Asymptotics of the order statistics for a process with a regenerative structure

Natalia Soja-Kukieła

Statistics & Probability Letters, 2017, vol. 131, issue C, 108-115

Abstract: In the paper, a regenerative process {Xn:n∈N} with finite mean cycle length is considered. For Mn(q) denoting the qth largest value in {Xk:1⩽k⩽n}, we prove that supx∈R|PMn(q)⩽x−G(x)n∑k=0q−1−logG(x)nkk!γq,k(x)|→0,asn→∞,for G and γq,k expressed in terms of maxima over the cycle. The result is illustrated with examples.

Keywords: Asymptotics; Order statistics; Regenerative process; Phantom distribution function (search for similar items in EconPapers)
Date: 2017
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DOI: 10.1016/j.spl.2017.08.017

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