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New Class of Unit-Power-Skew-Normal Distribution and Its Associated Regression Model for Bounded Responses

Author

Listed:
  • Guillermo Martínez-Flórez

    (Departamento de Matemáticas y Estadística, Facultad de Ciencias Básicas, Universidad de Córdoba, Montería 230002, Colombia
    These authors contributed equally to this work.)

  • Rafael B. Azevedo-Farias

    (Department of Statistics and Applied Mathematics, Federal University of Ceara, Fortaleza 60455-670, Brazil
    These authors contributed equally to this work.)

  • Roger Tovar-Falón

    (Departamento de Matemáticas y Estadística, Facultad de Ciencias Básicas, Universidad de Córdoba, Montería 230002, Colombia
    These authors contributed equally to this work.)

Abstract

Several papers on distributions to model rates and proportions have been recently published; their fitting in numerous instances is better than the alternative beta distribution, which has been the distribution to follow when it is necessary to quantify the average of a response variable based on a set of covariates. Despite the great usefulness of this distribution to fit the responses on the ( 0 , 1 ) unit interval, its relevance loses objectivity when the interest is quantifying the influence of these covariates on the quantiles of the variable response in ( 0 , 1 ) ; being the most critical situation when the distribution presents high asymmetry and/or kurtosis. The main objective of this work is to introduce a distribution for modeling rates and proportions. The introduced distribution is obtained from the alpha-power extension of the skew–normal distribution, which is known in the literature as the power–skew–normal distribution.

Suggested Citation

  • Guillermo Martínez-Flórez & Rafael B. Azevedo-Farias & Roger Tovar-Falón, 2022. "New Class of Unit-Power-Skew-Normal Distribution and Its Associated Regression Model for Bounded Responses," Mathematics, MDPI, vol. 10(17), pages 1-24, August.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:17:p:3035-:d:895309
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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. Josmar Mazucheli & Bruna Alves & Mustafa Ç. Korkmaz & Víctor Leiva, 2022. "Vasicek Quantile and Mean Regression Models for Bounded Data: New Formulation, Mathematical Derivations, and Numerical Applications," Mathematics, MDPI, vol. 10(9), pages 1-23, April.
    3. Cribari-Neto, Francisco & Zeileis, Achim, 2010. "Beta Regression in R," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 34(i02).
    4. Ortega, Edwin M. M. & Bolfarine, Heleno & Paula, Gilberto A., 2003. "Influence diagnostics in generalized log-gamma regression models," Computational Statistics & Data Analysis, Elsevier, vol. 42(1-2), pages 165-186, February.
    5. Ospina, Raydonal & Ferrari, Silvia L.P., 2012. "A general class of zero-or-one inflated beta regression models," Computational Statistics & Data Analysis, Elsevier, vol. 56(6), pages 1609-1623.
    6. Arne Henningsen & Ott Toomet, 2011. "maxLik: A package for maximum likelihood estimation in R," Computational Statistics, Springer, vol. 26(3), pages 443-458, September.
    7. Arthur Pewsey & Héctor Gómez & Heleno Bolfarine, 2012. "Likelihood-based inference for power distributions," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 21(4), pages 775-789, December.
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    Cited by:

    1. Guillermo Martínez-Flórez & Sandra Vergara-Cardozo & Roger Tovar-Falón & Luisa Rodriguez-Quevedo, 2023. "The Multivariate Skewed Log-Birnbaum–Saunders Distribution and Its Associated Regression Model," Mathematics, MDPI, vol. 11(5), pages 1-21, February.

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