[FR] Add order statistics pdf

Description

When we do CDF regressions, the order statistic pdf updates the target density with the appropriate change of variables. There are 2 possible parameterizations. One involving the k_th order statistic and one involving the quantile. I'm interesting in the quantile version but it's quite easy to swap out since you can swap out k_i with nq_i in the following

from https://arxiv.org/pdf/2008.06423.pdf.

Example

The code is quite simple given a CDF transformed vector U (i.e. U = F(x) where F(*) is a CDF), a vector of the corresponding quantiles, and the total sample size N (where size(U) can be << N):

 real orderstatistics_lpdf(vector U, data vector q, int N){
        int M = num_elements(q);
        real lpdf = lgamma(N + 1) - lgamma(N * q[1]) - lgamma(N * (1 - q[M]) + 1); // normalizing constant
        lpdf += (N * q[1] - 1) * log(U[1]);
        lpdf += N * (1 - q[M]) * log1m(U[M]);
        
        for (m in 2:M) {
            lpdf += -lgamma(N * (q[m] - q[m - 1])); // normalizing constant
            lpdf += (N * (q[m] - q[m - 1]) - 1) * log(U[m] - U[m - 1]); 
        }
        return lpdf;
    }

I'm assuming q is always data so the derivative is wrt to U. I have it on paper but will add to this post later.

No repository file or test is named in the issue. Start with the proposed orderstatistics_lpdf entry point and compare its quantile parameterization with the linked paper and stated change-of-variables assumptions. Done means the requested order-statistic PDF is added with derivatives taken with respect to U.