Exchangeable Occupancy Models and Discrete Processes with the Generalized Uniform Order Statistics Property

TL;DR

This paper unifies and generalizes the theory of Exchangeable Occupancy Models and their relation to the Uniform Order Statistics Property in discrete time processes, introducing new classes and characterization results.

Contribution

It introduces the $ ext{M}^{(a)}$-models class and a generalized UOSP, providing a unifying framework and new characterization results for EOMs in discrete processes.

Findings

Introduction of $ ext{M}^{(a)}$-models class.

Characterization of processes with generalized UOSP.

Analysis of closure properties of EOMs under transformations.

Abstract

This work focuses on Exchangeable Occupancy Models (EOM) 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 (2004) can be unified and generalized in the frame of occupancy models. We first show some general facts about EOM's. Then we introduce a class of EOM's, called $\mathcal{M}^{(a)}$-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 $\mathcal{M}^{(a)}$-models. Our interest is also focused on properties of closure w.r.t. some natural transformations of EOM's.