Discrete Burr XII-Gamma Distributions: Properties and Parameter Estimations

In this paper, we propose three discrete analogues of the Burr XII-gamma distribution to meet the need of modelling discrete lifetimes in reliability. It is shown that hazard rate functions of discrete analogues are increasing, U-shaped and modified unimodal. Then we investigate estimation of their parameters using three methods (maximum likelihood, moments and empirical). From the results of extensive simulation runs, their accuracies are compared. Finally, we fit three proposed discrete distributions and discrete Burr XII and discrete gamma distributions to a discrete real data set and use AIC to compare them.