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A Reliability Model Based on the Incomplete Generalized Integro-Exponential Function

Author

Listed:
  • Juan M. Astorga

    (Departamento de Tecnologías de la Energía, Facultad Tecnológica, Universidad de Atacama, Copiapó 1530000, Chile)

  • Jimmy Reyes

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

  • Karol I. Santoro

    (Departamento de Matemáticas, Facultad de Ciencias, Universidad Católica del Norte, Antofagasta 1240000, Chile)

  • Osvaldo Venegas

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

  • Héctor W. Gómez

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

Abstract

This article introduces an extension of the Power Muth (PM) distribution for modeling positive data sets with a high coefficient of kurtosis. The resulting distribution has greater kurtosis than the PM distribution. We show that the density can be represented based on the incomplete generalized integro-exponential function. We study some of its properties and moments, and its coefficients of asymmetry and kurtosis. We apply estimations using the moments and maximum likelihood methods and present a simulation study to illustrate parameter recovery. The results of application to two real data sets indicate that the new model performs very well in the presence of outliers.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:9:p:1537-:d:410689
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    References listed on IDEAS

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    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. 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.
    3. 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.
    4. 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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    Cited by:

    1. Jaime S. Castillo & Katherine P. Gaete & Héctor A. Muñoz & Diego I. Gallardo & Marcelo Bourguignon & Osvaldo Venegas & Héctor W. Gómez, 2023. "Scale Mixture of Maxwell-Boltzmann Distribution," Mathematics, MDPI, vol. 11(3), pages 1-16, January.

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