Top-<Emphasis Type="Italic">k</Emphasis>-lists

Top-k-lists are introduced as sequences of k-dimensional random vectors with ordered components being k largest observations from a sequence of independent identically distributed random variables. Such lists changing in time are natural stochastic models of ranking tables which appear in many situations in real life, when one wants to keep a track of several best results in a given field. Here we study basic properties of top-k-lists as joint distributions, conditional structures, representations, driving examples of top-k-lists from exponential and uniform distributions, asymptotics and a relation to generalized order statistics.