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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
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    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.
    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.
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