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Generalized Cardioid Distributions for Circular Data Analysis

Author

Listed:
  • Fernanda V. Paula

    (Mathematics Degree Course, Federal University of the Tocantins, Araguaína 77824-838, TO, Brazil
    These authors contributed equally to this work.)

  • Abraão D. C. Nascimento

    (Department of Statistics, Federal University of Pernambuco, Recife 50740-540, PE, Brazil
    These authors contributed equally to this work.)

  • Getúlio J. A. Amaral

    (Department of Statistics, Federal University of Pernambuco, Recife 50740-540, PE, Brazil
    These authors contributed equally to this work.)

  • Gauss M. Cordeiro

    (Department of Statistics, Federal University of Pernambuco, Recife 50740-540, PE, Brazil
    These authors contributed equally to this work.)

Abstract

The Cardioid (C) distribution is one of the most important models for modeling circular data. Although some of its structural properties have been derived, this distribution is not appropriate for asymmetry and multimodal phenomena in the circle, and then extensions are required. There are various general methods that can be used to produce circular distributions. This paper proposes four extensions of the C distribution based on the beta, Kumaraswamy, gamma, and Marshall–Olkin generators. We obtain a unique linear representation of their densities and some mathematical properties. Inference procedures for the parameters are also investigated. We perform two applications on real data, where the new models are compared to the C distribution and one of its extensions.

Suggested Citation

  • Fernanda V. Paula & Abraão D. C. Nascimento & Getúlio J. A. Amaral & Gauss M. Cordeiro, 2021. "Generalized Cardioid Distributions for Circular Data Analysis," Stats, MDPI, vol. 4(3), pages 1-16, August.
    • Handle: RePEc:gam:jstats:v:4:y:2021:i:3:p:38-649:d:612707
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    References listed on IDEAS

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    1. Riccardo Gatto, 2012. "Saddlepoint Approximations to Tail Probabilities and Quantiles of Inhomogeneous Discounted Compound Poisson Processes with Periodic Intensity Functions," Methodology and Computing in Applied Probability, Springer, vol. 14(4), pages 1053-1074, December.
    2. Pierre Broly & Jean-Louis Deneubourg, 2015. "Behavioural Contagion Explains Group Cohesion in a Social Crustacean," PLOS Computational Biology, Public Library of Science, vol. 11(6), pages 1-18, June.
    3. Abe, Toshihiro & Pewsey, Arthur & Shimizu, Kunio, 2009. "On Papakonstantinou's extension of the cardioid distribution," Statistics & Probability Letters, Elsevier, vol. 79(20), pages 2138-2147, October.
    4. Arne Henningsen & Ott Toomet, 2011. "maxLik: A package for maximum likelihood estimation in R," Computational Statistics, Springer, vol. 26(3), pages 443-458, September.
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