In this paper it is introduced a new two-parameter discrete distribution derived from the continuous Sushila distribution (Shanker et al., 2013). Its mathematical properties and estimation procedures for the parameters of the proposed model are presented assuming complete and right-censored data. This new model, in the same way as the continuous Sushila distribution, has the discrete Lindley distribution as a special case. An extensive simulation study is carried out to examine the bias and the roots of the mean squared errors for the maximum likelihood estimators as well the moments and Bayesian estimators of the proposed model parameters. Some examples using simulated data and real datasets are considered to show that the new proposed model performs at least as good as its particular case and some other traditional discrete models as the Poisson and geometric distributions.
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