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A new five-parameter distribution so-called the McDonald quasi Lindley distribution is proposed. The new distribution contains, as special submodels, several important distributions discussed in the literature, such as the beta quasi Lindley, Kumaraswamy quasi Lindley, beta Lindley, kumaraswamy Lindley and Lindley distributions, among others. The properties of this new distribution, including hazard function, reversed hazard function, shapes, moments, entropy and moment generating function are derived.We provide the density function of the order statistics and their moments. Method of maximum likelihood is used to estimate the parameters of the new and related distributions. The flexibility and usefulness of the new model are illustrated by means of an application to real data set.

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