IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v10y2022i21p4012-d956855.html
   My bibliography  Save this article

A Zero-and-One Inflated Cosine Geometric Distribution and Its Application

Author

Listed:
  • Sunisa Junnumtuam

    (Department of Applied Statistics, Faculty of Applied Science, King Mongkut’s University of Technology North Bangkok, Bangkok 10800, Thailand
    These authors contributed equally to this work.)

  • Sa-Aat Niwitpong

    (Department of Applied Statistics, Faculty of Applied Science, King Mongkut’s University of Technology North Bangkok, Bangkok 10800, Thailand
    These authors contributed equally to this work.)

  • Suparat Niwitpong

    (Department of Applied Statistics, Faculty of Applied Science, King Mongkut’s University of Technology North Bangkok, Bangkok 10800, Thailand
    These authors contributed equally to this work.)

Abstract

Count data containing both excess zeros and ones occur in many fields, and the zero-and-one inflated distribution is suitable for analyzing them. Herein, we construct confidence intervals (CIs) for the parameters of the zero-and-one inflated cosine geometric (ZOICG) distribution constructed by using five methods: a Wald CI based on the maximum likelihood estimate, equal-tailed Bayesian CIs based on the uniform or Jeffreys prior, and the highest posterior density intervals based on the uniform or Jeffreys prior. Their efficiencies were compared in terms of their coverage probabilities and average lengths via a simulation study. The results show that the highest posterior density intervals based on the uniform prior performed the best in most cases. The number of new daily COVID-19-related deaths in Luxembourg in 2020 involving data with a high proportion of zeros and ones were analyzed. It was found that the ZOICG model was appropriate for this scenario.

Suggested Citation

  • Sunisa Junnumtuam & Sa-Aat Niwitpong & Suparat Niwitpong, 2022. "A Zero-and-One Inflated Cosine Geometric Distribution and Its Application," Mathematics, MDPI, vol. 10(21), pages 1-22, October.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:21:p:4012-:d:956855
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/10/21/4012/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/10/21/4012/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Cameron,A. Colin & Trivedi,Pravin K., 2013. "Regression Analysis of Count Data," Cambridge Books, Cambridge University Press, number 9781107667273, June.
    2. Karlis, Dimitris, 2005. "EM Algorithm for Mixed Poisson and Other Discrete Distributions," ASTIN Bulletin, Cambridge University Press, vol. 35(1), pages 3-24, May.
    3. Christophe Chesneau & Hassan S. Bakouch & Tassaddaq Hussain & Bilal A. Para, 2021. "The cosine geometric distribution with count data modeling," Journal of Applied Statistics, Taylor & Francis Journals, vol. 48(1), pages 124-137, January.
    4. D. Böhning & E. Dietz & P. Schlattmann & L. Mendonça & U. Kirchner, 1999. "The zero‐inflated Poisson model and the decayed, missing and filled teeth index in dental epidemiology," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 162(2), pages 195-209.
    5. Morgan, B.J.T. & Palmer, K.J. & Ridout, M.S., 2007. "Negative Score Test Statistic," The American Statistician, American Statistical Association, vol. 61, pages 285-288, November.
    6. Joseph B. Kadane & Ramayya Krishnan & Galit Shmueli, 2006. "A Data Disclosure Policy for Count Data Based on the COM-Poisson Distribution," Management Science, INFORMS, vol. 52(10), pages 1610-1617, October.
    7. Yincai Tang & Wenchen Liu & Ancha Xu, 2017. "Statistical inference for zero-and-one-inflated poisson models," Statistical Theory and Related Fields, Taylor & Francis Journals, vol. 1(2), pages 216-226, July.
    8. Xiang Xiao & Yincai Tang & Ancha Xu & Guoqiang Wang, 2020. "Bayesian inference for zero-and-one-inflated geometric distribution regression model using Pólya-Gamma latent variables," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 49(15), pages 3730-3743, August.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Jussiane Nader Gonçalves & Wagner Barreto-Souza, 2020. "Flexible regression models for counts with high-inflation of zeros," METRON, Springer;Sapienza Università di Roma, vol. 78(1), pages 71-95, April.
    2. Wen-Han Hwang & Rachel V. Blakey & Jakub Stoklosa, 2020. "Right-Censored Mixed Poisson Count Models with Detection Times," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 25(1), pages 112-132, March.
    3. Shen-Ming Lee & T. Martin Lukusa & Chin-Shang Li, 2020. "Estimation of a zero-inflated Poisson regression model with missing covariates via nonparametric multiple imputation methods," Computational Statistics, Springer, vol. 35(2), pages 725-754, June.
    4. Zhang, Pengcheng & Calderin, Enrique & Li, Shuanming & Wu, Xueyuan, 2020. "On the Type I multivariate zero-truncated hurdle model with applications in health insurance," Insurance: Mathematics and Economics, Elsevier, vol. 90(C), pages 35-45.
    5. Luiz Paulo Fávero & Joseph F. Hair & Rafael de Freitas Souza & Matheus Albergaria & Talles V. Brugni, 2021. "Zero-Inflated Generalized Linear Mixed Models: A Better Way to Understand Data Relationships," Mathematics, MDPI, vol. 9(10), pages 1-28, May.
    6. Riccardo (Jack) Lucchetti & Luca Pedini, 2020. "ParMA: Parallelised Bayesian Model Averaging for Generalised Linear Models," Working Papers 2020:28, Department of Economics, University of Venice "Ca' Foscari".
    7. Landry, Craig E. & Shonkwiler, J. Scott & Whitehead, John C., 2020. "Economic Values of Coastal Erosion Management: Joint Estimation of Use and Existence Values with recreation demand and contingent valuation data," Journal of Environmental Economics and Management, Elsevier, vol. 103(C).
    8. Yip, Karen C.H. & Yau, Kelvin K.W., 2005. "On modeling claim frequency data in general insurance with extra zeros," Insurance: Mathematics and Economics, Elsevier, vol. 36(2), pages 153-163, April.
    9. Mónica Moreno-Gutiérrez & Víctor Hernández-Trejo & Ramón Valdivia-Alcalá & Judith Juárez-Mancilla & Plácido Roberto Cruz-Chávez & Ulianov Jakes-Cota, 2024. "Linking Tourist Willingness to Pay and Beach Management: A Travel Cost Analysis for Balandra Marine Park, Mexico," Tourism and Hospitality, MDPI, vol. 5(4), pages 1-20, October.
    10. Ghosh, Prasenjit & Rong, Jian & Khanna, Madhu & Wang, Weiwei & Miao, Ruiqing, 2017. "Have They Gone with the Wind? Indirect Effects of Wind Turbines on Bird Abundance," 2017 Annual Meeting, July 30-August 1, Chicago, Illinois 258100, Agricultural and Applied Economics Association.
    11. Kim, Hayoung, 2025. "Place-based policy and spillovers in the housing market," Economics Letters, Elsevier, vol. 248(C).
    12. Mullahy, John, 2024. "Analyzing health outcomes measured as bounded counts," Journal of Health Economics, Elsevier, vol. 95(C).
    13. Michel Beine & Ilan Noy & Christopher Parsons, 2021. "Climate change, migration and voice," Climatic Change, Springer, vol. 167(1), pages 1-27, July.
    14. Christian Kleiber & Achim Zeileis, 2016. "Visualizing Count Data Regressions Using Rootograms," The American Statistician, Taylor & Francis Journals, vol. 70(3), pages 296-303, July.
    15. D M Zimmer, 2023. "The effect of food stamps on fibre intake," Economic Issues Journal Articles, Economic Issues, vol. 28(2), pages 71-86, September.
    16. Jasna Atanasijević & Miloš Božović, 2016. "Exchange Rate as a Determinant of Corporate Loan Defaults in a Euroized Economy: Evidence from Micro-Level Data," Eastern European Economics, Taylor & Francis Journals, vol. 54(3), pages 228-250, May.
    17. Syed Muhammad All-E-Raza Rizvi & Marie-Ange Véganzonès-Varoudakis, 2019. "Economic, social, and institutional determinants of domestic conflict in fragile States," Working Papers hal-02340977, HAL.
    18. Kyriakos Drivas & Constantine Iliopoulos, 2017. "An Empirical Investigation in the Relationship Between PDOs/PGIs and Trademarks," Journal of the Knowledge Economy, Springer;Portland International Center for Management of Engineering and Technology (PICMET), vol. 8(2), pages 585-595, June.
    19. J. M. C. Santos Silva & Silvana Tenreyro, 2022. "The Log of Gravity at 15," Portuguese Economic Journal, Springer;Instituto Superior de Economia e Gestao, vol. 21(3), pages 423-437, September.
    20. Yanlin Tang & Liya Xiang & Zhongyi Zhu, 2014. "Risk Factor Selection in Rate Making: EM Adaptive LASSO for Zero‐Inflated Poisson Regression Models," Risk Analysis, John Wiley & Sons, vol. 34(6), pages 1112-1127, June.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:10:y:2022:i:21:p:4012-:d:956855. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.