k-th record times and their generalizations

A series of asymptotic results are given for the k-th record times and for their generalizations, the so-called k_n-record times. All possible limiting distributions are obtained for some generalizations of the k-th record variables. These distributions are closely related with the corresponding limit distributions of the extremal order statistics.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 153, pp. 115–121, 1986.