The balanced discrete Burr–Hatke model and mixing INAR(1) process: properties, estimation, forecasting and COVID-19 applications

References

• M. Ahsan-ul-Haq, A. Babar, S. Hashmi, A.S. Alghamdi, and A.Z. Afify, The discrete type-II half-logistic exponential distribution with applications to COVID-19 data, Pakistan J. Stat. Oper. Res. 17 (2021), pp. 921–932.
   Web of Science ®Google Scholar
• G.B. Al-Ani, Statistical modeling of the novel COVID-19 epidemic in Iraq, Epidemiol. Methods 10 (2021), Article ID 20200025.
   PubMedGoogle Scholar
• A.A. Al-Babtain, A.H.N. Ahmed, and A.Z. Afify, A new discrete analog of the continuous Lindley distribution, with reliability applications, Entropy 22 (2020), p. 603.
   PubMed Web of Science ®Google Scholar
• M.A. Al-Osh and E.E.A.A. Aly, First order autoregressive time series with negative binomial and geometric marginals, Commun. Stat. Theory Methods 21 (1992), pp. 2483–2492.
   Web of Science ®Google Scholar
• M.A. Al-Osh and A.A. Alzaid, First-order integer-valued autoregressive (INAR(1)) process, J. Time Ser. Anal. 8 (1987), pp. 261–275.
   Google Scholar
• A.A. Alzaid and M.A. Al-Osh, First-order integer-valued autoregressive (INAR(1)) process: Distributional and regression properties, Stat. Neerl. 42 (1988), pp. 53–61.
   Google Scholar
• A.A. Alzaid and M.A. Al-Osh, Some autoregressive moving average processes with generalized Poisson marginal distributions, Ann. Inst. Statist. Math. 45 (1993), pp. 223–232.
   Web of Science ®Google Scholar
• S. Chakaraborty and D. Chakaraborty, Discrete gamma distribution: Properties and parameter estimation, Commun. Stat.-Theory Methods 41 (2012), pp. 3301–3324.
   Web of Science ®Google Scholar
• S. Chattopadhyay, R. Maiti, S. Das, and A. Biswas, Change-point analysis through INAR process with application to some COVID-19 data, Stat. Neerl. 76 (2022), pp. 4–34.
   PubMed Web of Science ®Google Scholar
• C. Czado, T. Gneiting, and L. Held, Predictive model assessment for count data, Biom. J. 65 (2009), pp. 1254–1261.
   Google Scholar
• M. El-Morshedy, M.S. Eliwa, and E. Altun, Discrete Burr–Hatke distribution with properties, estimation methods and regression model, IEEE Access. 8 (2020), pp. 74359–74370.
   Web of Science ®Google Scholar
• M.S. Eliwa and M. El-Morshedy, A one-parameter discrete distribution for over-dispersed data: Statistical and reliability properties with applications, J. Appl. Stat. 49 (2022), pp. 2467–2487.
   PubMed Web of Science ®Google Scholar
• P. Gorgi, Integer-valued autoregressive models with survival probability driven by a stochastic recurrence equation, J. Time Ser. Anal. 39 (2018), pp. 150–171.
   Web of Science ®Google Scholar
• A.B. Gumel, E.A. Iboi, C.N. Ngonghala, and E.H. Elbasha, A primer on using mathematics to understand COVID-19 dynamics: Modeling, analysis and simulations, Infect. Dis. Model. 6 (2021), pp. 148–168.
   PubMedGoogle Scholar
• P.E. Hagmark, On construction and simulation of count data models, Math. Comput. Simul. 77 (2008), pp. 72–80.
   Web of Science ®Google Scholar
• H. Karlsen and D. Tjøstheim, Consistent estimates for the NEAR(2) and NLAR(2) time series models, J. R. Stat. Soc. Series. B. Stat. Methodol. 50 (1988), pp. 313–320.
   Google Scholar
• W.C. Khoo, S.H. Ong, and A. Biswas, Modeling time series of counts with a new class of INAR(1) model, Stat. Pap. 58 (2017), pp. 393–416.
   Web of Science ®Google Scholar
• M. Maleki, M.R. Mahmoudi, D. Wraith, and K.H. Pho, Time series modelling to forecast the confirmed and recovered cases of COVID-19, Travel. Med. Infect. Dis. 37 (2020), Article ID 101742.
   Web of Science ®Google Scholar
• A.H. Muse, A.H. Tolba, E. Fayad, O.A. Abu Ali, M. Nagy, and M. Yusuf, Modelling the COVID-19 mortality rate with a new versatile modification of the log-logistic distribution, Comput. Intell. Neurosci. 2021 (2021), Article ID 8640794.
   Web of Science ®Google Scholar
• L. Pascual, J. Romo, and E. Ruiz, Bootstrap predictive inference for ARIMA processes, J. Time Ser. Anal. 25 (2004), pp. 449–465.
   Web of Science ®Google Scholar
• H. Pourreza, E. Baloui Jamkhaneh, and E. Deiri, A family of gamma-generated distributions: Statistical properties and applications, Stat. Methods. Med. Res. 30 (2021), pp. 1850–1873.
   PubMed Web of Science ®Google Scholar
• M.M. Ristić, H.S. Bakouch, and A.S. Nastić, A new geometric first-order integer-valued autoregressive (NGINAR(1)) process, J. Stat. Plan. Inference. 139 (2009), pp. 2218–2226.
   Web of Science ®Google Scholar
• D. Roy, The discrete normal distribution, Commun. Stat. Theory Methods 32 (2003), pp. 1871–1883.
   Web of Science ®Google Scholar
• D. Roy, Discrete Rayleigh distribution, IEEE Trans. Reliab. 53 (2004), pp. 255–260.
   Web of Science ®Google Scholar
• N. Shamma and M. Mohammadpour, Alternative procedures in dependent counting INAR process with application on COVID-19, Commun. Stat. Simul. Comput. (2021). https://doi.org/10.1080/03610918.2021.1987468
   Web of Science ®Google Scholar
• M. Shirozhan and M. Mohammadpour, An INAR(1) model based on the Pegram and thinning operators with serially dependent innovation, Commun. Stat. Simul. Comput. 49 (2018), pp. 2617–2638.
   Web of Science ®Google Scholar
• M. Shirozhan and M. Mohammadpour, A new class of INAR(1) model for count time series, J. Stat. Comput. Simul. 88 (2018), pp. 1348–1368.
   Web of Science ®Google Scholar
• M. Shirozhan, M. Mohammadpour, and H.S. Bakouch, A new geometric INAR(1) model with mixing Pegram and generalized binomial thinning operators, Iran. J. Sci. Technol. Trans. A Sci. 43 (2019), pp. 1011–1020.
   Web of Science ®Google Scholar
• C.F. Tovissodé, S.H. Honfo, J.T. Doumaté, and R. Glélé Kakaï, On the discretization of continuous probability distributions using a probabilistic rounding mechanism, Mathematics 9 (2021), p. 555.
   Web of Science ®Google Scholar
• M. Triacca and U. Triacca, Forecasting the number of confirmed new cases of COVID-19 in Italy for the period from 19 May to 2 June 2020, Infect. Dis. Model. 6 (2021), pp. 362–369.
   PubMedGoogle Scholar
• C.H. Weiß, Thinning operations for modeling time series of count – a survey, AStA Adv. Stat. Anal. 92 (2008), pp. 319–341.
   Web of Science ®Google Scholar