The extremal independence problem

Iddo Eliazar

Physica A: Statistical Mechanics and its Applications, 2010, vol. 389, issue 4, 659-666

Abstract: Consider a finite sequence of independent–though not, necessarily, identically distributed–real-valued random scores. If the scores are absolutely continuous random variables, the sequence possesses a unique maximum (minimum). We say that “maximal (minimal) independence” holds if the value and the identity of the sequence’s unique maximal (minimal) score are independent random variables. In this research we study the class of statistics for which maximal (minimal) independence holds, and: (i) establish explicit characterizations of this class; (ii) connect this class with the class of Lévy processes; (iii) unveil the underlying spatial Poissonian structure of this class.

Keywords: Maxima and minima of random scores; Hazard rates; Extreme value theory; Lévy processes; Poisson processes (search for similar items in EconPapers)
Date: 2010
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:389:y:2010:i:4:p:659-666

DOI: 10.1016/j.physa.2009.10.021

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