Geodesic
Characterization of distributions by equalities of order statistics
Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 11, Tome 341 (2007), pp. 168-173

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It is proved that the equality of two different order statistics holds for degenerate or two-point distributions only. Several samples of such equalities are considered and particular values of corresponding distribution functions are obtained. 
@article{ZNSL_2007_341_a11,
     author = {V. K. Saghatelyan},
     title = {Characterization of distributions by equalities of order statistics},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {168--173},
     publisher = {mathdoc},
     volume = {341},
     year = {2007},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2007_341_a11/}
}
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V. K. Saghatelyan. Characterization of distributions by equalities of order statistics. Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 11, Tome 341 (2007), pp. 168-173. http://geodesic.mathdoc.fr/item/ZNSL_2007_341_a11/