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Top-\(k\)-lists. (English) Zbl 1105.62050
Summary: Top-\(k\)-lists are introduced as sequences of \(k\)-dimensional random vectors with the ordered components being the \(k\) 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.

MSC:
62G30 Order statistics; empirical distribution functions
62E15 Exact distribution theory in statistics
62G32 Statistics of extreme values; tail inference
62G20 Asymptotic properties of nonparametric inference
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References:
[1] Arnold BC, Balakrishnan N, Nagaraja HN (1998) Records. Wiley, New York
[2] David HA, Nagaraja HN (2003) Order statistics. Wiley, New York
[3] Kamps U (1995) A concept of generalized order statistics. Teubner, Stuttgart · Zbl 0851.62035
[4] Nevzorov VB (2001) Records: a mathematical theory. American Mathematical Society, Providence
[5] Resnick SI (1973) Limit laws for record values. Stoch Process Appl 1:67–87 · Zbl 0253.60028
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