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I am investigating the following problem.

Consider N Normal variables with same mean, but difefrent variances. What is the PDF of the linear combination of the largest K random variables being greater than a given threhold? I aprreciate if anyone give pointers.

Thanks

kamesh

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  • $\begingroup$ The question is unclear to me: What do you mean by "being greater than ..."? Is something conditioned on being greater than the threshold? If yes, what? The $K$ random variables or their mean? $\endgroup$ Mar 5, 2013 at 15:44

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This is studied exhaustively in this paper. (On the exact distribution of the sum of the largest n − k out of n normal random variables with differing mean values DOUGLAS P. WIENS*†, NORMAN C. BEAULIEU‡ and PAVEL LOSKOT‡)

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    $\begingroup$ It's not quite the same problem. The OP asked about equal means but different variances, and the linked paper deals with equal variances and different means. $\endgroup$ Aug 31, 2012 at 17:49
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    $\begingroup$ True, my oversight, but I am quite sure that the methods work fine in the different setting. $\endgroup$
    – Igor Rivin
    Aug 31, 2012 at 19:20

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