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Compound Poisson approximation for extremes of moving minima in arrays of independent random variables

Jadwiga Dudkiewicz — 1998

Applicationes Mathematicae

We present conditions sufficient for the weak convergence to a compound Poisson distribution of the distributions of the kth order statistics for extremes of moving minima in arrays of independent random variables.

On the limit distributions of kth order statistics for semi-pareto processes

Magdalena Chrapek; Jadwiga Dudkiewicz; Wiesław Dziubdziela — 1997

Applicationes Mathematicae

Asymptotic properties of the kth largest values for semi-Pareto processes are investigated. Conditions for convergence in distribution of the kth largest values are given. The obtained limit laws are represented in terms of a compound Poisson distribution.

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