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Scale Mixture of Rayleigh Distribution

Departamento de Matemáticas, Facultad de Ciencias Básicas, Universidad de Antofagasta, Antofagasta 1240000, Chile
Departamento de Estadística e I.O., Facultad de Matemáticas, Universidad de Sevilla, 41000 Sevilla, Spain
Departamento de Matemática, Facultad de Ingeniería, Universidad de Atacama, Copiapó 1530000, Chile
Author to whom correspondence should be addressed.
Mathematics 2020, 8(10), 1842;
Received: 22 September 2020 / Revised: 14 October 2020 / Accepted: 14 October 2020 / Published: 20 October 2020
(This article belongs to the Special Issue Probability, Statistics and Their Applications)
In this paper, the scale mixture of Rayleigh (SMR) distribution is introduced. It is proven that this new model, initially defined as the quotient of two independent random variables, can be expressed as a scale mixture of a Rayleigh and a particular Generalized Gamma distribution. Closed expressions are obtained for its pdf, cdf, moments, asymmetry and kurtosis coefficients. Its lifetime analysis, properties and Rényi entropy are studied. Inference based on moments and maximum likelihood (ML) is proposed. An Expectation-Maximization (EM) algorithm is implemented to estimate the parameters via ML. This algorithm is also used in a simulation study, which illustrates the good performance of our proposal. Two real datasets are considered in which it is shown that the SMR model provides a good fit and it is more flexible, especially as for kurtosis, than other competitor models, such as the slashed Rayleigh distribution. View Full-Text
Keywords: Rayleigh distribution; slashed Rayleigh distribution; kurtosis; Rényi entropy; EM algorithm; maximum likelihood Rayleigh distribution; slashed Rayleigh distribution; kurtosis; Rényi entropy; EM algorithm; maximum likelihood
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MDPI and ACS Style

Rivera, P.A.; Barranco-Chamorro, I.; Gallardo, D.I.; Gómez, H.W. Scale Mixture of Rayleigh Distribution. Mathematics 2020, 8, 1842.

AMA Style

Rivera PA, Barranco-Chamorro I, Gallardo DI, Gómez HW. Scale Mixture of Rayleigh Distribution. Mathematics. 2020; 8(10):1842.

Chicago/Turabian Style

Rivera, Pilar A., Inmaculada Barranco-Chamorro, Diego I. Gallardo, and Héctor W. Gómez 2020. "Scale Mixture of Rayleigh Distribution" Mathematics 8, no. 10: 1842.

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