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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

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