A noncentral Lindley construction illustrated in an INAR(1) environment

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Authors

Ferreira, Johannes Theodorus
Van der Merwe, Ane

Journal Title

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Publisher

MDPI

Abstract

This paper proposes a previously unconsidered generalization of the Lindley distribution by allowing for a measure of noncentrality. Essential structural characteristics are investigated and derived in explicit and tractable forms, and the estimability of the model is illustrated via the fit of this developed model to 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 Poisson-noncentral Lindley is also systematically investigated and characteristics are derived. The value of this count model is illustrated and implemented as the count error distribution in an integer autoregressive environment, and juxtaposed against other popular models. The effect of the systematically-induced noncentrality parameter is illustrated and paves the way for future flexible modelling not only as a standalone contender in continuous Lindleytype scenarios but also in discrete and discrete time series scenarios when the often-encountered equidispersed assumption is not adhered to in practical data environments.

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DATA AVAILABILITY STATEMENT : Data in this study is available at https://drive.google.com/drive/ folders/1pxymEy37SqJ8nqdBjj4MJ_-DxhiJ8TXC?usp=sharing accessed on 1 December 2021.

Keywords

Compounding, Maximum likelihood, Moments, Poisson, Transition probability, Lindley distribution

Sustainable Development Goals

Citation

Ferreira, J.; van der Merwe, A. A Noncentral Lindley Construction Illustrated in an INAR(1) Environment. Stats 2022, 5, 70–88. https://DOI.org/10.3390/stats5010005.