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A Noncentral Lindley Construction Illustrated in an INAR(1) Environment

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  • Johannes Ferreira

    (Department of Statistics, Faculty of Natural and Agricultural Sciences, University of Pretoria, Pretoria 0028, South Africa
    Centre of Excellence in Mathematical and Statistical Sciences, Johannesburg 2050, South Africa)

  • Ané van der Merwe

    (Department of Statistics, Faculty of Natural and Agricultural Sciences, University of Pretoria, Pretoria 0028, South Africa)

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 Lindley-type scenarios but also in discrete and discrete time series scenarios when the often-encountered equidispersed assumption is not adhered to in practical data environments.

Suggested Citation

  • Johannes Ferreira & Ané van der Merwe, 2022. "A Noncentral Lindley Construction Illustrated in an INAR(1) Environment," Stats, MDPI, vol. 5(1), pages 1-19, January.
    • Handle: RePEc:gam:jstats:v:5:y:2022:i:1:p:5-88:d:721120
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    References listed on IDEAS

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    1. M. E. Ghitany & D. K. Al-Mutairi, 2008. "Size-biased Poisson-Lindley distribution and its application," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(3), pages 299-311.
    2. A. Alzaid & M. Al‐Osh, 1988. "First‐Order Integer‐Valued Autoregressive (INAR (1)) Process: Distributional and Regression Properties," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 42(1), pages 53-61, March.
    3. Christian Weiß, 2008. "Thinning operations for modeling time series of counts—a survey," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 92(3), pages 319-341, August.
    4. Nosakhare Ekhosuehi & Festus Opone, 2018. "A Three Parameter Generalized Lindley Distribution: Properties And Application," Statistica, Department of Statistics, University of Bologna, vol. 78(3), pages 233-249.
    5. Tito Lívio & Naushad Mamode Khan & Marcelo Bourguignon & Hassan S. Bakouch, 2018. "An INAR(1) model with Poisson-Lindley innovations," Economics Bulletin, AccessEcon, vol. 38(3), pages 1505-1513.
    6. M. A. Al‐Osh & A. A. Alzaid, 1987. "First‐Order Integer‐Valued Autoregressive (Inar(1)) Process," Journal of Time Series Analysis, Wiley Blackwell, vol. 8(3), pages 261-275, May.
    7. Izabela Oliveira & Daniel Ferreira, 2013. "Computing the noncentral gamma distribution, its inverse and the noncentrality parameter," Computational Statistics, Springer, vol. 28(4), pages 1663-1680, August.
    8. Ghitany, M.E. & Al-Mutairi, D.K. & Nadarajah, S., 2008. "Zero-truncated Poisson–Lindley distribution and its application," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(3), pages 279-287.
    9. Ghitany, M.E. & Atieh, B. & Nadarajah, S., 2008. "Lindley distribution and its application," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 78(4), pages 493-506.
    10. M. M. E. Abd El-Monsef, 2016. "A new Lindley distribution with location parameter," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 45(17), pages 5204-5219, September.
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