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Families of Discrete Circular Distributions with Some Novel Applications

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  • Kanti V. Mardia

    (University of Leeds
    University of Oxford)

  • Karthik Sriram

    (Indian Institute of Management Ahmedabad)

Abstract

We give a unified treatment of constructing families of circular discrete distributions. Some of these families are deduced from established distributions such as von Mises and wrapped Cauchy. Some others are derived directly such as a flexible family based on trigonometric sums and the circular location family. Results interrelating these families are discussed. These distributions have been motivated by two examples of discrete circular data: casino roulette spins and smart health acrophase monitoring, and these data are analyzed using our proposed models. We discuss how using continuous circular models for circular discrete data can be misleading.

Suggested Citation

  • Kanti V. Mardia & Karthik Sriram, 2023. "Families of Discrete Circular Distributions with Some Novel Applications," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 85(1), pages 1-42, February.
    • Handle: RePEc:spr:sankha:v:85:y:2023:i:1:d:10.1007_s13171-022-00298-z
    DOI: 10.1007/s13171-022-00298-z
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    References listed on IDEAS

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    1. Arthur Pewsey & Eduardo García-Portugués, 2021. "Rejoinder on: Recent advances in directional statistics," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 30(1), pages 76-82, March.
    2. Arthur Pewsey, 2004. "The large-sample joint distribution of key circular statistics," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 60(1), pages 25-32, July.
    3. F. Lombard & R. K. Maxwell, 2012. "A cusum procedure to detect deviations from uniformity in angular data," Journal of Applied Statistics, Taylor & Francis Journals, vol. 39(9), pages 1871-1880, April.
    4. Arthur Pewsey & Eduardo García-Portugués, 2021. "Recent advances in directional statistics," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 30(1), pages 1-58, March.
    5. Shogo Kato & M. C. Jones, 2015. "A tractable and interpretable four-parameter family of unimodal distributions on the circle," Biometrika, Biometrika Trust, vol. 102(1), pages 181-190.
    6. Kanti V. Mardia, 2021. "Comments on: Recent advances in directional statistics," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 30(1), pages 59-63, March.
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