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The extremal independence problem

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  • Eliazar, Iddo

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.

Suggested Citation

  • Eliazar, Iddo, 2010. "The extremal independence problem," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(4), pages 659-666.
    • Handle: RePEc:eee:phsmap:v:389:y:2010:i:4:p:659-666
    DOI: 10.1016/j.physa.2009.10.021
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    References listed on IDEAS

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    1. Aleksander Janicki & Aleksander Weron, 1994. "Simulation and Chaotic Behavior of Alpha-stable Stochastic Processes," HSC Books, Hugo Steinhaus Center, Wroclaw University of Technology, number hsbook9401.
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