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Say I have some exponential distribution with rate parameter 1. The expected value of the order statistics for this has a nice closed form see here. Now say I want to truncate this distribution to the interval [0,1]. Does the expected value for this also have a closed form solution? More generally if you have a order statistic for a distribution is finding the order statistic for the truncated distribution easy?

TPaul
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    It's unlikely that you'll find a nice closed form here. The density for the minimum of $n$ $\mathsf{Exp}(1)$ random variables truncated to $(0,1]$ is already fairly nasty:

    $$(e-1)^{-n} n e^{n-t} \left(e^{-t}-\frac{1}{e}\right)^{n-1}$$

     – Math1000 Jul 25 '18 at 03:25

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