a new discrete distribution based on geometric odds ratio

In this paper, a new discrete distribution is studied based on geometric odds ratio. this new distribution has three parameters and can be a unimodal or a bimodal discrete distribution. some important distributional properties are studied. for example, moments, the behaviour of the hazard rate function, stochastic orders, mixing processes, infinite divisibility, rényi and shannon entropies and the distributions of order statistics are investigated. we will see that the hazard rate function of the new discrete distribution can be monotonically increasing and decreasing and bathtub-shaped. the parameters of the distribution are estimated by the maximum likelihood method, and a real data set is analyzed in order to show the effectiveness of the model.