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Title: Computational discussions within an integer time series setup using a novel Poisson-Lindley model Authors:  Ane van der Merwe - University of Pretoria (South Africa) [presenting]
JT Ferreira - University of Pretoria (South Africa)
Abstract: A generalization of the Lindley distribution is proposed by allowing for a measure of noncentrality via a mixture approach. Essential structural properties are investigated and derived in explicit and tractable forms, and the estimability of the model is illustrated via real data. Subsequently, this model is used as a candidate for the parameter of a Poisson model, which allows for departure from the usual equidispersion restriction that the Poisson offers when modelling count data. This more robust Poisson-noncentral Lindley is also systematically investigated and characteristics are derived. The computational impact and value of these continuous- and discrete models are illustrated in both simulation studies as well as real data fittings. The discrete model is further illustrated within an integer autoregressive environment as the error choice, and the effect of the systematically-induced noncentrality parameter is investigated. The extended binomial thinning operator, as a generalized case of usual binomial thinning, is also implemented within this time series context for this previously unconsidered discrete model. This paves the way for future flexible modeling, not only as a stand-alone contender in Lindley-type scenarios but also in discrete time series scenarios when the often-assumed equidispersed assumption is not adhered to in practical data environments.