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Scale Mixture of Rayleigh Distribution

Author

Listed:
  • 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)

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.

Suggested Citation

  • Pilar A. Rivera & Inmaculada Barranco-Chamorro & Diego I. Gallardo & Héctor W. Gómez, 2020. "Scale Mixture of Rayleigh Distribution," Mathematics, MDPI, vol. 8(10), pages 1-22, October.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:10:p:1842-:d:431509
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    References listed on IDEAS

    as
    1. Kalaiselvi S. & Loganathan A. & Vijayaraghavan R., 2014. "Bayesian Reliability Sampling Plans under the Conditions of Rayleigh-Inverse-Rayleigh Distribution," Stochastics and Quality Control, De Gruyter, vol. 29(1), pages 29-38, June.
    2. 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.
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