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Article

A New Kumaraswamy Generalized Family of Distributions with Properties, Applications, and Bivariate Extension

1
Department of Statistics, The Islamia University of Bahawalpur, Bahawalpur 63100, Pakistan
2
Department of Statistics, Federal University of Pernambuco, Recife 50740-540, PE, Brazil
3
Department of Mathematics, College of Science and Humanities in Al-Kharj, Prince Sattam bin Abdulaziz University, Al-Kharj 11942, Saudi Arabia
4
Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt
*
Author to whom correspondence should be addressed.
Mathematics 2020, 8(11), 1989; https://doi.org/10.3390/math8111989
Received: 28 September 2020 / Revised: 1 November 2020 / Accepted: 2 November 2020 / Published: 7 November 2020
(This article belongs to the Special Issue Statistics 2020)
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. View Full-Text
Keywords: bivariate family; Kumaraswamy-G family; Marshall and Olkin shock model; maximum likelihood method; parameter induction; T-X family; Weibull distribution bivariate family; Kumaraswamy-G family; Marshall and Olkin shock model; maximum likelihood method; parameter induction; T-X family; Weibull distribution
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MDPI and ACS Style

Tahir, M.H.; Hussain, M.A.; Cordeiro, G.M.; El-Morshedy, M.; Eliwa, M.S. A New Kumaraswamy Generalized Family of Distributions with Properties, Applications, and Bivariate Extension. Mathematics 2020, 8, 1989. https://doi.org/10.3390/math8111989

AMA Style

Tahir MH, Hussain MA, Cordeiro GM, El-Morshedy M, Eliwa MS. A New Kumaraswamy Generalized Family of Distributions with Properties, Applications, and Bivariate Extension. Mathematics. 2020; 8(11):1989. https://doi.org/10.3390/math8111989

Chicago/Turabian Style

Tahir, Muhammad H., Muhammad A. Hussain, Gauss M. Cordeiro, M. El-Morshedy, and M. S. Eliwa 2020. "A New Kumaraswamy Generalized Family of Distributions with Properties, Applications, and Bivariate Extension" Mathematics 8, no. 11: 1989. https://doi.org/10.3390/math8111989

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