Abstract
Let X1, . . . , Xn, be a sequence of independent and identically distributed random variables with a continuous distribution function F and let Xn-kn+1 be the corresponding knth largest order statistics. Gather and Tomkins (J. Statist. Plann. Inference (1995), 175-183) proved that the condition (C) lim supx→ωr (1 - F (x + ε))/(1 - F (x)) < 1, where ωr := sup{x: F (x) < 1}, is sufficient for every sequence of upper-intermediate order statistics being absolutely stable. In this paper we prove that the condition (C) is also necessary, which solves an open problem by Gather and Tomkins (J. Statist. Plann. Inference (1995), 175-183). As an application of this result we give a criterion for every sequence of order statistics being absolutely stable.
Original language | English (US) |
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Pages (from-to) | 21-25 |
Number of pages | 5 |
Journal | Journal of Statistical Planning and Inference |
Volume | 64 |
Issue number | 1 |
DOIs | |
State | Published - Oct 30 1997 |
Externally published | Yes |
Bibliographical note
Funding Information:1 Supported by the Netherlands Foundation for Mathematics SMC with a grant from the Netherlands Organization for Scientific Research NWO. The author would like to thank Prof. L. de Haan for his hospitality.
Copyright:
Copyright 2020 Elsevier B.V., All rights reserved.
Keywords
- Order statistics
- Stability