Top-\(k\)-lists.

*(English)*Zbl 1105.62050Summary: 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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\textit{F. López-Blázquez} and \textit{J. Wesołowski}, Metrika 65, No. 1, 69--82 (2007; Zbl 1105.62050)

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##### References:

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[2] | David HA, Nagaraja HN (2003) Order statistics. Wiley, New York |

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