Hostname: page-component-cd9895bd7-8ctnn Total loading time: 0 Render date: 2024-12-27T07:19:14.605Z Has data issue: false hasContentIssue false
  • English
  • Français

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: [email protected]
Fabrizio Leisen
Affiliation:
Departamento de Estadística, Universidad Carlos III de Madrid, Calle Madrid 126, 28903 Getafe (Madrid), Spain E-mail: [email protected]
Fabio Spizzichino
Affiliation:
Dipartimento di Matematica, Sapienza Università di Roma, Piazzale Aldo Moro 5, 00185 Roma, Italy E-mail: [email protected]
Florentina Suter
Affiliation:
Facultatea de Matematica si Informatica, Universitatea din Bucuresti, Str. Academiei, 14, 010014 Bucuresti, Romania, E-mail: [email protected]
Get access Rights & Permissions [Opens in a new window]

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 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1.Aruka, Y. (2011). Avatamsaka game experiment as a nonlinear Pólya urn process. In New Frontiers in Artificial Intelligence, Berlin: Springer, pp. 153–161.Google Scholar
2.Charalambides, C.A. (2005). Combinatorial methods in discrete distributions. Wiley Series in Probability and Statistics. Hoboken, NJ: Wiley-Interscience, John Wiley & Sons.CrossRefGoogle Scholar
3.Crimaldi, I. & Leisen, F. (2008). Asymptotic results for a generalized Pólya urn with multi-updating and applications to clinical trials. Communications in Statistics–Theory and Methods 37(17): 2777–2794.CrossRefGoogle Scholar
4.Feller, W. (1968). An introduction to probability theory and its applications. Volume I. Third edition. John Wiley & Sons Inc., New York.Google Scholar
5.Gadrich, T. & Ravid, R. (2011). The sequential occupancy problem through group throwing of indistinguishable balls. Methodology and Computing in Applied Probability, 13(2): 433–448.CrossRefGoogle Scholar
6.Huang, W.J. & Shoung, J.M. (1994). On a study of some properties of point processes. Sankhyā, Series A, 56(1): 67–76.Google Scholar
7.Mahmoud, H.M. (2009). Pólya urn models. Baca Raton: CRC Press.Google Scholar
8.Shaked, M., Spizzichino, F. & Suter, F. (2004). Uniform order statistics property and ℓ∞-spherical densities. Probability in the Engineering and Informational Sciences 18(3): 275–297.Google Scholar
9.Shaked, M., Spizzichino, F., & Suter, F. (2008). Errata: “Uniform order statistics property and ℓ∞-spherical densities” [Probability in the Engineering and Informational Sciences, 18(3):275–297, 2004]. Probability in the Engineering and Informational Sciences, 22(1): 161–162.CrossRefGoogle Scholar
10.Shah, S., Kothari, R., Jayadeva & Chandra, S. (2011). Trail formation in ants. A generalized Pólya urn process. Swarm Intelligence, 4(2): 145–171.CrossRefGoogle Scholar