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In this paper, we propose the zero, one and zero-and-one-inflated New unit-Lindley distributions as natural extensions of the New unit-Lindley distribution to model continuous responses measured at the following intervals [0, 1), (0, 1] and [0, 1]. They were constructed based on convex combinations between the New unit-Lindley distribution and the distributions degenerate at zero, one, and Bernoulli distribution. They also have a number of interesting properties, such as being members of the exponential family. Besides, they have closed forms for the cumulative distribution functions, quantiles, and moments. Inferential aspects and regression structures are
discussed in this work as well as a Monte Carlo simulation study to evaluate the
performance of the regressors. Finally, we bring an application to real data on the suicide rate in the year 2016.
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