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On Stochastic Representations of the Zero–One-Inflated Poisson Lindley Distribution

Author

Listed:
  • Razik Ridzuan Mohd Tajuddin

    (Department of Mathematical Sciences, Universiti Kebangsaan Malaysia, Bangi 43600, Malaysia)

  • Noriszura Ismail

    (Department of Mathematical Sciences, Universiti Kebangsaan Malaysia, Bangi 43600, Malaysia)

Abstract

A zero–one-inflated Poisson Lindley distribution has been introduced recently as an alternative to the zero–one-inflated Poisson distribution for describing count data with a substantial number of zeros and ones. Several stochastic representations of the zero–one-inflated Poisson Lindley distribution and their equivalence to some well-known distributions under some conditions are presented. Using these stochastic representations, the distributional properties such as the n th moments, as well as the conditional distributions are discussed. These stochastic representations can be used to explain the relationship between two or more distributions. Several likelihood ratio tests are developed and examined for the presence of one-inflation and fixed rate parameters. The likelihood ratio tests are found to be powerful and have ability to control the error rates as the sample size increases. A sample size of 1000 is acceptable and sufficient for the likelihood ratio tests to be useful.

Suggested Citation

  • Razik Ridzuan Mohd Tajuddin & Noriszura Ismail, 2024. "On Stochastic Representations of the Zero–One-Inflated Poisson Lindley Distribution," Mathematics, MDPI, vol. 12(5), pages 1-16, March.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:5:p:778-:d:1351862
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    References listed on IDEAS

    as
    1. Chanakarn Jornsatian & Winai Bodhisuwan, 2022. "Zero-one inflated negative binomial - beta exponential distribution for count data with many zeros and ones," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 51(24), pages 8517-8531, December.
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