Review Articles

On the MLE of the Waring distribution

Yanlin Tang ,

KLATASDS-MOE, School of Statistics, East China Normal University Shanghai, People's Republic of China

Jinglong Wang ,

KLATASDS-MOE, School of Statistics, East China Normal University Shanghai, People's Republic of China

Zhongyi Zhu

Department of Statistics and Data Science, Fudan University Shanghai, People's Republic of China

Pages | Received 17 Sep. 2022, Accepted 27 Jan. 2023, Published online: 13 Feb. 2023,
  • Abstract
  • Full Article
  • References
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The two-parameter Waring is an important heavy-tailed discrete distribution, which extends the famous Yule-Simon distribution and provides more flexibility when modelling the data. The commonly used EFF (Expectation-First Frequency) for parameter estimation can only be applied when the first moment exists, and it only uses the information of the expectation and the first frequency, which is not as efficient as the maximum likelihood estimator (MLE). However, the MLE may not exist for some sample data. We apply the profile method to the log-likelihood function and derive the necessary and sufficient conditions for the existence of the MLE of the Waring parameters. We use extensive simulation studies to compare the MLE and EFF methods, and the goodness-of-fit comparison with the Yule-Simon distribution. We also apply the Waring distribution to fit an insurance data.


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To cite this article: Yanlin Tang, Jinglong Wang & Zhongyi Zhu (2023) On the MLE of the Waring distribution, Statistical Theory and Related Fields, 7:2, 144-158, DOI: 10.1080/24754269.2023.2176608

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