IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v9y2021i16p1894-d611281.html
   My bibliography  Save this article

An Extension of the Truncated-Exponential Skew- Normal Distribution

Author

Listed:
  • Pilar A. Rivera

    (Departamento de Matemáticas, Facultad de Ciencias Básicas, Universidad de Antofagasta, Antofagasta 1240000, Chile)

  • Diego I. Gallardo

    (Departamento de Matemática, Facultad de Ingeniería, Universidad de Atacama, Copiapó 1530000, Chile)

  • Osvaldo Venegas

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

  • Marcelo Bourguignon

    (Departamento de Estatística, Universidade Federal do Rio Grande do Norte, Natal 59078-970, Brazil)

  • Héctor W. Gómez

    (Departamento de Matemáticas, Facultad de Ciencias Básicas, Universidad de Antofagasta, Antofagasta 1240000, Chile)

Abstract

In the paper, we present an extension of the truncated-exponential skew-normal (TESN) distribution. This distribution is defined as the quotient of two independent random variables whose distributions are the TESN distribution and the beta distribution with shape parameters q and 1, respectively. The resulting distribution has a more flexible coefficient of kurtosis. We studied the general probability density function (pdf) of this distribution, its survival and hazard functions, some of its properties, moments and inference by the maximum likelihood method. We carried out a simulation and applied the methodology to a real dataset.

Suggested Citation

  • Pilar A. Rivera & Diego I. Gallardo & Osvaldo Venegas & Marcelo Bourguignon & Héctor W. Gómez, 2021. "An Extension of the Truncated-Exponential Skew- Normal Distribution," Mathematics, MDPI, vol. 9(16), pages 1-11, August.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:16:p:1894-:d:611281
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/9/16/1894/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/9/16/1894/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Diego I. Gallardo & Heleno Bolfarine & Atonio Carlos Pedroso-de-Lima, 2017. "A clustering cure rate model with application to a sealant study," Journal of Applied Statistics, Taylor & Francis Journals, vol. 44(16), pages 2949-2962, December.
    2. William H. Rogers & John W. Tukey, 1972. "Understanding some long‐tailed symmetrical distributions," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 26(3), pages 211-226, September.
    3. Ferreira, Jose T.A.S. & Steel, Mark F.J., 2006. "A Constructive Representation of Univariate Skewed Distributions," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 823-829, June.
    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.
    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. Francisco A. Segovia & Yolanda M. Gómez & Osvaldo Venegas & Héctor W. Gómez, 2020. "A Power Maxwell Distribution with Heavy Tails and Applications," Mathematics, MDPI, vol. 8(7), pages 1-20, July.
    2. Talha Arslan, 2021. "An α -Monotone Generalized Log-Moyal Distribution with Applications to Environmental Data," Mathematics, MDPI, vol. 9(12), pages 1-18, June.
    3. Jimmy Reyes & Yuri A. Iriarte, 2023. "A New Family of Modified Slash Distributions with Applications," Mathematics, MDPI, vol. 11(13), pages 1-15, July.
    4. del Castillo, J.M., 2016. "Slash distributions of the sum of independent logistic random variables," Statistics & Probability Letters, Elsevier, vol. 110(C), pages 111-118.
    5. 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.
    6. Peter Zörnig, 2019. "On Generalized Slash Distributions: Representation by Hypergeometric Functions," Stats, MDPI, vol. 2(3), pages 1-17, July.
    7. 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.
    8. 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.
    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. Rubio, F.J. & Steel, M.F.J., 2011. "Inference for grouped data with a truncated skew-Laplace distribution," Computational Statistics & Data Analysis, Elsevier, vol. 55(12), pages 3218-3231, December.
    11. Guillermo Martínez-Flórez & Artur J. Lemonte & Germán Moreno-Arenas & Roger Tovar-Falón, 2022. "The Bivariate Unit-Sinh-Normal Distribution and Its Related Regression Model," Mathematics, MDPI, vol. 10(17), pages 1-26, August.
    12. Lachos, Victor H. & Prates, Marcos O. & Dey, Dipak K., 2021. "Heckman selection-t model: Parameter estimation via the EM-algorithm," Journal of Multivariate Analysis, Elsevier, vol. 184(C).
    13. Ali Genç, 2013. "A skew extension of the slash distribution via beta-normal distribution," Statistical Papers, Springer, vol. 54(2), pages 427-442, May.
    14. Vijverberg, Wim P. & Hasebe, Takuya, 2015. "GTL Regression: A Linear Model with Skewed and Thick-Tailed Disturbances," IZA Discussion Papers 8898, Institute of Labor Economics (IZA).
    15. Mario A. Rojas & Yuri A. Iriarte, 2022. "A Lindley-Type Distribution for Modeling High-Kurtosis Data," Mathematics, MDPI, vol. 10(13), pages 1-19, June.
    16. Ferreira, Jose T.A.S. & Steel, Mark F.J., 2007. "Model comparison of coordinate-free multivariate skewed distributions with an application to stochastic frontiers," Journal of Econometrics, Elsevier, vol. 137(2), pages 641-673, April.
    17. Klein, Ingo & Fischer, Matthias J., 2003. "Skewness by splitting the scale parameter," Discussion Papers 55/2003, Friedrich-Alexander University Erlangen-Nuremberg, Chair of Statistics and Econometrics.
    18. Francisco J. Rubio & Yili Hong, 2016. "Survival and lifetime data analysis with a flexible class of distributions," Journal of Applied Statistics, Taylor & Francis Journals, vol. 43(10), pages 1794-1813, August.
    19. Nguyen, Hoang & Virbickaitė, Audronė, 2023. "Modeling stock-oil co-dependence with Dynamic Stochastic MIDAS Copula models," Energy Economics, Elsevier, vol. 124(C).
    20. Hasanov, Akram Shavkatovich & Poon, Wai Ching & Al-Freedi, Ajab & Heng, Zin Yau, 2018. "Forecasting volatility in the biofuel feedstock markets in the presence of structural breaks: A comparison of alternative distribution functions," Energy Economics, Elsevier, vol. 70(C), pages 307-333.

    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:9:y:2021:i:16:p:1894-:d:611281. 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.