It is shown that any uniform fractional order statistic can be represented in distribution by a random convex combination of any number of neighboring uniform fractional order statistics with weights being products of independent beta distributed random variables. In particular, the result is valid for ordinary order statistics.
Beutner, E. A., & Kamps, U. (2009). Identical distributions of single variates and random corvex combinations of uniform fractional order statistics. Communications in Statistics - Theory and Methods, 38(12), 1950-1959. https://doi.org/10.1080/03610920802503388