Discrete Zipf-PSS INAR(1) processes

M. Pérez Casany, A. Duarte-López, M. Gonzalez-Scotto

The Zipf-PSS distribution is a Poisson Stopped-Sum with a Zipf distribution as secondary distribution. In this work, we consider two INAR(1) processes: The Zipf-PSS-INAR(1) innovations process, whose innovations follow a Zipf-PSS distribution, and the Zipf-PSS-INAR(1) marginal process, whose stationary marginal distribution is Zipf-PSS. Working with the marginal process is more complex than working with the innovation process, because it requires to compute the unknown distribution of the innovations. Nevertheless, the distribution of the innovation has a notable feature: it depends on the survival parameter (a larger survival parameter implies less immigration). This property is appealing from an applied perspective, and it is never achieved in the INAR(1) processes which is defined specifiying the innovation distribution.

Keywords: Zipf, Poisson-Stopped-Sum, INAR process,

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