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The unit ratio-extended Weibull family and the dropout rate in Brazilian undergraduate courses

Author

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  • Fernando A Peña-Ramírez
  • Renata R Guerra
  • Charles Peixoto Mafalda

Abstract

We propose a new family of distributions, so-called the unit ratio-extended Weibull family (U R E W). It is derived from ratio transformation in an extended Weibull random variable. The use of this transformation is a novelty of the work since it has been less explored than the exponential and has not yet been studied within the extended Weibull class. Moreover, we offer a valuable alternative to model double-bounded variables on the unit interval. Five U R E W special models are studied in detail, namely the: i) unit ratio-Gompertz; ii) unit ratio-Burr XII; iii) unit ratio-Lomax; v) unit ratio-Rayleigh, and vi) unit ratio-Weibull distributions. We propose a quantile-parameterization for the new family. The maximum likelihood estimators (MLEs) are presented. A Monte Carlo study is performed to evaluate the behavior of the MLEs of unit ratio-Gompertz and unit ratio-Rayleigh distributions. This last model has closed-form and approximately unbiased MLE for small sample sizes. Further, the U R E W submodels are adjusted to the dropout rate in Brazilian undergraduate courses. We focus on the areas of civil engineering, economics, computer sciences, and control engineering. The applications show that the new family is suitable for modeling educational data and may provide effective alternatives compared to other usual unit models, such as the Beta, Kumaraswamy, and unit gamma distributions. They can also outperform some recent contributions in the unit distribution literature. Thus, the U R E W family can provide competitive alternatives when those models are unsuitable.

Suggested Citation

  • Fernando A Peña-Ramírez & Renata R Guerra & Charles Peixoto Mafalda, 2023. "The unit ratio-extended Weibull family and the dropout rate in Brazilian undergraduate courses," PLOS ONE, Public Library of Science, vol. 18(11), pages 1-22, November.
    • Handle: RePEc:plo:pone00:0290885
    DOI: 10.1371/journal.pone.0290885
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    References listed on IDEAS

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    1. Tatiane Fontana Ribeiro & Fernando A Peña-Ramírez & Renata Rojas Guerra & Gauss M Cordeiro, 2022. "Another unit Burr XII quantile regression model based on the different reparameterization applied to dropout in Brazilian undergraduate courses," PLOS ONE, Public Library of Science, vol. 17(11), pages 1-25, November.
    2. Barndorff-Nielsen, O. E. & Jørgensen, B., 1991. "Some parametric models on the simplex," Journal of Multivariate Analysis, Elsevier, vol. 39(1), pages 106-116, October.
    3. 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.
    4. Pablo Mitnik & Sunyoung Baek, 2013. "The Kumaraswamy distribution: median-dispersion re-parameterizations for regression modeling and simulation-based estimation," Statistical Papers, Springer, vol. 54(1), pages 177-192, February.
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