Geldenhuys, ClaireEhlers, ReneBekker, Andriette, 1958-2026-02-252026-02-252026-03Geldenhuys, C., Ehlers, R. & Bekker, A. 2026, 'Type I multivariate Pólya-Aeppli distributions with applications', Journal of Multivariate Analysis, vol. 212, art. 105556, pp. 1-15, doi : 10.1016/j.jmva.2025.105556.0047-259X (print)1095-7243 (online)10.1016/j.jmva.2025.105556http://hdl.handle.net/2263/108620This article is part of a Special issue entitled: ‘YJMVA_Learning in Multi-Analysis’ published in Journal of Multivariate Analysis.An extensive body of literature exists that specifically addresses the univariate case of zero-inflated count models. In contrast, research pertaining to multivariate models is notably less developed. We propose two new parsimonious multivariate models that can be used to model correlated multivariate overdispersed count data. Furthermore, for different parameter settings and sample sizes, various simulations are performed. In conclusion, we demonstrate the performance of the newly proposed multivariate candidates on two benchmark datasets, which surpasses that of several alternative approaches.en© 2025 The Authors. Published by Elsevier Inc. This is an open access article under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).Australian Health Care survey datasetAutomobile insurance datasetGeneralized dispersion indexNewton–Raphson methodOverdispersionWeighted distributionArticle