Geometric stable and semistable distributions on (Z+)^d

  1. Nadjib Bouzar


The aim of this article is to study geometric F-semistable and geometric F-stable distributions on the d-dimensional lattice Z+d. We obtain several properties for these distributions, including characterizations in terms of their probability generating functions.We describe a relation between geometric F-semistability and geometric F-stability and their counterparts on R+d and, as a consequence, we derive some mixture representations and construct some examples.We establish limit theorems and discuss the related concepts of complete and partial geometric attraction for distributions on Z+d. As an application, we derive the marginal distribution of the innovation sequence of a Z+d-valued stationary autoregressive process of order p with a geometric F-stable marginal distribution.

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Probability and Mathematical Statistics

35, z. 2, 2015

Pages from 223 to 245

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