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A Power Maxwell Distribution with Heavy Tails and Applications

Author

Listed:
  • Francisco A. Segovia

    (Departamento de Matemáticas, Facultad de Ingeniería, Universidad de Atacama, Copiapó 1530000, Chile)

  • Yolanda M. Gómez

    (Departamento de Matemáticas, Facultad de Ingeniería, Universidad de Atacama, Copiapó 1530000, Chile)

  • Osvaldo Venegas

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

  • Héctor W. Gómez

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

Abstract

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.

Suggested Citation

  • Francisco A. Segovia & Yolanda M. Gómez & Osvaldo Venegas & Héctor W. Gómez, 2020. "A Power Maxwell Distribution with Heavy Tails and Applications," Mathematics, MDPI, vol. 8(7), pages 1-20, July.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:7:p:1116-:d:381375
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    References listed on IDEAS

    as
    1. Yuri A. Iriarte & F. Vilca & Héctor Varela & Héctor W. Gómez, 2017. "Slashed generalized Rayleigh distribution," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 46(10), pages 4686-4699, May.
    2. Gómez, Héctor W. & Quintana, Fernando A. & Torres, Francisco J., 2007. "A new family of slash-distributions with elliptical contours," Statistics & Probability Letters, Elsevier, vol. 77(7), pages 717-725, April.
    3. 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.
    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.
    5. Gómez, Héctor W. & Olivares-Pacheco, Juan F. & Bolfarine, Heleno, 2009. "An extension of the generalized Birnbaum-Saunders distribution," Statistics & Probability Letters, Elsevier, vol. 79(3), pages 331-338, February.
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    Cited by:

    1. 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.

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