Geodesic
A note on limit behaviour of extremal order statistics
Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 8, Tome 320 (2004), pp. 106-109
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Anderson (1970) and Sethuraman (2003) described a class of distributions concentrated on positive integers for which sample maximum and other extremes asymptotically cluster on $k$ values. We prove a similar result for distributions of general structure. 
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A. I. Martikainen. A note on limit behaviour of extremal order statistics. Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 8, Tome 320 (2004), pp. 106-109. http://geodesic.mathdoc.fr/item/ZNSL_2004_320_a7/

[1] B. V. Gnedenko, “Sur la distribution limite du terme maximum d'une série aléatoire”, Ann. Math., 44 (1943), 423–453 | DOI | MR | Zbl

[2] C. Anderson, “Extreme value theory for a class of discrete distributions with applications to some stochastic processes”, J. Appl. Prob., 7 (1970), 99–113 | DOI | MR | Zbl

[3] Atthreya, S. Sethuraman, “On the asymptotics of discrete order statistics”, Stat. Probab. Lett., 54 (2001), 243–249 | DOI | MR

[4] S. Sethuraman, “A clustering law for some discrete order statistics”, J. Appl. Prob., 40 (2003), 226–241 | DOI | MR | Zbl