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Reparameterized Scale Mixture of Rayleigh Distribution Regression Models with Varying Precision

Author

Listed:
  • Pilar A. Rivera

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

  • Diego I. Gallardo

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

  • Osvaldo Venegas

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

  • Emilio Gómez-Déniz

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

  • Héctor W. Gómez

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

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.

Suggested Citation

  • Pilar A. Rivera & Diego I. Gallardo & Osvaldo Venegas & Emilio Gómez-Déniz & Héctor W. Gómez, 2024. "Reparameterized Scale Mixture of Rayleigh Distribution Regression Models with Varying Precision," Mathematics, MDPI, vol. 12(13), pages 1-16, June.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:13:p:1982-:d:1423311
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    References listed on IDEAS

    as
    1. Silvia Ferrari & Francisco Cribari-Neto, 2004. "Beta Regression for Modelling Rates and Proportions," Journal of Applied Statistics, Taylor & Francis Journals, vol. 31(7), pages 799-815.
    2. R. A. Rigby & D. M. Stasinopoulos, 2005. "Generalized additive models for location, scale and shape," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 54(3), pages 507-554, June.
    3. Stasinopoulos, D. Mikis & Rigby, Robert A., 2007. "Generalized Additive Models for Location Scale and Shape (GAMLSS) in R," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 23(i07).
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