\(q\)-analogs of order statistics. (English) Zbl 1218.60040

Kordecki, Wojciech; Łyczkowska-Hanćkowiak, Anna

Probab. Math. Stat. 30, No. 2, 207-214 (2010).

Summary: We introduce the notion of the \(q \)-analog of the \(k \)-th order statistics. We give a distribution and asymptotic distributions of \(q \)-analogs of the \(k \)-th order statistics and the intermediate order statistics with \(r \rightarrow \infty \) and \(r- k \rightarrow \infty \) in the projective geometry \(PG (r - 1,q) \).

MSC:

60G70	Extreme value theory; extremal stochastic processes
51E20	Combinatorial structures in finite projective spaces

Keywords:

order statistics; limit theorems; \(q \)-analog; finite projective geometry