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A New Family of Modified Slash Distributions with Applications

Author

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  • Jimmy Reyes

    (Departamento de Estadística y Ciencia de Datos, Facultad de Ciencias Básicas, Universidad de Antofagasta, Antofagasta 1240000, Chile
    These authors contributed equally to this work.)

  • Yuri A. Iriarte

    (Departamento de Estadística y Ciencia de Datos, Facultad de Ciencias Básicas, Universidad de Antofagasta, Antofagasta 1240000, Chile
    These authors contributed equally to this work.)

Abstract

This article presents a new family of symmetric heavy-tailed distributions. This model is based on the ratio of two independent random variables; one with a normal distribution in the numerator and another with a Birnbaum–Saunders distribution in the denominator. The result is a new slash-like distribution capable of modeling high levels of kurtosis, so it can be considered as a viable alternative to other heavy-tailed distributions in the literature. Fundamental properties such as density and raw moments are derived. Parameter estimation is performed using the moment and maximum likelihood methods. A simulation study to evaluate the behavior of the estimators is carried out. Finally, the utility of the new distribution is illustrated by fitting two real datasets.

Suggested Citation

  • Jimmy Reyes & Yuri A. Iriarte, 2023. "A New Family of Modified Slash Distributions with Applications," Mathematics, MDPI, vol. 11(13), pages 1-15, July.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:13:p:3018-:d:1188764
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    References listed on IDEAS

    as
    1. Jimmy Reyes & Inmaculada Barranco-Chamorro & Héctor W. Gómez, 2020. "Generalized modified slash distribution with applications," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 49(8), pages 2025-2048, April.
    2. Ali Genç, 2013. "A skew extension of the slash distribution via beta-normal distribution," Statistical Papers, Springer, vol. 54(2), pages 427-442, May.
    3. Arslan, Olcay, 2008. "An alternative multivariate skew-slash distribution," Statistics & Probability Letters, Elsevier, vol. 78(16), pages 2756-2761, November.
    4. 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.
    5. Gómez, Héctor W. & Olivares-Pacheco, Juan F. & Bolfarine, Heleno, 2009. "An extension of the generalized Birnbaum-Saunders distribution," Statistics & Probability Letters, Elsevier, vol. 79(3), pages 331-338, February.
    6. Jones, M.C. & Pewsey, Arthur, 2005. "A Family of Symmetric Distributions on the Circle," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 1422-1428, December.
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    Cited by:

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