Scale Mixture of Maxwell-Boltzmann Distribution

Jaime S. Castillo, Katherine P. Gaete, Héctor A. Muñoz, Diego I. Gallardo (), Marcelo Bourguignon, Osvaldo Venegas and Héctor W. Gómez
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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

Mathematics, 2023, vol. 11, issue 3, 1-16

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.

Keywords: Maxwell-Boltzmann distribution; generalized gamma distribution; kurtosis; maximum likelihood; EM algorithm (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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