Scale Mixture of Rayleigh Distribution

Pilar A. Rivera, Inmaculada Barranco-Chamorro, Diego I. Gallardo and Héctor W. Gómez
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Pilar A. Rivera: Departamento de Matemáticas, Facultad de Ciencias Básicas, Universidad de Antofagasta, Antofagasta 1240000, Chile
Inmaculada Barranco-Chamorro: Departamento de Estadística e I.O., Facultad de Matemáticas, Universidad de Sevilla, 41000 Sevilla, Spain
Diego I. Gallardo: Departamento de Matemática, Facultad de Ingeniería, Universidad de Atacama, Copiapó 1530000, Chile
Héctor W. Gómez: Departamento de Matemáticas, Facultad de Ciencias Básicas, Universidad de Antofagasta, Antofagasta 1240000, Chile

Mathematics, 2020, vol. 8, issue 10, 1-22

Abstract: 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.

Keywords: Rayleigh distribution; slashed Rayleigh distribution; kurtosis; Rényi entropy; EM algorithm; maximum likelihood (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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