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. Mathematics2020, 8, 1989.
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.
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. Mathematics2020, 8, 1989.
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.
Abstract
For bounded unit interval, we propose a new Kumaraswamy generalized (G) family of distributions from 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 estimating the family parameters. We investigate the properties of one special model called a new Kumaraswamy-Weibull (NKwW) distribution. Parameter estimation is dealt and maximum likelihood estimators are assessed through simulation study. Two real life data sets are analyzed to illustrate the importance and flexibility of this distribution. 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, exponentiated-Weibull and Weibull distributions when applied to these data sets. The bivariate extension of the family is proposed and the estimation of parameters is given. The usefulness of the bivariate NKwW model is illustrated empirically by means of a real-life data set.
Keywords
Bivariate family, Kumaraswamy-G family; Marshall and Olkin shock model; maximum likelihood method; parameter induction; T-X family; Weibull distribution
Subject
Computer Science and Mathematics, Probability and Statistics
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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