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We propose and study a new continuous model named the Marshall-Olkin exponentiated Burr XII (MOEBXII) distribution. It contains several special cases, namely the Marshall-Olkin exponentiated log-logistic, Marshall-Olkin exponentiated Lomax, Marshall-Olkin Burr XII, Marshall-Olkin log-logistic, Marshall-Olkin Lomax distributions, among others, and most importantly includes all four of the most common types of hazard function: monotonically increasing or decreasing, bathtub and arc-shaped hazard functions. Some of its structural properties are obtained such as the ordinary and incomplete moments, quantile and generating functions, order statistics and probability weighted moments. The maximum likelihood and least square methods are used to estimate the model parameters. A simulation study is performed to evaluate the precision of the estimates from both methods. The usefulness of the new model is illustrated by means of two real data sets.
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