The unit ratio-extended Weibull family and the dropout rate in Brazilian undergraduate courses.
We propose a new family of distributions, so-called the unit ratio-extended Weibull family ([Formula: see text]). 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 exponenti...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Public Library of Science (PLoS)
2023-01-01
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| Series: | PLoS ONE |
| Online Access: | https://journals.plos.org/plosone/article/file?id=10.1371/journal.pone.0290885&type=printable |
| _version_ | 1797394541662175232 |
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| author | Fernando A Peña-Ramírez Renata R Guerra Charles Peixoto Mafalda |
| author_facet | Fernando A Peña-Ramírez Renata R Guerra Charles Peixoto Mafalda |
| author_sort | Fernando A Peña-Ramírez |
| collection | DOAJ |
| description | We propose a new family of distributions, so-called the unit ratio-extended Weibull family ([Formula: see text]). 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 [Formula: see text] 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 [Formula: see text] 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 [Formula: see text] family can provide competitive alternatives when those models are unsuitable. |
| first_indexed | 2024-03-09T00:21:16Z |
| format | Article |
| id | doaj.art-62f4620c5a494b09b4f15130a4c9ba1c |
| institution | Directory Open Access Journal |
| issn | 1932-6203 |
| language | English |
| last_indexed | 2024-03-09T00:21:16Z |
| publishDate | 2023-01-01 |
| publisher | Public Library of Science (PLoS) |
| record_format | Article |
| series | PLoS ONE |
| spelling | doaj.art-62f4620c5a494b09b4f15130a4c9ba1c2023-12-12T05:34:05ZengPublic Library of Science (PLoS)PLoS ONE1932-62032023-01-011811e029088510.1371/journal.pone.0290885The unit ratio-extended Weibull family and the dropout rate in Brazilian undergraduate courses.Fernando A Peña-RamírezRenata R GuerraCharles Peixoto MafaldaWe propose a new family of distributions, so-called the unit ratio-extended Weibull family ([Formula: see text]). 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 [Formula: see text] 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 [Formula: see text] 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 [Formula: see text] family can provide competitive alternatives when those models are unsuitable.https://journals.plos.org/plosone/article/file?id=10.1371/journal.pone.0290885&type=printable |
| spellingShingle | Fernando A Peña-Ramírez Renata R Guerra Charles Peixoto Mafalda The unit ratio-extended Weibull family and the dropout rate in Brazilian undergraduate courses. PLoS ONE |
| title | The unit ratio-extended Weibull family and the dropout rate in Brazilian undergraduate courses. |
| title_full | The unit ratio-extended Weibull family and the dropout rate in Brazilian undergraduate courses. |
| title_fullStr | The unit ratio-extended Weibull family and the dropout rate in Brazilian undergraduate courses. |
| title_full_unstemmed | The unit ratio-extended Weibull family and the dropout rate in Brazilian undergraduate courses. |
| title_short | The unit ratio-extended Weibull family and the dropout rate in Brazilian undergraduate courses. |
| title_sort | unit ratio extended weibull family and the dropout rate in brazilian undergraduate courses |
| url | https://journals.plos.org/plosone/article/file?id=10.1371/journal.pone.0290885&type=printable |
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