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Processes of rth largest

Buchmann, Boris; Maller, Ross; Resnick, Sidney I.

Description

For integers n ≥ r, we treat the rth largest of a sample of size n as an R∞ -valued stochastic process in r which we denote as M(r). We show that the sequence regarded in this way satisfies the Markov property. We go on to study the asymptotic behavior of M(r) as r → ∞, and, borrowing from classical extreme value theory, show that left-tail domain of attraction conditions on the underlying distribution of the sample guarantee weak limits for both the range of M(r) and M(r) itself, after...[Show more]

CollectionsANU Research Publications
Date published: 2018
Type: Journal article
URI: http://hdl.handle.net/1885/219353
Source: Extremes
DOI: 10.1007/s10687-018-0308-x
Access Rights: Open Access

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