IDEAS home Printed from https://ideas.repec.org/a/gam/jstats/v4y2021i3p38-649d612707.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2571-905X/4/3/38/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2571-905X/4/3/38/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Maness, Michael & Cirillo, Cinzia, 2016. "An indirect latent informational conformity social influence choice model: Formulation and case study," Transportation Research Part B: Methodological, Elsevier, vol. 93(PA), pages 75-101.
    2. Mazen Nassar & Refah Alotaibi & Ahmed Elshahhat, 2023. "Reliability Estimation of XLindley Constant-Stress Partially Accelerated Life Tests using Progressively Censored Samples," Mathematics, MDPI, vol. 11(6), pages 1-24, March.
    3. John-Fritz Thony & Jean Vaillant, 2022. "Parameter Estimation for a Fractional Black–Scholes Model with Jumps from Discrete Time Observations," Mathematics, MDPI, vol. 10(22), pages 1-17, November.
    4. Badamasi Abba & Hong Wang, 2024. "A new failure times model for one and two failure modes system: A Bayesian study with Hamiltonian Monte Carlo simulation," Journal of Risk and Reliability, , vol. 238(2), pages 304-323, April.
    5. Logar, Ivana & Brouwer, Roy & Campbell, Danny, 2020. "Does attribute order influence attribute-information processing in discrete choice experiments?," Resource and Energy Economics, Elsevier, vol. 60(C).
    6. Padayachee Trishanta & Khamiakova Tatsiana & Shkedy Ziv & Salo Perttu & Perola Markus & Burzykowski Tomasz, 2019. "A multivariate linear model for investigating the association between gene-module co-expression and a continuous covariate," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 18(2), pages 1-13, April.
    7. 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.
    8. Wang, Shengjie & Kang, Yanfei & Petropoulos, Fotios, 2024. "Combining probabilistic forecasts of intermittent demand," European Journal of Operational Research, Elsevier, vol. 315(3), pages 1038-1048.
    9. Refah Alotaibi & Mazen Nassar & Hoda Rezk & Ahmed Elshahhat, 2022. "Inferences and Engineering Applications of Alpha Power Weibull Distribution Using Progressive Type-II Censoring," Mathematics, MDPI, vol. 10(16), pages 1-21, August.
    10. Muhammet Burak Kılıç & Yusuf Şahin & Melih Burak Koca, 2021. "Genetic algorithm approach with an adaptive search space based on EM algorithm in two-component mixture Weibull parameter estimation," Computational Statistics, Springer, vol. 36(2), pages 1219-1242, June.
    11. Manisera, Marica & Zuccolotto, Paola, 2014. "Modeling rating data with Nonlinear CUB models," Computational Statistics & Data Analysis, Elsevier, vol. 78(C), pages 100-118.
    12. Teresa Backhaus, 2022. "Training in Late Careers - A Structural Approach," CRC TR 224 Discussion Paper Series crctr224_2022_382, University of Bonn and University of Mannheim, Germany.
    13. Hancock, Thomas O. & Broekaert, Jan & Hess, Stephane & Choudhury, Charisma F., 2020. "Quantum choice models: A flexible new approach for understanding moral decision-making," Journal of choice modelling, Elsevier, vol. 37(C).
    14. Granado-Díaz, Rubén & Villanueva, Anastasio J. & Gómez-Limón, José A., 2022. "Willingness to accept for rewilding farmland in environmentally sensitive areas," Land Use Policy, Elsevier, vol. 116(C).
    15. Xu, Meng & Jiang, Mengke & Wang, Hua-Feng, 2021. "Integrating metabolic scaling variation into the maximum entropy theory of ecology explains Taylor's law for individual metabolic rate in tropical forests," Ecological Modelling, Elsevier, vol. 455(C).
    16. Thoralf Meyer & Paul Holloway & Thomas B. Christiansen & Jennifer A. Miller & Paolo D’Odorico & Gregory S. Okin, 2019. "An Assessment of Multiple Drivers Determining Woody Species Composition and Structure: A Case Study from the Kalahari, Botswana," Land, MDPI, vol. 8(8), pages 1-14, August.
    17. K Hervé Dakpo & Laure Latruffe & Yann Desjeux & Philippe Jeanneaux, 2021. "Latent Class Modelling for a Robust Assessment of Productivity: Application to French Grazing Livestock Farms," Journal of Agricultural Economics, Wiley Blackwell, vol. 72(3), pages 760-781, September.
    18. Lee, Kyungsub & Seo, Byoung Ki, 2017. "Modeling microstructure price dynamics with symmetric Hawkes and diffusion model using ultra-high-frequency stock data," Journal of Economic Dynamics and Control, Elsevier, vol. 79(C), pages 154-183.
    19. Ahmed Elshahhat & EL-Sayed A. El-Sherpieny & Amal S. Hassan, 2023. "The Pareto–Poisson Distribution: Characteristics, Estimations and Engineering Applications," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 85(1), pages 1058-1099, February.
    20. Authelet, Manon & Subervie, Julie & Meyfroidt, Patrick & Asquith, Nigel & Ezzine-de-Blas, Driss, 2021. "Economic, pro-social and pro-environmental factors influencing participation in an incentive-based conservation program in Bolivia," World Development, Elsevier, vol. 145(C).

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jstats:v:4:y:2021:i:3:p:38-649:d:612707. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.