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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
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    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.
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