Ehlers, René2025-07-302025-07-302025-09-012025-07-30*S2025http://hdl.handle.net/2263/103690Thesis (PhD)--University of Pretoria, 2025.Count data are frequently encountered in fields such as biomedicine, social sciences, economics, and ecological research. However, count data often exhibit overdispersion, which can compromise the accuracy of model parameter estimates. This thesis introduces new bivariate and multivariate Pólya-Aeppli distributions that offer greater flexibility for modelling overdispersed count data, including scenarios involving zero- and zero-and-one inflation. This study presents a significant advantage through the formulation of probability mass functions and their associated distributional properties using Laguerre polynomials. This approach effectively addresses existing limitations in current methodologies, thereby enhancing the applicability and relevance of the distributions to real-world data. The methodology is validated through comprehensive simulation studies and applications to real datasets, showcasing its effectiveness and superiority compared to various existing approaches or models.en© 2024 University of Pretoria. All rights reserved. The copyright in this work vests in the University of Pretoria. No part of this work may be reproduced or transmitted in any form or by any means, without the prior written permission of the University of Pretoria.UCTDSustainable Development Goals (SDGs)Bivariate distributionsCount dataLaguerre polynomialsMultivariate distributionsOverdispersionPólya-Aeppli distributionsZero-and-one inflationZero-inflationThesisu29090777https://doi.org/10.1002/jae.3950010104, https://doi.org/10.1080/10920277.2007.10597487, https://doi.org/10.2307/3001656, https://doi.org/10.1080/00401706.1972.10488881