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A tractable and interpretable four-parameter family of unimodal distributions on the circle

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  • Shogo Kato
  • M. C. Jones

Abstract

This article presents a class of four-parameter distributions for circular data that are unimodal, possess simple characteristic and density functions and a tractable distribution function, can be interpretably parameterized directly in terms of their trigonometric moments, afford a very wide range of skewness and kurtosis, envelop numerous interesting submodels including the wrapped Cauchy and cardioid distributions, allow straightforward parameter estimation by both method of moments and maximum likelihood, and are closed under convolution. This class of distributions exhibits the widest range of attractive properties yet available while retaining unimodality.

Suggested Citation

  • 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.
    • Handle: RePEc:oup:biomet:v:102:y:2015:i:1:p:181-190.
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    File URL: http://hdl.handle.net/10.1093/biomet/asu059
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    Cited by:

    1. Sara Salvador & Riccardo Gatto, 2022. "Bayesian tests of symmetry for the generalized Von Mises distribution," Computational Statistics, Springer, vol. 37(2), pages 947-974, April.
    2. 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.
    3. Jose Ameijeiras-Alonso & Christophe Ley & Arthur Pewsey & Thomas Verdebout, 2021. "On optimal tests for circular reflective symmetry about an unknown central direction," Statistical Papers, Springer, vol. 62(4), pages 1651-1674, August.
    4. Abe, Toshihiro & Miyata, Yoichi & Shiohama, Takayuki, 2023. "Bayesian estimation for mode and anti-mode preserving circular distributions," Econometrics and Statistics, Elsevier, vol. 27(C), pages 136-160.
    5. 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.
    6. Andrade, Ana C.C. & Pereira, Gustavo H.A. & Artes, Rinaldo, 2023. "The circular quantile residual," Computational Statistics & Data Analysis, Elsevier, vol. 178(C).
    7. Corinne Sinner & Yves Dominicy & Julien Trufin & Wout Waterschoot & Patrick Weber & Christophe Ley, 2023. "From Pareto to Weibull – A Constructive Review of Distributions on ℝ+," International Statistical Review, International Statistical Institute, vol. 91(1), pages 35-54, April.
    8. Ameijeiras-Alonso, Jose & Gijbels, Irène & Verhasselt, Anneleen, 2022. "On a family of two–piece circular distributions," Computational Statistics & Data Analysis, Elsevier, vol. 168(C).
    9. Yogendra P. Chaubey & Shamal C. Karmaker, 2021. "On Some Circular Distributions Induced by Inverse Stereographic Projection," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 83(2), pages 319-341, November.
    10. Shogo Kato & Arthur Pewsey & M. C. Jones, 2022. "Tractable circula densities from Fourier series," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 31(3), pages 595-618, September.
    11. Imoto, Tomoaki & Abe, Toshihiro, 2021. "Simple construction of a toroidal distribution from independent circular distributions," Journal of Multivariate Analysis, Elsevier, vol. 186(C).
    12. Masanobu Taniguchi & Shogo Kato & Hiroaki Ogata & Arthur Pewsey, 2020. "Models for circular data from time series spectra," Journal of Time Series Analysis, Wiley Blackwell, vol. 41(6), pages 808-829, November.
    13. Gugliani, G.K. & Sarkar, A. & Ley, C. & Mandal, S., 2018. "New methods to assess wind resources in terms of wind speed, load, power and direction," Renewable Energy, Elsevier, vol. 129(PA), pages 168-182.

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