Geodesic
On $k$-th record times and their generalizations
Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 18, Tome 153 (1986), pp. 115-121

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Some asymptotic results are given for $k$-th record times and their generalizations – so-called $k_n$-record times. All possible limit distributions are obtained for several generalizations of $k$-th record values. These distributions are closely related with the corresponding limit distributions of extremal order statistics. 
@article{ZNSL_1986_153_a9,
     author = {V. B. Nevzorov},
     title = {On $k$-th record times and their generalizations},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {115--121},
     publisher = {mathdoc},
     volume = {153},
     year = {1986},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1986_153_a9/}
}
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V. B. Nevzorov. On $k$-th record times and their generalizations. Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 18, Tome 153 (1986), pp. 115-121. http://geodesic.mathdoc.fr/item/ZNSL_1986_153_a9/