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Scale Mixture of Maxwell-Boltzmann Distribution

Author

Listed:
  • Jaime S. Castillo

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

  • Katherine P. Gaete

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

  • Héctor A. Muñoz

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

  • Diego I. Gallardo

    (Departamento de Matemática, Facultad de Ingeniería, Universidad de Atacama, Copiapó 7820436, Chile)

  • Marcelo Bourguignon

    (Departamento de Estatística, Universidade Federal do Rio Grande do Norte, Natal 59078-970, RN, Brazil)

  • 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 paper presents a new distribution, the product of the mixture between Maxwell-Boltzmann and a particular case of the generalized gamma distributions. The resulting distribution, called the Scale Mixture Maxwell-Boltzmann, presents greater kurtosis than the recently introduced slash Maxwell-Boltzmann distribution. We obtained closed-form expressions for its probability density and cumulative distribution functions. We studied some of its properties and moments, as well as its skewness and kurtosis coefficients. Parameters were estimated by the moments and maximum likelihood methods, via the Expectation-Maximization algorithm for the latter case. A simulation study was performed to illustrate the parameter recovery. The results of an application to a real data set indicate that the new model performs very well in the presence of outliers compared with other alternatives in the literature.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:3:p:529-:d:1040383
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    References listed on IDEAS

    as
    1. 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.
    2. M. Shakil & B. Golam Kibria & Kuang-Chao Chang, 2008. "Distributions of the product and ratio of Maxwell and Rayleigh random variables," Statistical Papers, Springer, vol. 49(4), pages 729-747, October.
    3. Jimmy Reyes & Inmaculada Barranco-Chamorro & Héctor W. Gómez, 2020. "Generalized modified slash distribution with applications," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 49(8), pages 2025-2048, April.
    4. Yuri A. Iriarte & Juan M. Astorga & Heleno Bolfarine & Héctor W. Gómez, 2017. "Gamma-Maxwell distribution," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 46(9), pages 4264-4274, May.
    Full references (including those not matched with items on IDEAS)

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