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A New Regression Model on the Unit Interval: Properties, Estimation, and Application

Author

Listed:
  • Yury R. Benites

    (Department of Applied Mathematics and Statistics, University of São Paulo, São Carlos 13566-590, Brazil
    These authors contributed equally to this work.)

  • Vicente G. Cancho

    (Department of Applied Mathematics and Statistics, University of São Paulo, São Carlos 13566-590, Brazil
    These authors contributed equally to this work.)

  • Edwin M. M. Ortega

    (Department of Exact Sciences, University of São Paulo, Piracicaba 13418-900, Brazil
    These authors contributed equally to this work.)

  • Roberto Vila

    (Department of Statistics, University of Brasilia, Brasilia 70910-900, Brazil
    These authors contributed equally to this work.)

  • Gauss M. Cordeiro

    (Department of Statistics, Federal University of Pernambuco, Recife 50670-901, Brazil
    These authors contributed equally to this work.)

Abstract

A new and flexible distribution is introduced for modeling proportional data based on the quantile of the generalized extreme value distribution. We obtain explicit expressions for the moments, quantiles, and other structural properties. An extended regression model is constructed as an alternative to compete with the beta regression. Some simulations from the Bayesian perspectives are developed, and an illustrative application to real data involving the comparison of models and influence diagnostics is also addressed.

Suggested Citation

  • Yury R. Benites & Vicente G. Cancho & Edwin M. M. Ortega & Roberto Vila & Gauss M. Cordeiro, 2022. "A New Regression Model on the Unit Interval: Properties, Estimation, and Application," Mathematics, MDPI, vol. 10(17), pages 1-17, September.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:17:p:3198-:d:906462
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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.
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    3. 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.
    4. Krysicki, Wlodzimierz, 1999. "On some new properties of the beta distribution," Statistics & Probability Letters, Elsevier, vol. 42(2), pages 131-137, April.
    5. Jalmar M.F. Carrasco & Silvia L.P. Ferrari & Reinaldo B. Arellano-Valle, 2014. "Errors-in-variables beta regression models," Journal of Applied Statistics, Taylor & Francis Journals, vol. 41(7), pages 1530-1547, July.
    6. Simas, Alexandre B. & Barreto-Souza, Wagner & Rocha, Andréa V., 2010. "Improved estimators for a general class of beta regression models," Computational Statistics & Data Analysis, Elsevier, vol. 54(2), pages 348-366, February.
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