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On a flexible construction of a negative binomial model

Author

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  • Leisen, Fabrizio
  • Mena, Ramsés H.
  • Palma, Freddy
  • Rossini, Luca

Abstract

This work presents a construction of stationary Markov models with negative-binomial marginal distributions. A simple closed form expression for the corresponding transition probabilities is given, linking the proposal to well-known classes of birth and death processes and thus revealing interesting characterizations. The advantage of having such closed form expressions is tested on simulated and real data.

Suggested Citation

  • Leisen, Fabrizio & Mena, Ramsés H. & Palma, Freddy & Rossini, Luca, 2019. "On a flexible construction of a negative binomial model," Statistics & Probability Letters, Elsevier, vol. 152(C), pages 1-8.
    • Handle: RePEc:eee:stapro:v:152:y:2019:i:c:p:1-8
    DOI: 10.1016/j.spl.2019.04.004
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    References listed on IDEAS

    as
    1. Ramses H. Mena & Stephen G. Walker, 2009. "On a Construction of Markov Models in Continuous Time," ICER Working Papers - Applied Mathematics Series 25-2009, ICER - International Centre for Economic Research.
    2. Ramses H. Mena & Stephen G. Walker, 2009. "On a construction of Markov models in continuous time," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(3), pages 303-323.
    3. Ramsés H. Mena & Stephen G. Walker, 2005. "Stationary Autoregressive Models via a Bayesian Nonparametric Approach," Journal of Time Series Analysis, Wiley Blackwell, vol. 26(6), pages 789-805, November.
    4. Michelle Anzarut & Ramsés H. Mena & Consuelo R. Nava & Igor Prünster, 2018. "Poisson-Driven Stationary Markov Models," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 36(4), pages 684-694, October.
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    6. Paolo Gorgi, 2018. "Integer†Valued Autoregressive Models With Survival Probability Driven By A Stochastic Recurrence Equation," Journal of Time Series Analysis, Wiley Blackwell, vol. 39(2), pages 150-171, March.
    7. 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.
    8. Michael K. Pitt & Chris Chatfield & Stephen G. Walker, 2002. "Constructing First Order Stationary Autoregressive Models via Latent Processes," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 29(4), pages 657-663, December.
    9. Ole E. Barndorff‐Nielsen & Neil Shephard, 2001. "Non‐Gaussian Ornstein–Uhlenbeck‐based models and some of their uses in financial economics," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 63(2), pages 167-241.
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