Skip to main content
SpringerLink
Log in

The Bayesian Confidence Interval for the Mean of the Zero-Inflated Poisson Distribution

  • Conference paper
  • First Online:
Integrated Uncertainty in Knowledge Modelling and Decision Making (IUKM 2020)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 12482))

  • 627 Accesses

Abstract

In this paper, the aim is to propose the confidence interval for the mean of Zero-inflated Poisson distribution. The two methods namely the Markov chain Monte Carlo (MCMC) and the highest posterior density (HPD) are applied to avoid the complex variance of mean of Zero-inflated Poisson distribution. Both the simulation study and the real-life data of the number of new daily COVID-19 cases in Laos are considered. The results show that Markov chain Monte Carlo method perform better than the highest posterior density method.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 79.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 99.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Cameron, A.C., Trivedi, P.K.: Regression Analysis of Count Data, 4th edn. Cambridge University Press, New York (2013)

    Book  Google Scholar 

  2. Lambert, D.: Zero-inflated poisson regression with an application to defects in manufacturing. Technometrics 34, 1–14 (1992)

    Article  Google Scholar 

  3. Böhning, D., Dietz, E., Schlattmann, P., Mendonça, L., Kirchner, U.: The zero-inflated Poisson model and the decayed, missing and filled teeth index in dental epidemiology. J. Roy. Stat. Soc. Ser. A (Stat. Soc.) 162(2), 195–209 (1999)

    Article  Google Scholar 

  4. Kusuma, R.D., Purwono, Y.: Zero-inflated poisson regression analysis on frequency of health insurance claim PT. XYZ. In: Proceedings of the 12th International Conference on Business and Management Research (ICBMR 2018) (2019)

    Google Scholar 

  5. Lee, C., Kim, S.: Applicability of zero-inflated models to fit the torrential rainfall count data with extra zeros in South Korea. Water 9(2), 123 (2017)

    Article  Google Scholar 

  6. Beckett, S., et al.: Zero-Inflated Poisson (ZIP) distribution: parameter estimation and applications to model data from natural calamities. Involve J. Math. 7(6), 751–767 (2014)

    Article  MathSciNet  Google Scholar 

  7. Xie, M., He, B., Goh, T.N.: Zero-inflated Poisson model in statistical process control. Comput. Stat. Data Anal. 38, 191–201 (2001)

    Article  MathSciNet  Google Scholar 

  8. Rodrigues, J.: Bayesian analysis of zero-inflated distributions. Commun. Stat. Theo. Meth. 32(2), 281–289 (2003)

    Article  MathSciNet  Google Scholar 

  9. Xu, H.-Y., Xie, M., Goh, T.N.: Objective Bayes analysis of zero-inflated Poisson distribution with application to healthcare data. IIE Trans. 46(8), 843–852 (2014)

    Article  Google Scholar 

  10. Unhapipat, S., Tiensuwan, M., Pal, N.: Bayesian predictive inference for zero-inflated poisson (ZIP) distribution with applications. Am. J. Math. Manage. Sci. 37(1), 66–79 (2018)

    Google Scholar 

  11. Yip, P.: Inference about the mean of a Poisson distribution in the presence of a nuisance parameter. Austral. J. Statist. 30(3), 299–306 (1988)

    Article  MathSciNet  Google Scholar 

  12. Tanusit, M.: Two-side confidence intervals for the Poisson means. Int. J. Model. Optimization 2(5), 589–591 (2012)

    Article  Google Scholar 

  13. Patil, V.V., Kulkarni, H.V.: Comparison of confidence intervals for the poisson mean: some new aspects. REVSTAT-Stat. J. 10(2), 211–227 (2012)

    MathSciNet  MATH  Google Scholar 

  14. Bityukov, S.I., Krasnikov, N.V., & Taperechkina, V.A., Confidence intervals for poisson distribution parameter. https://arxiv.org/abs/hep-ex/0108020v1 (2001)

  15. Valencia, D.N.: Brief Review on COVID-19: The 2020 Pandemic Caused by SARS-CoV-2. Cureus 12(3) (2020)

    Google Scholar 

  16. Tanner, M.A., Wong, W.H.: The calculation of posterior distributions by data augmentation. J. Am. Stat. Assoc. 82(398), 528–540 (1987)

    Article  MathSciNet  Google Scholar 

  17. Chen, M.-H., Shao, Q.-M.: Monte Carlo estimation of Bayesian credible and HPD intervals. J. Comput. Graph. Stat. 8(1), 69–92 (1999)

    MathSciNet  Google Scholar 

  18. Box, G.E.P., Tiao, G.C.: Bayesian Inference in Statistical Analysis. Wiley, New York (1992)

    Book  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Applied Statistics, King Mongkut’s University of Technology North Bangkok, Bangkok, 10800, Thailand

    Sunisa Junnumtuam, Sa-Aat Niwitpong & Suparat Niwitpong

Authors
  1. Sunisa Junnumtuam
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Sa-Aat Niwitpong
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Suparat Niwitpong
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Sa-Aat Niwitpong .

Editor information

Editors and Affiliations

  1. Japan Advanced Institute of Science and Technology, Nomi, Ishikawa, Japan

    Van-Nam Huynh

  2. University of Hyogo, Kobe, Japan

    Tomoe Entani

  3. Sirindhorn International Institute of Technology, Thammasat University, Pathum Thani, Thailand

    Chawalit Jeenanunta

  4. Graduate School of Engineering Science, Osaka University, Toyonaka, Osaka, Japan

    Masahiro Inuiguchi

  5. Sirindhorn International Institute of Technology, Thammasat University, Pathum Thani, Thailand

    Pisal Yenradee

Rights and permissions

Reprints and permissions

Copyright information

© 2020 Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Junnumtuam, S., Niwitpong, SA., Niwitpong, S. (2020). The Bayesian Confidence Interval for the Mean of the Zero-Inflated Poisson Distribution. In: Huynh, VN., Entani, T., Jeenanunta, C., Inuiguchi, M., Yenradee, P. (eds) Integrated Uncertainty in Knowledge Modelling and Decision Making. IUKM 2020. Lecture Notes in Computer Science(), vol 12482. Springer, Cham. https://doi.org/10.1007/978-3-030-62509-2_35

Download citation

  • DOI: https://doi.org/10.1007/978-3-030-62509-2_35

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-62508-5

  • Online ISBN: 978-3-030-62509-2

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation