Reparameterized Scale Mixture of Rayleigh Distribution Regression Models with Varying Precision

Rivera, Pilar A.; Gallardo, Diego I.; Venegas, Osvaldo; Gómez-Déniz, Emilio; Gómez, Héctor W.

doi:10.3390/math12131982

Open AccessArticle

Reparameterized Scale Mixture of Rayleigh Distribution Regression Models with Varying Precision

by

Pilar A. Rivera

¹,

Diego I. Gallardo

²

,

Osvaldo Venegas

^3,*

,

Emilio Gómez-Déniz

⁴

and

Héctor W. Gómez

¹

Departamento de Estadística y Ciencias de Datos, Facultad de Ciencias Básicas, Universidad de Antofagasta, Antofagasta 1240000, Chile

²

Departamento de Estadística, Facultad de Ciencias, Universidad del Bío-Bío, Concepción 4081112, Chile

³

Departamento de Ciencias Matemáticas y Físicas, Facultad de Ingeniería, Universidad Católica de Temuco, Temuco 4780000, Chile

⁴

Department of Quantitative Methods in Economics and TIDES Institute, University of Las Palmas de Gran Canaria, 35017 Las Palmas de Gran Canaria, Spain

^*

Author to whom correspondence should be addressed.

Mathematics 2024, 12(13), 1982; https://doi.org/10.3390/math12131982

Submission received: 29 May 2024 / Revised: 19 June 2024 / Accepted: 23 June 2024 / Published: 27 June 2024

(This article belongs to the Section D1: Probability and Statistics)

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Abstract

In this paper, we introduce a new parameterization for the scale mixture of the Rayleigh distribution, which uses a mean linear regression model indexed by mean and precision parameters to model asymmetric positive real data. To test the goodness of fit, we introduce two residuals for the new model. A Monte Carlo simulation study is performed to evaluate the parameter estimation of the proposed model. We compare our proposed model with existing alternatives and illustrate its advantages and usefulness using Gilgais data in R software version 4.2.3 with the gamlss package.

Keywords: scale mixture of Rayleigh distribution; maximum likelihood estimator; regression models; residuals

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MDPI and ACS Style

Rivera, P.A.; Gallardo, D.I.; Venegas, O.; Gómez-Déniz, E.; Gómez, H.W. Reparameterized Scale Mixture of Rayleigh Distribution Regression Models with Varying Precision. Mathematics 2024, 12, 1982. https://doi.org/10.3390/math12131982

AMA Style

Rivera PA, Gallardo DI, Venegas O, Gómez-Déniz E, Gómez HW. Reparameterized Scale Mixture of Rayleigh Distribution Regression Models with Varying Precision. Mathematics. 2024; 12(13):1982. https://doi.org/10.3390/math12131982

Chicago/Turabian Style

Rivera, Pilar A., Diego I. Gallardo, Osvaldo Venegas, Emilio Gómez-Déniz, and Héctor W. Gómez. 2024. "Reparameterized Scale Mixture of Rayleigh Distribution Regression Models with Varying Precision" Mathematics 12, no. 13: 1982. https://doi.org/10.3390/math12131982

APA Style

Rivera, P. A., Gallardo, D. I., Venegas, O., Gómez-Déniz, E., & Gómez, H. W. (2024). Reparameterized Scale Mixture of Rayleigh Distribution Regression Models with Varying Precision. Mathematics, 12(13), 1982. https://doi.org/10.3390/math12131982

Note that from the first issue of 2016, this journal uses article numbers instead of page numbers. See further details here.

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Reparameterized Scale Mixture of Rayleigh Distribution Regression Models with Varying Precision

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