A New Kumaraswamy Generalized Family of Distributions with Properties, Applications, and Bivariate Extension
For bounded unit interval, we propose a new Kumaraswamy generalized (G) family of distributions through a new generator which could be an alternate to the Kumaraswamy-G family proposed earlier by Cordeiro and de Castro in 2011. This new generator can also be used to develop alternate G-classes such...
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MDPI AG
2020-11-01
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| author | Muhammad H. Tahir Muhammad Adnan Hussain Gauss M. Cordeiro M. El-Morshedy M. S. Eliwa |
| author_facet | Muhammad H. Tahir Muhammad Adnan Hussain Gauss M. Cordeiro M. El-Morshedy M. S. Eliwa |
| author_sort | Muhammad H. Tahir |
| collection | DOAJ |
| description | For bounded unit interval, we propose a new Kumaraswamy generalized (G) family of distributions through a new generator which could be an alternate to the Kumaraswamy-G family proposed earlier by Cordeiro and de Castro in 2011. This new generator can also be used to develop alternate G-classes such as beta-G, McDonald-G, Topp-Leone-G, Marshall-Olkin-G, and Transmuted-G for bounded unit interval. Some mathematical properties of this new family are obtained and maximum likelihood method is used for the estimation of G-family parameters. We investigate the properties of one special model called the new Kumaraswamy-Weibull (NKwW) distribution. Parameters of NKwW model are estimated by using maximum likelihood method, and the performance of these estimators are assessed through simulation study. Two real life data sets are analyzed to illustrate the importance and flexibility of the proposed model. In fact, this model outperforms some generalized Weibull models such as the Kumaraswamy-Weibull, McDonald-Weibull, beta-Weibull, exponentiated-generalized Weibull, gamma-Weibull, odd log-logistic-Weibull, Marshall-Olkin-Weibull, transmuted-Weibull and exponentiated-Weibull distributions when applied to these data sets. The bivariate extension of the family is also proposed, and the estimation of parameters is dealt. The usefulness of the bivariate NKwW model is illustrated empirically by means of a real-life data set. |
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| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T15:01:33Z |
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| spelling | doaj.art-e321112959ab4627a64fd6d4f3476b222023-11-20T20:09:28ZengMDPI AGMathematics2227-73902020-11-01811198910.3390/math8111989A New Kumaraswamy Generalized Family of Distributions with Properties, Applications, and Bivariate ExtensionMuhammad H. Tahir0Muhammad Adnan Hussain1Gauss M. Cordeiro2M. El-Morshedy3M. S. Eliwa4Department of Statistics, The Islamia University of Bahawalpur, Bahawalpur 63100, PakistanDepartment of Statistics, The Islamia University of Bahawalpur, Bahawalpur 63100, PakistanDepartment of Statistics, Federal University of Pernambuco, Recife 50740-540, PE, BrazilDepartment of Mathematics, College of Science and Humanities in Al-Kharj, Prince Sattam bin Abdulaziz University, Al-Kharj 11942, Saudi ArabiaDepartment of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, EgyptFor bounded unit interval, we propose a new Kumaraswamy generalized (G) family of distributions through a new generator which could be an alternate to the Kumaraswamy-G family proposed earlier by Cordeiro and de Castro in 2011. This new generator can also be used to develop alternate G-classes such as beta-G, McDonald-G, Topp-Leone-G, Marshall-Olkin-G, and Transmuted-G for bounded unit interval. Some mathematical properties of this new family are obtained and maximum likelihood method is used for the estimation of G-family parameters. We investigate the properties of one special model called the new Kumaraswamy-Weibull (NKwW) distribution. Parameters of NKwW model are estimated by using maximum likelihood method, and the performance of these estimators are assessed through simulation study. Two real life data sets are analyzed to illustrate the importance and flexibility of the proposed model. In fact, this model outperforms some generalized Weibull models such as the Kumaraswamy-Weibull, McDonald-Weibull, beta-Weibull, exponentiated-generalized Weibull, gamma-Weibull, odd log-logistic-Weibull, Marshall-Olkin-Weibull, transmuted-Weibull and exponentiated-Weibull distributions when applied to these data sets. The bivariate extension of the family is also proposed, and the estimation of parameters is dealt. The usefulness of the bivariate NKwW model is illustrated empirically by means of a real-life data set.https://www.mdpi.com/2227-7390/8/11/1989bivariate familyKumaraswamy-G familyMarshall and Olkin shock modelmaximum likelihood methodparameter inductionT-X family |
| spellingShingle | Muhammad H. Tahir Muhammad Adnan Hussain Gauss M. Cordeiro M. El-Morshedy M. S. Eliwa A New Kumaraswamy Generalized Family of Distributions with Properties, Applications, and Bivariate Extension Mathematics bivariate family Kumaraswamy-G family Marshall and Olkin shock model maximum likelihood method parameter induction T-X family |
| title | A New Kumaraswamy Generalized Family of Distributions with Properties, Applications, and Bivariate Extension |
| title_full | A New Kumaraswamy Generalized Family of Distributions with Properties, Applications, and Bivariate Extension |
| title_fullStr | A New Kumaraswamy Generalized Family of Distributions with Properties, Applications, and Bivariate Extension |
| title_full_unstemmed | A New Kumaraswamy Generalized Family of Distributions with Properties, Applications, and Bivariate Extension |
| title_short | A New Kumaraswamy Generalized Family of Distributions with Properties, Applications, and Bivariate Extension |
| title_sort | new kumaraswamy generalized family of distributions with properties applications and bivariate extension |
| topic | bivariate family Kumaraswamy-G family Marshall and Olkin shock model maximum likelihood method parameter induction T-X family |
| url | https://www.mdpi.com/2227-7390/8/11/1989 |
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