IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v11y2023i22p4626-d1278869.html
   My bibliography  Save this article

A Heavy-Tailed Distribution Based on the Lomax–Rayleigh Distribution with Applications to Medical Data

Author

Listed:
  • Karol I. Santoro

    (Departamento de Estadística y Ciencias de Datos, Facultad de Ciencias Básicas, Universidad de Antofagasta, Antofagasta 1240000, Chile)

  • Diego I. Gallardo

    (Departamento de Estadística, Facultad de Ciencias, Universidad del Bío-Bío, Concepción 4081112, Chile)

  • Osvaldo Venegas

    (Departamento de Ciencias Matemáticas y Físicas, Facultad de Ingeniería, Universidad Católica de Temuco, Temuco 4780000, Chile)

  • Isaac E. Cortés

    (Instituto de Ciências Matemáticas e de Computação, Universidade de São Paulo, São Carlos 13560-095, Brazil)

  • Héctor W. Gómez

    (Departamento de Estadística y Ciencias de Datos, Facultad de Ciencias Básicas, Universidad de Antofagasta, Antofagasta 1240000, Chile)

Abstract

In this paper, we extend the Lomax–Rayleigh distribution to increase its kurtosis. The construction of this distribution is based on the idea of the Slash distribution, that is, its representation is based on the quotient of two independent random variables, one being a random variable with a Lomax–Rayleigh distribution and the other a beta ( q , 1 ) . Based on the representation of this family, we study its basic properties, such as moments, coefficients of skewness, and kurtosis. We perform statistical inference using the methods of moments and maximum likelihood. To illustrate this methodology, we apply it to two real data sets.

Suggested Citation

  • Karol I. Santoro & Diego I. Gallardo & Osvaldo Venegas & Isaac E. Cortés & Héctor W. Gómez, 2023. "A Heavy-Tailed Distribution Based on the Lomax–Rayleigh Distribution with Applications to Medical Data," Mathematics, MDPI, vol. 11(22), pages 1-15, November.
  • Handle: RePEc:gam:jmathe:v:11:y:2023:i:22:p:4626-:d:1278869
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/11/22/4626/pdf
    Download Restriction: no

    File URL: https://www.mdpi.com/2227-7390/11/22/4626/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Neveka Olmos & Héctor Varela & Heleno Bolfarine & Héctor Gómez, 2014. "An extension of the generalized half-normal distribution," Statistical Papers, Springer, vol. 55(4), pages 967-981, November.
    2. Marco Cococcioni & Francesco Fiorini & Michele Pagano, 2023. "Modelling Heavy Tailed Phenomena Using a LogNormal Distribution Having a Numerically Verifiable Infinite Variance," Mathematics, MDPI, vol. 11(7), pages 1-16, April.
    3. Alexander Shapiro & Jos Berge, 2002. "Statistical inference of minimum rank factor analysis," Psychometrika, Springer;The Psychometric Society, vol. 67(1), pages 79-94, March.
    4. Neveka Olmos & Héctor Varela & Héctor Gómez & Heleno Bolfarine, 2012. "An extension of the half-normal distribution," Statistical Papers, Springer, vol. 53(4), pages 875-886, November.
    5. Corrado Gini, 2005. "On the measurement of concentration and variability of characters," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(1), pages 1-38.
    6. Gómez, Héctor W. & Quintana, Fernando A. & Torres, Francisco J., 2007. "A new family of slash-distributions with elliptical contours," Statistics & Probability Letters, Elsevier, vol. 77(7), pages 717-725, April.
    7. Gauss Cordeiro & Cláudio Cristino & Elizabeth Hashimoto & Edwin Ortega, 2013. "The beta generalized Rayleigh distribution with applications to lifetime data," Statistical Papers, Springer, vol. 54(1), pages 133-161, February.
    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. Talha Arslan, 2021. "An α -Monotone Generalized Log-Moyal Distribution with Applications to Environmental Data," Mathematics, MDPI, vol. 9(12), pages 1-18, June.
    2. Jimmy Reyes & Yuri A. Iriarte & Pedro Jodrá & Héctor W. Gómez, 2019. "The Slash Lindley-Weibull Distribution," Methodology and Computing in Applied Probability, Springer, vol. 21(1), pages 235-251, March.
    3. Neveka M. Olmos & Emilio Gómez-Déniz & Osvaldo Venegas, 2022. "The Heavy-Tailed Gleser Model: Properties, Estimation, and Applications," Mathematics, MDPI, vol. 10(23), pages 1-16, December.
    4. Neveka Olmos & Héctor Varela & Heleno Bolfarine & Héctor Gómez, 2014. "An extension of the generalized half-normal distribution," Statistical Papers, Springer, vol. 55(4), pages 967-981, November.
    5. Juan M. Astorga & Jimmy Reyes & Karol I. Santoro & Osvaldo Venegas & Héctor W. Gómez, 2020. "A Reliability Model Based on the Incomplete Generalized Integro-Exponential Function," Mathematics, MDPI, vol. 8(9), pages 1-12, September.
    6. Gómez, Yolanda M. & Bolfarine, Heleno & Gómez, Héctor W., 2019. "Gumbel distribution with heavy tails and applications to environmental data," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 157(C), pages 115-129.
    7. Leonardo Barrios & Yolanda M. Gómez & Osvaldo Venegas & Inmaculada Barranco-Chamorro & Héctor W. Gómez, 2022. "The Slashed Power Half-Normal Distribution with Applications," Mathematics, MDPI, vol. 10(9), pages 1-21, May.
    8. Neveka M. Olmos & Emilio Gómez-Déniz & Osvaldo Venegas & Héctor W. Gómez, 2024. "A Composite Half-Normal-Pareto Distribution with Applications to Income and Expenditure Data," Mathematics, MDPI, vol. 12(11), pages 1-17, May.
    9. Jaime S. Castillo & Inmaculada Barranco-Chamorro & Osvaldo Venegas & Héctor W. Gómez, 2023. "Slash-Weighted Lindley Distribution: Properties, Inference, and Applications," Mathematics, MDPI, vol. 11(18), pages 1-14, September.
    10. Nowak, Piotr Bolesław, 2016. "The MLE of the mean of the exponential distribution based on grouped data is stochastically increasing," Statistics & Probability Letters, Elsevier, vol. 111(C), pages 49-54.
    11. Jianu, Ionuț & Tudorache, Maria-Daniela & Nicolescu, Andreea Florentina, 2024. "Investigating the effects of education and labour market challenges on income inequality," EconStor Conference Papers 289591, ZBW - Leibniz Information Centre for Economics.
    12. Koen Decancq, 2020. "Measuring cumulative deprivation and affluence based on the diagonal dependence diagram," METRON, Springer;Sapienza Università di Roma, vol. 78(2), pages 103-117, August.
    13. Camilo Alberto Cárdenas-Hurtado & Aaron Levi Garavito-Acosta & Jorge Hernán Toro-Córdoba, 2018. "Asymmetric Effects of Terms of Trade Shocks on Tradable and Non-tradable Investment Rates: The Colombian Case," Borradores de Economia 1043, Banco de la Republica de Colombia.
    14. Anastasiou, Andreas, 2017. "Bounds for the normal approximation of the maximum likelihood estimator from m-dependent random variables," Statistics & Probability Letters, Elsevier, vol. 129(C), pages 171-181.
    15. Evelina Di Corso & Tania Cerquitelli & Daniele Apiletti, 2018. "METATECH: METeorological Data Analysis for Thermal Energy CHaracterization by Means of Self-Learning Transparent Models," Energies, MDPI, vol. 11(6), pages 1-24, May.
    16. Silva, Ivair R., 2017. "Confidence intervals through sequential Monte Carlo," Computational Statistics & Data Analysis, Elsevier, vol. 105(C), pages 112-124.
    17. Denter, Philipp & Sisak, Dana, 2015. "Do polls create momentum in political competition?," Journal of Public Economics, Elsevier, vol. 130(C), pages 1-14.
    18. Salgado Alfredo, 2018. "Incomplete Information and Costly Signaling in College Admissions," Working Papers 2018-23, Banco de México.
    19. Albrecht, James & Anderson, Axel & Vroman, Susan, 2010. "Search by committee," Journal of Economic Theory, Elsevier, vol. 145(4), pages 1386-1407, July.
    20. Stegeman, Alwin, 2016. "A new method for simultaneous estimation of the factor model parameters, factor scores, and unique parts," Computational Statistics & Data Analysis, Elsevier, vol. 99(C), pages 189-203.

    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:jmathe:v:11:y:2023:i:22:p:4626-:d:1278869. 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.