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The unit-Weibull distribution as an alternative to the Kumaraswamy distribution for the modeling of quantiles conditional on covariates

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  • J. Mazucheli
  • A. F. B. Menezes
  • L. B. Fernandes
  • R. P. de Oliveira
  • M. E. Ghitany

Abstract

The Beta distribution is the standard model for quantifying the influence of covariates on the mean of a response variable on the unit interval. However, this well-known distribution is no longer useful when we are interested in quantifying the influence of such covariates on the quantiles of the response variable. Unlike Beta, the Kumaraswamy distribution has a closed-form expression for its quantile and can be useful for the modeling of quantiles in the absence/presence of covariates. As an alternative to the Kumaraswamy distribution for the modeling of quantiles, in this paper the unit-Weibull distribution was considered. This distribution was obtained by the transformation of a random variable with Weibull distribution. The same transformation applied to a random variable with Exponentiated Exponential distribution generates the Kumaraswamy distribution. The suitability of our proposal was demonstrated to model quantiles, conditional on covariates, with two simulated examples and three real applications with datasets from health, accounting and social science. For such data sets, the obtained fits of the proposed regression model were compared with those provided by the Beta and Kumaraswamy regression models.

Suggested Citation

  • J. Mazucheli & A. F. B. Menezes & L. B. Fernandes & R. P. de Oliveira & M. E. Ghitany, 2020. "The unit-Weibull distribution as an alternative to the Kumaraswamy distribution for the modeling of quantiles conditional on covariates," Journal of Applied Statistics, Taylor & Francis Journals, vol. 47(6), pages 954-974, April.
    • Handle: RePEc:taf:japsta:v:47:y:2020:i:6:p:954-974
    DOI: 10.1080/02664763.2019.1657813
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    Cited by:

    1. Mustafa Ç. Korkmaz & Emrah Altun & Morad Alizadeh & M. El-Morshedy, 2021. "The Log Exponential-Power Distribution: Properties, Estimations and Quantile Regression Model," Mathematics, MDPI, vol. 9(21), pages 1-19, October.
    2. Rashad A. R. Bantan & Christophe Chesneau & Farrukh Jamal & Mohammed Elgarhy & Muhammad H. Tahir & Aqib Ali & Muhammad Zubair & Sania Anam, 2020. "Some New Facts about the Unit-Rayleigh Distribution with Applications," Mathematics, MDPI, vol. 8(11), pages 1-23, November.
    3. Francesca Condino & Filippo Domma, 2023. "Unit Distributions: A General Framework, Some Special Cases, and the Regression Unit-Dagum Models," Mathematics, MDPI, vol. 11(13), pages 1-25, June.
    4. Anum Shafiq & Tabassum Naz Sindhu & Sanku Dey & Showkat Ahmad Lone & Tahani A. Abushal, 2023. "Statistical Features and Estimation Methods for Half-Logistic Unit-Gompertz Type-I Model," Mathematics, MDPI, vol. 11(4), pages 1-24, February.
    5. 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.
    6. Diego I. Gallardo & Marcelo Bourguignon & Yolanda M. Gómez & Christian Caamaño-Carrillo & Osvaldo Venegas, 2022. "Parametric Quantile Regression Models for Fitting Double Bounded Response with Application to COVID-19 Mortality Rate Data," Mathematics, MDPI, vol. 10(13), pages 1-21, June.
    7. Rashad A. R. Bantan & Farrukh Jamal & Christophe Chesneau & Mohammed Elgarhy, 2021. "Theory and Applications of the Unit Gamma/Gompertz Distribution," Mathematics, MDPI, vol. 9(16), pages 1-22, August.
    8. Helton Saulo & Roberto Vila & Giovanna V. Borges & Marcelo Bourguignon & Víctor Leiva & Carolina Marchant, 2023. "Modeling Income Data via New Parametric Quantile Regressions: Formulation, Computational Statistics, and Application," Mathematics, MDPI, vol. 11(2), pages 1-25, January.

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