Van der Merwe, AneFerreira, Johannes Theodorus2023-09-042023-09-042022-11Van der Merwe, A.; Ferreira, J.T. An Adapted Discrete Lindley Model Emanating from Negative Binomial Mixtures for Autoregressive Counts. Mathematics 2022, 10, 4141. https://DOI.org/10.3390/math10214141.2227-739010.3390/math10214141http://hdl.handle.net/2263/92198Analysing autoregressive counts over time remains a relevant and evolving matter of interest, where oftentimes the assumption of normality is made for the error terms. In the case when data are discrete, the Poisson model may be assumed for the structure of the error terms. In order to address the equidispersion restriction of the Poisson distribution, various alternative considerations have been investigated in such an integer environment. This paper, inspired by the integer autoregressive process of order 1, incorporates negative binomial shape mixtures via a compound Poisson Lindley model for the error terms. The systematic construction of this model is offered and motivated, and is analysed comparatively against common alternate candidates with a number of simulation and data analyses. This work provides insight into noncentral-type behaviour in both the continuous Lindley model and in the discrete case for meaningful application and consideration in integer autoregressive environments.en© 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license.CompoundingMaximum likelihoodMomentsTransition probabilityArticle