IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v12y2024i1p156-d1312551.html
   My bibliography  Save this article

Scale Mixture of Exponential Distribution with an Application

Author

Listed:
  • Jorge A. Barahona

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

  • Yolanda M. Gómez

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

  • Emilio Gómez-Déniz

    (Department of Quantitative Methods in Economics and TIDES Institute, University of Las Palmas de Gran Canaria, 35017 Las Palmas de Gran Canaria, Spain)

  • Osvaldo Venegas

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

  • Héctor W. Gómez

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

Abstract

This article presents an extended distribution that builds upon the exponential distribution. This extension is based on a scale mixture between the exponential and beta distributions. By utilizing this approach, we obtain a distribution that offers increased flexibility in terms of the kurtosis coefficient. We explore the general density, properties, moments, asymmetry, and kurtosis coefficients of this distribution. Statistical inference is performed using both the moments and maximum likelihood methods. To show the performance of this new model, it is applied to a real dataset with atypical observations. The results indicate that the new model outperforms two other extensions of the exponential distribution.

Suggested Citation

  • Jorge A. Barahona & Yolanda M. Gómez & Emilio Gómez-Déniz & Osvaldo Venegas & Héctor W. Gómez, 2024. "Scale Mixture of Exponential Distribution with an Application," Mathematics, MDPI, vol. 12(1), pages 1-17, January.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:1:p:156-:d:1312551
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/12/1/156/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/12/1/156/
    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. Fernández, Carmen & Steel, Mark F.J., 2000. "Bayesian Regression Analysis With Scale Mixtures Of Normals," Econometric Theory, Cambridge University Press, vol. 16(1), pages 80-101, February.
    3. 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.
    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. 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.
    3. 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.
    4. 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.
    5. 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.
    6. Ley, Eduardo & Steel, Mark F.J., 2012. "Mixtures of g-priors for Bayesian model averaging with economic applications," Journal of Econometrics, Elsevier, vol. 171(2), pages 251-266.
    7. 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).
    8. Laura Liu, 2017. "Density Forecasts in Panel Models: A semiparametric Bayesian Perspective," PIER Working Paper Archive 17-006, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania, revised 28 Apr 2017.
    9. Gernot Doppelhofer & Melvyn Weeks, 2011. "Robust Growth Determinants," CESifo Working Paper Series 3354, CESifo.
    10. Hazan, Alon & Landsman, Zinoviy & E Makov, Udi, 2003. "Robustness via a mixture of exponential power distributions," Computational Statistics & Data Analysis, Elsevier, vol. 42(1-2), pages 111-121, February.
    11. Bickel, David R., 2002. "Robust estimators of the mode and skewness of continuous data," Computational Statistics & Data Analysis, Elsevier, vol. 39(2), pages 153-163, April.
    12. Rubio, Francisco Javier & Liseo, Brunero, 2014. "On the independence Jeffreys prior for skew-symmetric models," Statistics & Probability Letters, Elsevier, vol. 85(C), pages 91-97.
    13. 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.
    14. Salas-Gonzalez, Diego & Kuruoglu, Ercan E. & Ruiz, Diego P., 2009. "A heavy-tailed empirical Bayes method for replicated microarray data," Computational Statistics & Data Analysis, Elsevier, vol. 53(5), pages 1535-1546, March.
    15. Wilcox, Rand R., 2003. "Inferences based on multiple skipped correlations," Computational Statistics & Data Analysis, Elsevier, vol. 44(1-2), pages 223-236, October.
    16. Yongho Ko & Seungwoo Han, 2017. "A Duration Prediction Using a Material-Based Progress Management Methodology for Construction Operation Plans," Sustainability, MDPI, vol. 9(4), pages 1-12, April.
    17. 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.
    18. Luz Marina Rondon & Heleno Bolfarine, 2016. "Bayesian analysis of generalized elliptical semi-parametric models," Journal of Applied Statistics, Taylor & Francis Journals, vol. 43(8), pages 1508-1524, June.
    19. Jung, Yeun Ji & Hobert, James P., 2014. "Spectral properties of MCMC algorithms for Bayesian linear regression with generalized hyperbolic errors," Statistics & Probability Letters, Elsevier, vol. 95(C), pages 92-100.
    20. Peter Zörnig, 2019. "On Generalized Slash Distributions: Representation by Hypergeometric Functions," Stats, MDPI, vol. 2(3), pages 1-17, July.

    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:12:y:2024:i:1:p:156-:d:1312551. 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.