We introduce a new family of distributions using truncated the Discrete Mittag-Leffler distribution. It can be considered as a generalization of the Marshall-Olkin family of distributions. Some properties of this new family are derived. As a particular case, a three parameter generalization of Uniform distribution is given special attention. The shape properties, moments, distributions of the order statistics, entropies are derived and estimation of the unknown parameters is discussed. An application in autoregressive time series modeling is also included.
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