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Abstract
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In this work, we introduce a new class of continuous distributions called the generalized Poisson family which extends the quadratic rank transmutation map. We provide some special models for the new family. Some of its mathematical properties including Rényi and q-entropies, order statistics and characterizations are derived. The estimations of the model parameters are performed by maximum likelihood method. The Monte Carlo simulation is used for assessing the performance of the maximum likelihood estimators. The flexibility of the proposed family is illustrated by means of two applications to real data sets.
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