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What would the conventional or an otherwise useful notation for the second-highest value of $v_i, i=1,\ldots,n$ be?

I use $v_{n-1:n}$, which I used in statistics, but that may not be quite intuitively graspable. $v_{(n-1)}$ seems like asking for trouble.

So perhaps I am missing an obvious candidate. Any suggestions?

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The name for what you're after is order statistic.

If you have a sample $X_1, \dots, X_n$ the conventional notation for the $i$th order statistic is $X_{(i)}$, so the second highest value in the sample would be $X_{(n-1)}$ as you suggested.

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  • $\begingroup$ Thanks. Nothing along the lines of $v_{(n)}=\max_i v_i, v_{(n-1)}=\mathrm{blabla}_i v_i$? $\endgroup$
    – Řídící
    Commented Feb 14, 2013 at 18:16
  • $\begingroup$ I found this and there's nothing like $\mathrm{blabla}$ there. Done. $\endgroup$
    – Řídící
    Commented Feb 15, 2013 at 7:56

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