Abstract

A new six-parameter extended fatigue lifetime model named the McDonald-Burr XII distribution is introduced, which generalizes the Burr XII, beta Burr XII (Parana\'iba {\it et al.}, 2011) and Kumaraswamy-Burr XII (Parana\'iba {\it et al.}, 2012) distributions. The proposed distribution is characterized in terms of truncated moments. We obtain the ordinary and incomplete moments and quantile and ge\-ne\-ra\-ting functions. We estimate the model parameters by maximum likelihood. A Monte Carlo simulation is performed to study the asymptotic normality of the estimates. We also propose an extended regression model based on the logarithm of the McDonald-Burr XII distribution that can be more realistic in the analysis of real data than other special regression models. Two applications to real data validate the importance of the new models.

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