A New Extended Weibull Distribution with Application to Influenza and Hepatitis Data
The Weibull is a popular distribution that models monotonous failure rate data. In this work, we introduce the four-parameter Weibull extended Weibull distribution that presents greater flexibility, thus modeling data with bathtub-shaped and unimodal failure rate. Some of its mathematical properties...
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| Format: | Article |
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MDPI AG
2023-05-01
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| Series: | Stats |
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| Online Access: | https://www.mdpi.com/2571-905X/6/2/42 |
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| author | Gauss M. Cordeiro Elisângela C. Biazatti Luís H. de Santana |
| author_facet | Gauss M. Cordeiro Elisângela C. Biazatti Luís H. de Santana |
| author_sort | Gauss M. Cordeiro |
| collection | DOAJ |
| description | The Weibull is a popular distribution that models monotonous failure rate data. In this work, we introduce the four-parameter Weibull extended Weibull distribution that presents greater flexibility, thus modeling data with bathtub-shaped and unimodal failure rate. Some of its mathematical properties such as quantile function, linear representation and moments are provided. The maximum likelihood estimation is adopted to estimate its parameters, and the log-Weibull extended Weibull regression model is presented. In addition, some simulations are carried out to show the consistency of the estimators. We prove the greater flexibility and performance of this distribution and the regression model through applications to influenza and hepatitis data. The new models perform much better than some of their competitors. |
| first_indexed | 2024-03-11T01:56:19Z |
| format | Article |
| id | doaj.art-b8958b067dbd47199ee36662edadaa1a |
| institution | Directory Open Access Journal |
| issn | 2571-905X |
| language | English |
| last_indexed | 2024-03-11T01:56:19Z |
| publishDate | 2023-05-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Stats |
| spelling | doaj.art-b8958b067dbd47199ee36662edadaa1a2023-11-18T12:39:20ZengMDPI AGStats2571-905X2023-05-016265767310.3390/stats6020042A New Extended Weibull Distribution with Application to Influenza and Hepatitis DataGauss M. Cordeiro0Elisângela C. Biazatti1Luís H. de Santana2Department of Statistics, Federal University of Pernambuco, Recife 50670-901, BrazilDepartment of Mathematics and Statistics, Federal University of Rondônia, Ji-Paraná 76900-726, BrazilDepartment of Technology, State University of Maringá, Umuarama 87506-370, BrazilThe Weibull is a popular distribution that models monotonous failure rate data. In this work, we introduce the four-parameter Weibull extended Weibull distribution that presents greater flexibility, thus modeling data with bathtub-shaped and unimodal failure rate. Some of its mathematical properties such as quantile function, linear representation and moments are provided. The maximum likelihood estimation is adopted to estimate its parameters, and the log-Weibull extended Weibull regression model is presented. In addition, some simulations are carried out to show the consistency of the estimators. We prove the greater flexibility and performance of this distribution and the regression model through applications to influenza and hepatitis data. The new models perform much better than some of their competitors.https://www.mdpi.com/2571-905X/6/2/42maximum likelihood estimationmomentMonte Carlo simulationregressionWeibull-G class |
| spellingShingle | Gauss M. Cordeiro Elisângela C. Biazatti Luís H. de Santana A New Extended Weibull Distribution with Application to Influenza and Hepatitis Data Stats maximum likelihood estimation moment Monte Carlo simulation regression Weibull-G class |
| title | A New Extended Weibull Distribution with Application to Influenza and Hepatitis Data |
| title_full | A New Extended Weibull Distribution with Application to Influenza and Hepatitis Data |
| title_fullStr | A New Extended Weibull Distribution with Application to Influenza and Hepatitis Data |
| title_full_unstemmed | A New Extended Weibull Distribution with Application to Influenza and Hepatitis Data |
| title_short | A New Extended Weibull Distribution with Application to Influenza and Hepatitis Data |
| title_sort | new extended weibull distribution with application to influenza and hepatitis data |
| topic | maximum likelihood estimation moment Monte Carlo simulation regression Weibull-G class |
| url | https://www.mdpi.com/2571-905X/6/2/42 |
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