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A Power Maxwell Distribution with Heavy Tails and Applications

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Departamento de Matemáticas, Facultad de Ingeniería, Universidad de Atacama, Copiapó 1530000, Chile
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Departamento de Ciencias Matemáticas y Físicas, Facultad de Ingeniería, Universidad Católica de Temuco, Temuco 4780000, Chile
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Departamento de Matemática, Facultad de Ciencias Básicas, Universidad de Antofagasta, Antofagasta 1240000, Chile
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Author to whom correspondence should be addressed.
Mathematics 2020, 8(7), 1116; https://doi.org/10.3390/math8071116
Received: 28 May 2020 / Revised: 26 June 2020 / Accepted: 28 June 2020 / Published: 7 July 2020
(This article belongs to the Section Probability and Statistics Theory)
In this paper we introduce a distribution which is an extension of the power Maxwell distribution. This new distribution is constructed based on the quotient of two independent random variables, the distributions of which are the power Maxwell distribution and a function of the uniform distribution (0,1) respectively. Thus the result is a distribution with greater kurtosis than the power Maxwell. We study the general density of this distribution, and some properties, moments, asymmetry and kurtosis coefficients. Maximum likelihood and moments estimators are studied. We also develop the expectation–maximization algorithm to make a simulation study and present two applications to real data. View Full-Text
Keywords: Maxwell distribution; slash distribution; kurtosis; maximum likelihood; EM algorithm Maxwell distribution; slash distribution; kurtosis; maximum likelihood; EM algorithm
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MDPI and ACS Style

Segovia, F.A.; Gómez, Y.M.; Venegas, O.; Gómez, H.W. A Power Maxwell Distribution with Heavy Tails and Applications. Mathematics 2020, 8, 1116. https://doi.org/10.3390/math8071116

AMA Style

Segovia FA, Gómez YM, Venegas O, Gómez HW. A Power Maxwell Distribution with Heavy Tails and Applications. Mathematics. 2020; 8(7):1116. https://doi.org/10.3390/math8071116

Chicago/Turabian Style

Segovia, Francisco A., Yolanda M. Gómez, Osvaldo Venegas, and Héctor W. Gómez 2020. "A Power Maxwell Distribution with Heavy Tails and Applications" Mathematics 8, no. 7: 1116. https://doi.org/10.3390/math8071116

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