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The Integer-valued Moving-Average Random Field
[Submitted on 15 Apr 2026 (v1), last revised 22 Jul 2026 (this v · 2026-04-15 · via stat updates on arXiv.org

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Abstract:An integer-valued moving average (INMA) model for count random fields is proposed and investigated. Closed-form expressions are derived for both its marginal distribution and spatial dependence structure, for arbitrary model order and also covering the multilateral case. In particular, general expressions for bivariate distributions and autocovariances are provided. It is shown that the INMA random field can be equipped (among others) with a Poisson marginal distribution. It is also demonstrated that different and well-interpretable dependence structures are possible. For illustration, we discuss a real-world data example and propose an INMA approximation to a given spatial dependence structure.

Submission history

From: Angelika Silbernagel [view email]
[v1] Wed, 15 Apr 2026 12:09:54 UTC (17 KB)
[v2] Fri, 22 May 2026 13:50:17 UTC (30 KB)
[v3] Wed, 22 Jul 2026 09:17:25 UTC (32 KB)