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The Weibull distribution is a very popular distribution for modelling lifetime data. Many modications of the Weibull distribution have been proposed in recent years. Inspired by the T-X method (ALZAATREH; LEE; FAMOYE, 2013), we propose a class of generalized Weibull distributions which generalizes the Weibull-X class. We investigate some of its mathematical properties including an expansion for the density function and explicit expressions for the ordinary and central moments, generating function and characteristic function. We discuss a particular case of the new generator and present briefly some of its structural properties. As an alternative to maximum likelihood, we performed Bootstrap simulations and corrected Bootstrap in order to compare these methods of estimation. The Bootstrap method is employed to estimate the model parameters. We t one special model of the new class to four real data sets to demonstrate the flexibility of the proposed class.
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