May 20, 2021 at 1:02 | history | bumped | CommunityBot | This question has answers that may be good or bad; the system has marked it active so that they can be reviewed. | |
| Apr 20, 2021 at 0:39 | history | edited | Sam Hopkins |
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| Apr 19, 2021 at 17:30 | answer | added | Iosif Pinelis | timeline score: 1 | |
| Apr 19, 2021 at 16:58 | comment | added | Hanan | @IosifPinelis (i) & (iii) yes but there is a way to generally proof that regardless the distribution the independence proof will still hold, check lemma 3.2.3 in extreme value theory an introduction. (ii) the summation is from 0 to k. but regardless the same I need to see if there is dependence between the OS $X_{n-k:n}$ and the difference $Y_{n-i:n}-Y_{n-k:n}$ ! | |
| Apr 19, 2021 at 16:54 | comment | added | Hanan | @DieterKadelka OS are done separately but there is dependence between the main variables. do you have a way to reason why this dependence is valid?! | |
| Apr 19, 2021 at 16:49 | history | edited | Hanan | CC BY-SA 4.0 |
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| Apr 5, 2021 at 15:25 | comment | added | Iosif Pinelis | Also, what is $k$? | |
| Apr 5, 2021 at 13:45 | comment | added | Iosif Pinelis | (i) Renyi's representation is only for the case when the $X_i$'s have an exponential distribution. (ii) What are the summation limits in $\sum_i$? (iii) References/proofs for "$X_{n-k:n}$ and $\sum\limits_i X_{n-i:n}-X_{n-k:n}$ are independent"? | |
| Apr 5, 2021 at 10:35 | comment | added | Dieter Kadelka | I have problems with the index notation. Is the order statistic $1:n,\ldots,n:n$ of $Y$ the same as that for $X$ (i.e. defined by ordering $X$) or is this done separately? In the latter case I see no reason why there should be independence. | |
| Apr 5, 2021 at 9:57 | review | Close votes | |||
| May 5, 2021 at 3:03 | |||||
| Apr 5, 2021 at 8:37 | review | First posts | |||
| Apr 5, 2021 at 9:41 | |||||
| Apr 5, 2021 at 8:36 | history | asked | Hanan | CC BY-SA 4.0 |