A New Flexible Univariate and Bivariate Family of Distributions for Unit Interval (0, 1)
We propose a new generator for unit interval which is used to establish univariate and bivariate families of distributions. The univariate family can serve as an alternate to the Kumaraswamy-G univariate family proposed earlier by Cordeiro and de-Castro in 2011. Further, the new generator can also b...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-05-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/14/5/1040 |
| _version_ | 1797495061509832704 |
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| author | Mahmoud El-Morshedy Muhammad H. Tahir Muhammad Adnan Hussain Afrah Al-Bossly Mohamed S. Eliwa |
| author_facet | Mahmoud El-Morshedy Muhammad H. Tahir Muhammad Adnan Hussain Afrah Al-Bossly Mohamed S. Eliwa |
| author_sort | Mahmoud El-Morshedy |
| collection | DOAJ |
| description | We propose a new generator for unit interval which is used to establish univariate and bivariate families of distributions. The univariate family can serve as an alternate to the Kumaraswamy-G univariate family proposed earlier by Cordeiro and de-Castro in 2011. Further, the new generator can also be used to develop more alternate univariate and bivariate G-classes such as beta-G, McDonald-G, Topp-Leone-G, Marshall-Olkin-G and Transmuted-G for support (0, 1). Some structural properties of the univariate family are derived and the estimation of parameters is dealt. The properties of a special model of this new univariate family called a New Kumaraswamy-Weibull (NKwW) distribution are obtained and parameter estimation is considered. A Monte Carlo simulation is reported to assess NKwW model parameters. The bivariate extension of the family is proposed and the estimation of parameters is described. The simulation study is also conducted for bivariate model. Finally, the usefulness of the univariate NKwW model is illustrated empirically by means of three real-life data sets on Air Conditioned Failures, Flood and Breaking Strength of Fibers, and one real-life data on UEFA Champion’s League for bivariate model. |
| first_indexed | 2024-03-10T01:43:08Z |
| format | Article |
| id | doaj.art-3bae4b1ff389443ab11f768063a16fb8 |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-10T01:43:08Z |
| publishDate | 2022-05-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-3bae4b1ff389443ab11f768063a16fb82023-11-23T13:20:26ZengMDPI AGSymmetry2073-89942022-05-01145104010.3390/sym14051040A New Flexible Univariate and Bivariate Family of Distributions for Unit Interval (0, 1)Mahmoud El-Morshedy0Muhammad H. Tahir1Muhammad Adnan Hussain2Afrah Al-Bossly3Mohamed S. Eliwa4Department of Mathematics, College of Science and Humanities in Al-Kharj, Prince Sattam Bin Abdulaziz University, Al-Kharj 11942, Saudi ArabiaDepartment of Statistics, Faculty of Computing, The Islamia University of Bahawalpur, Bahawalpur 63100, PakistanDepartment of Statistics, Faculty of Computing, The Islamia University of Bahawalpur, Bahawalpur 63100, PakistanDepartment of Mathematics, College of Science and Humanities in Al-Kharj, Prince Sattam Bin Abdulaziz University, Al-Kharj 11942, Saudi ArabiaDepartment of Statistics and Operation Research, College of Science, Qassim University, P.O. Box 6644, Buraydah 51482, Saudi ArabiaWe propose a new generator for unit interval which is used to establish univariate and bivariate families of distributions. The univariate family can serve as an alternate to the Kumaraswamy-G univariate family proposed earlier by Cordeiro and de-Castro in 2011. Further, the new generator can also be used to develop more alternate univariate and bivariate G-classes such as beta-G, McDonald-G, Topp-Leone-G, Marshall-Olkin-G and Transmuted-G for support (0, 1). Some structural properties of the univariate family are derived and the estimation of parameters is dealt. The properties of a special model of this new univariate family called a New Kumaraswamy-Weibull (NKwW) distribution are obtained and parameter estimation is considered. A Monte Carlo simulation is reported to assess NKwW model parameters. The bivariate extension of the family is proposed and the estimation of parameters is described. The simulation study is also conducted for bivariate model. Finally, the usefulness of the univariate NKwW model is illustrated empirically by means of three real-life data sets on Air Conditioned Failures, Flood and Breaking Strength of Fibers, and one real-life data on UEFA Champion’s League for bivariate model.https://www.mdpi.com/2073-8994/14/5/1040bivariate familyKumaraswamy-G familyMarshall and Olkin shock modelmaximum likelihood methodparameter inductionT-X family |
| spellingShingle | Mahmoud El-Morshedy Muhammad H. Tahir Muhammad Adnan Hussain Afrah Al-Bossly Mohamed S. Eliwa A New Flexible Univariate and Bivariate Family of Distributions for Unit Interval (0, 1) Symmetry bivariate family Kumaraswamy-G family Marshall and Olkin shock model maximum likelihood method parameter induction T-X family |
| title | A New Flexible Univariate and Bivariate Family of Distributions for Unit Interval (0, 1) |
| title_full | A New Flexible Univariate and Bivariate Family of Distributions for Unit Interval (0, 1) |
| title_fullStr | A New Flexible Univariate and Bivariate Family of Distributions for Unit Interval (0, 1) |
| title_full_unstemmed | A New Flexible Univariate and Bivariate Family of Distributions for Unit Interval (0, 1) |
| title_short | A New Flexible Univariate and Bivariate Family of Distributions for Unit Interval (0, 1) |
| title_sort | new flexible univariate and bivariate family of distributions for unit interval 0 1 |
| topic | bivariate family Kumaraswamy-G family Marshall and Olkin shock model maximum likelihood method parameter induction T-X family |
| url | https://www.mdpi.com/2073-8994/14/5/1040 |
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