New bivariate Poisson extended exponential distributions and associated BINAR(1) processes with applications

This study proposes two types of bivariate Poisson extended exponential distributions: the basic bivariate Poisson extended exponential distribution and the Sarmanov-based bivariate Poisson extended exponential distribution. The two bivariate Poisson extended exponential distributions are then intro...

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Veröffentlicht in:Decision analytics journal 2023-06, Vol.7, p.1-13, Article 100261
Hauptverfasser: Maya, R., Krishna, Anuresha, Khan, Naushad Mamode, Irshad, M.R.
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Sprache:eng
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Zusammenfassung:This study proposes two types of bivariate Poisson extended exponential distributions: the basic bivariate Poisson extended exponential distribution and the Sarmanov-based bivariate Poisson extended exponential distribution. The two bivariate Poisson extended exponential distributions are then introduced as joint innovation distributions in a bivariate first-order integer-valued autoregressive process based on binomial thinning. The model parameters are estimated using maximum likelihood in basic bivariate Poisson extended exponential and Sarmanov-based bivariate Poisson extended exponential distributions. Conditional maximum likelihood is applied to the bivariate first-order integer-valued autoregressive process. Simulation experiments are used to evaluate the performance of small and large samples. In addition, the newly developed bivariate first-order integer-valued autoregressive models are then applied to the Pittsburgh crime series data and candies data. We show that they fit better than existing bivariate first-order integer-valued autoregressive models described in the literature. •Bivariate extensions are proposed using the Poisson extended exponential distribution.•New models are used as innovations in bivariate integer-valued autoregressive model.•Simulation study was carried out based on different estimation methods.•The newly developed models compete well with the existing models.
ISSN:2772-6622
2772-6622
DOI:10.1016/j.dajour.2023.100261