Next Article in Journal
Modeling of Strength Characteristics of Polymer Concrete Via the Wave Equation with a Fractional Derivative
Next Article in Special Issue
Expanded Fréchet Model: Mathematical Properties, Copula, Different Estimation Methods, Applications and Validation Testing
Previous Article in Journal
Understanding Factors Affecting Innovation Resistance of Mobile Payments in Taiwan: An Integrative Perspective
Previous Article in Special Issue
Mutually Complementary Measure-Correlate-Predict Method for Enhanced Long-Term Wind-Resource Assessment
Article

Scale Mixture of Rayleigh Distribution

1
Departamento de Matemáticas, Facultad de Ciencias Básicas, Universidad de Antofagasta, Antofagasta 1240000, Chile
2
Departamento de Estadística e I.O., Facultad de Matemáticas, Universidad de Sevilla, 41000 Sevilla, Spain
3
Departamento de Matemática, Facultad de Ingeniería, Universidad de Atacama, Copiapó 1530000, Chile
*
Author to whom correspondence should be addressed.
Mathematics 2020, 8(10), 1842; https://doi.org/10.3390/math8101842
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
Show Figures

Figure 1

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. https://doi.org/10.3390/math8101842

AMA Style

Rivera PA, Barranco-Chamorro I, Gallardo DI, Gómez HW. Scale Mixture of Rayleigh Distribution. Mathematics. 2020; 8(10):1842. https://doi.org/10.3390/math8101842

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. https://doi.org/10.3390/math8101842

Find Other Styles
Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Article Access Map by Country/Region

1
Back to TopTop