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Article

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

1
Departamento de Tecnologías de la Energía, Facultad Tecnológica, Universidad de Atacama, Copiapó 1530000, Chile
2
Departamento de Matemáticas, Facultad de Ciencias Básicas, Universidad de Antofagasta, Antofagasta 1240000, Chile
3
Departamento de Matemáticas, Facultad de Ciencias, Universidad Católica del Norte, Antofagasta 1240000, Chile
4
Departamento de Ciencias Matemáticas y Físicas, Facultad de Ingeniería, Universidad Católica de Temuco, Temuco 4780000, Chile
*
Author to whom correspondence should be addressed.
Mathematics 2020, 8(9), 1537; https://doi.org/10.3390/math8091537
Received: 15 August 2020 / Revised: 2 September 2020 / Accepted: 2 September 2020 / Published: 8 September 2020
(This article belongs to the Section Probability and Statistics Theory)
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. View Full-Text
Keywords: generalized integro-exponential function; kurtosis; maximum likelihood; power muth distribution; slash distribution generalized integro-exponential function; kurtosis; maximum likelihood; power muth distribution; slash distribution
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MDPI and ACS Style

Astorga, J.M.; Reyes, J.; Santoro, K.I.; Venegas, O.; Gómez, H.W. A Reliability Model Based on the Incomplete Generalized Integro-Exponential Function. Mathematics 2020, 8, 1537. https://doi.org/10.3390/math8091537

AMA Style

Astorga JM, Reyes J, Santoro KI, Venegas O, Gómez HW. A Reliability Model Based on the Incomplete Generalized Integro-Exponential Function. Mathematics. 2020; 8(9):1537. https://doi.org/10.3390/math8091537

Chicago/Turabian Style

Astorga, Juan M., Jimmy Reyes, Karol I. Santoro, Osvaldo Venegas, and Héctor W. Gómez 2020. "A Reliability Model Based on the Incomplete Generalized Integro-Exponential Function" Mathematics 8, no. 9: 1537. https://doi.org/10.3390/math8091537

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