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As Matt pointed out in the comments - it is indeed a hard problem. The answer below is a more credible attempt that (in my opinion) better approximates the quantity. A general prior for the distribution The reformulated question Fix $r < N$, what is the distribution across all $s \in \{1, ..., N\}$, where $X_i$ generated $Y_{(r)}$ and $Z_i = X_i + \...


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There is an analytic answer for a slightly different distribution, the Ali-Mikhail-Haq copula. If $0\le r \le \frac12$, we can choose this copula to have the same standard normal distribution of $X$'s as the bivariate normal the same standard normal distribution of $Y$'s as the bivariate normal the same Kendall's tau measure of correlation between the two ...


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