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EXCHANGEABLE OCCUPANCY MODELS AND DISCRETE PROCESSES WITH THE GENERALIZED UNIFORM ORDER STATISTICS PROPERTY

Published online by Cambridge University Press:  14 August 2013

Francesca Collet ,
Fabrizio Leisen ,
Fabio Spizzichino  and
Florentina Suter
Francesca Collet
Affiliation:
Dipartimento di Matematica, Alma Mater Studiorum Università di Bologna, Piazza di Porta San Donato 5, 40126 Bologna, Italy E-mail: francesca.collet@unibo.it
Fabrizio Leisen
Affiliation:
Departamento de Estadística, Universidad Carlos III de Madrid, Calle Madrid 126, 28903 Getafe (Madrid), Spain E-mail: fabrizio.leisen@gmail.com
Fabio Spizzichino
Affiliation:
Dipartimento di Matematica, Sapienza Università di Roma, Piazzale Aldo Moro 5, 00185 Roma, Italy E-mail: fabio.spizzichino@uniroma1.it
Florentina Suter
Affiliation:
Facultatea de Matematica si Informatica, Universitatea din Bucuresti, Str. Academiei, 14, 010014 Bucuresti, Romania, E-mail: florentina.suter@fmi.unibuc.ro
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Abstract

This work focuses on Exchangeable Occupancy Models (EOMs) and their relations with the Uniform Order Statistics Property (UOSP) for point processes in discrete time. As our main purpose, we show how definitions and results presented in Shaked, Spizzichino, and Suter [8] can be unified and generalized in the frame of occupancy models. We first show some general facts about EOMs. Then we introduce a class of EOMs, called ℳ(a)-models, and a concept of generalized Uniform Order Statistics Property in discrete time. For processes with this property, we prove a general characterization result in terms of ℳ(a)-models. Our interest is also focused on properties of closure w.r.t. some natural transformations of EOMs.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 27 , Issue 4 , October 2013 , pp. 533 - 552
Copyright
Copyright © Cambridge University Press 2013 

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