This paper discussed the Bayesian estimation for the unknown parameters, survival, hazard rate, and alternative hazard rate functions of the discrete Zubair Weibull distribution. Informative priors (gamma and beta) for the parameters of the distribution are assumed. The Bayes estimators are derived under the squared error and linear-exponential loss functions based on Type-II censored sample. Credible intervals for the parameters, survival, hazard rate, and alternative hazard rate functions are obtained. The Bayes predictors (point and interval) for the future observation are obtained considering two-sample prediction. A simulation study is performed using the Markov Chain Monte Carlo algorithm for different sample sizes, and censoring rates to assess the performance of the estimators. Moreover, three real data sets were applied to investigate the flexibility and applicability of the distribution.

This paper presented a two discrete family of life distributions called discrete complementary exponentiated-G Poisson family and discrete Zubair-G family as a special case from discrete complementary exponentiated-G Poisson family. Some basic distributional properties are derived. Such as hazard rate, moments, quantiles, order statistics and Rényi Entropy. A special sub-model of the discrete Zubair-G family, called the discrete Zubair Weibull distribution is considered in detail. Discrete Zubair exponential distribution and discrete Zubair Rayleigh distribution are obtained as two special cases from discrete Zubair Weibull distribution. Method of maximum likelihood is used under Type-II censored samples for estimating the unknown parameters, survival, hazard rate and alternative hazard rate functions. Confidence intervals for the parameters are obtained. A simulation study is carried out to illustrate the theoretical results of the maximum likelihood estimation. Finally, the performance of the new distribution is compared with existing distributions using applications of three real data sets to show the suitability and flexibility of the proposed model.